Citation |

- Permanent Link:
- http://ufdc.ufl.edu/UF00091422/00001
## Material Information- Title:
- Trapping organic-rich fine sediment in an estuary
- Series Title:
- Trapping organic-rich fine sediment in an estuary
- Creator:
- Ganju, Neil Kamal
- Place of Publication:
- Gainesville, Fla.
- Publisher:
- Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
- Language:
- English
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
## UFDC Membership |

Full Text |

UFL/COEL -2001/007
TRAPPING ORGANIC-RICH FINE SEDIMENT IN AN ESTUARY by Neil Kamal Ganju Thesis 2001 TRAPPING ORGANIC-RICH FINE SEDIMENT IN AN ESTUARY By NEIL KAMAL GANJU A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2001 ACKNOWLEDGMENT I would like to thank Dr. Ashish Mehta for his guidance in my education and research, as well as the entire Coastal and Oceanographic Engineering Program faculty. Also deserving praise for their assistance are Dr. John Jaeger, Dr. D. Max Sheppard, Helen Twedell, Kim Hunt, Vernon Sparkman, Viktor Adams, Jim Joiner, Sidney Schofield, Jaime MacMahan, and Justin Davis, as well as Leonid Parshukov for analyzing ADCP and tidal data. Fernando Marvdn should receive recognition for the original development of the models used in this study and for his support throughout the process. Diana Loomis deserves kudos for her graphical wizardry and emotional support. My mother and father merit unlimited praise for providing me with mind, body, and soul, as do my sisters for helping me develop my mind and soul. Last, but not least, I would like to thank the eternal and undying Self for providing the basis for the Universe and everything contained within. TABLE OF CONTENTS p, Ze A CKN OW LED GM EN T ..................................................................................................... ii LIST OF TABLES ............................................................................................................. vi LIST OF FIGU RES ......................................................................................................... viii LIST OF SYM BOLS ......................................................................................................... xi A BSTRA CT ...................................................................................................................... xv I IN TRODU CTION ........................................................................................................... 1 1.1 Problem Statem ent .................................................................................................. 1 1.2 Problem Approach .................................................................................................. 3 1.3 Outline of Chapters ................................................................................................. 3 2 TRA P EFFICIEN CY M ODELIN G ................................................................................. 4 2.1 Introduction ............................................................................................................. 4 2.2 Flow M odeling ........................................................................................................ 4 2.2.1 Governing Equations ...................................................................................... 4 2.2.2 M odel Operation ............................................................................................. 6 2.2.3 Flow Boundary Conditions ............................................................................. 6 2.2.4 Flow M odel Input/Output Param eters ............................................................ 6 2.3 Sedim ent Transport M odeling ................................................................................ 7 2.3.1 Governing A dvection-D infusion Equation ...................................................... 7 2.3.2 Erosion Flux .................................................................................................... 7 2.3.3 Deposition Flux ............................................................................................... 8 2.3.4 Suspended Sedim ent Boundary Conditions .................................................... 9 2.3.5 Sedim ent M odel Input/Output Param eters ...................................................... 9 2.4 Sedim entation, Sedim ent Trap, and Trap Effi ciency ............................................ 10 2.4.1 Sedim entation ............................................................................................... 10 2.4.2 Definition of Trap ......................................................................................... 10 2.4.3 Definition of Trap Efficiency ........................................................................ 10 2.4.4 Calculation of Trap Effi ciency ...................................................................... 11 2.4.5 Calculation of Trap Efficiency as a Function of Organic Content ............... 11 3 FIELD AND LABORATORY INFORMATION ......................................................... 12 3.1 Site Description ..................................................................................................... 12 3.2 Tributary Flow s ..................................................................................................... 18 3.3 Tides ...................................................................................................................... 21 3.4 Currents ................................................................................................................. 22 3.5 Sedim entation ....................................................................................................... 24 3.6 Sedim ent Rating Curves ....................................................................................... 25 3.7 Sedim ent Com position .......................................................................................... 27 3.7.1 Organic Fraction Com position ...................................................................... 27 3.7.2 Inorganic Fraction Com position ................................................................... 28 3.8 Sedim ent Erodibility ............................................................................................. 30 3.9 Settling V elocity ................................................................................................... 32 4 M ODEL CA LIBRATION ............................................................................................. 35 4.1 Introduction ........................................................................................................... 35 4.2 Grid D evelopm ent ................................................................................................. 36 4.3 Flow M odel Calibration ........................................................................................ 38 4.3.1 Initial and Boundary Conditions ................................................................... 38 4.3.2 Comparison of Measured and Simulated Discharges ................................... 44 4.3.3 N eap Tide Sim ulation ................................................................................... 46 4.3.4 Comparison with Analytical Solution for a Co-oscillating Tide .................. 49 4.3.5 Tributary Boundary Conditions .................................................................... 51 4.4 Sedim ent Transport M odel Calibration ................................................................ 52 4.4.1 Sedim ent Bed Properties ............................................................................... 52 4.4.2 Suspended Sedim ent Boundary Conditions .................................................. 53 4.4.3 Governing Transport Equation ..................................................................... 54 4.4.4 Erosion Function Calibration ........................................................................ 55 4.4.5 D eposition Function Calibration ................................................................... 55 4.4.6 Sensitivity Analysis for Longitudinal Dispersion Constant ......................... 57 4.4.7 Comparison with Analytical Solution for Advection-Diffusion ................... 58 4.4.8 Comparison with Flume Data for Deposition Under Turbulent Flow .......... 61 5 SEDIM EN TA TION AN D TRA P EFFICIEN CY .......................................................... 63 5.1 H istoric Sedim entation Rates ................................................................................ 63 5.2 Sedim ent Trap and Trap Effi ciency Calculation .................................................. 63 5.2.1 Trap Efficiency as a Function of C-1 8 Canal Discharge ............................. 63 5.2.2 Trap Efficiency as a Function of C-1 8 Canal Sediment Concentration ....... 63 5.2.3 Trap Efficiency as a Function of Organic Content ....................................... 63 6 CON CLU SION S ............................................................................................................ 63 6.1 Sum m ary ............................................................................................................... 63 6.2 Conclusions ........................................................................................................... 63 6.3 Recom m endations for Future W ork ...................................................................... 63 REFEREN CES ................................................................................................................. 63 BIO G RA PH ICA L SK ETCH ............................................................................................ 63 LIST OF TABLES Table pMge 3.1 Basin areas in the Loxahatchee River estuary watershed ............................. 15 3.2 Chronology of hydrology-related events in the Loxahatchee River watershed, 19281980 ...................................................................................... 18 3.3 Median, high, and maximum flows in three tributaries ................................ 20 3.4 Spring/neap tidal ranges and phase lags for three gauges.............................. 22 3.5 Selected transect discharges and times of discharge, 08/30/00....................... 24 3.6 Shoaling rates in three locations of the estuary......................................... 25 3.7 Median and high flow concentration data and coefficients for Equation 3.3 ....... 26 3.8 Likely organisms in the Loxahatchee River and corresponding organic materials. 28 3.9 Percent fines and percent organic content for combined samples.................... 29 3. 10 Density measurements of composite sample............................................ 30 3. 11 PES test consolidation times, erosion rate constants, shear strengths ............... 32 3.12 Settling column testing parameters ...................................................... 33 4.1 Fourier coefficients for tidal forcing at Jupiter Inlet.................................... 41 4.2 Comparison of measured (08/30/00) and simulated discharges at two transects..46 4.3 Fourier coefficients for neap tidal forcing at Jupiter Inlet flow boundary........... 47 4.4 Input sediment concentrations at the tributaries ........................................ 54 5.1 C- 18 discharges and input concentrations for determination of sedimentation rate as a function of discharge.................................................................... 63 5.2 Sedimentation rate in the C- 18 canal .................................................... 63 5.3 Flows and suspended sediment concentrations for trap efficiency as a function of C18 canal discharge ......................................................................... 63 5.4 Removal ratio for three C- 18 discharges, with two different trap locations......... 63 5.5 Simulation parameters for trap efficiency as a function of input sediment concentration to the C-18 canal (Qc-18=1.7 m3/s)....................................... 63 5.6 Values used for coefficient a, dry density, and granular density, for simulation of removal ratio as a function of organic content .......................................... 63 LIST OF FIGURES Figure a 3.1 Loxahatchee River estuary and tributaries .............................................. 12 3.2 Dredging plans for C- 18 canal, 1956 .................................................... 14 3.3 Loxahatchee River estuary watershed basins, estuarine limits, and central embayment ................................................................................ 15 3.4 Normalized salinity in the Northwest Fork vs. normalized freshwater discharge to the Northwest Fork ........................................................................ 17 3.5a Cumulative frequency distribution of tributary flow, Northwest Fork .............. 19 3.5b Cumulative frequency distribution of tributary flow, North Fork .................... 19 3.5c Cumulative frequency distribution of tributary flow, Southwest Fork .............. 20 3.6 Tributary flow over a one month period, 10/10/81-11/10/81 ......................... 21 3.7 Locations of tide gauges (UFG#), current transects (T#), grab samples (GSH), suspended sediment data locations (SSD) ............................................... 22 3.8 Sample records of tidal measurements at three locations (09/14/00-09/15/00) ....23 3.9 Poling depth bed thicknesses in the C- 18 canal......................................... 25 3. 10 Erosion rate vs. shear stress for beds with three pre-test consolidation times .......31 3. 11 Erosion rate constant vs. shear strength ................................................. 32 3.12 Settling velocity vs. concentration for composite fine sample........................ 34 4.1 Bathymetry of Loxahatchee River estuary, as used in the flow/sediment transport model ..................................................................................... 37 4.2 Computational grid, with flow boundaries in black cells, simulated tide gauge and current transect locations.................................................................. 38 4.3 Mid-tide elevation at UFG1 vs. average wind speed from two offshore buoys ....40 4.4a Tidal data from UFG1, 09/14/00-10/13/00. Raw data................................. 42 4.4b Tidal data from UFG1, 09/14/00-10/13/00. After mid-tide trend is removed .......42 4.5 Selection of Manning's n throughout model domain................................... 44 4.6a UFG1 measured tide vs. model result, 09/20/00........................................ 45 4.6b UFG2 measured tide vs. model result, 09/20/00........................................ 45 4.6c UFG3 measured tide vs. model result, 09/20/00........................................ 46 4.7a UFG1 measured neap tide vs. model result, 10/02/00 .................................. 47 4.7b UFG2 measured neap tide vs. model result, 10/02/00.................................. 48 4.7c UFG3 measured neap tide vs. model result, 10/02/00 .................................. 48 4.8 Definition sketch for tide entering a channel with a reflecting wall ................. 49 4.9 Comparison of Equation 4.3 and model results for C-18 canal ...................... 51 4. 10 Variation of granular, bulk, and dry densities with organic content using data from three Florida locations and the Loxahatchee River ..................................... 53 4.11 a Variation of coefficient a (Equation 2.16) with organic content .................... 56 4.1 lb Variation of settling velocity (Equation 2.16, with C=0.5 kg/in3) with organic content.................................................................................... 56 4.12 Sedimentation rate in C- 18 canal as a function of longitudinal dispersion constant, KL .............................................................................................. 58 4.13 Definition sketch for substance concentration in uniform 1 -D channel, with barrier separating zones of constant concentration and zero concentration at t=0 .......... 59 4.14 Comparison of analytical solution and numerical model prediction for concentration in a 1-D channel, at t=750 s and 1500 s ................................................. 62 4.15 Comparison of flume data (Krone, 1962) with model result for deposition under turbulent flow .............................................................................. 63 5.1 Sedimentation rate 480 in downstream of the S-46 structure in the C- 18 canal as a function of canal discharge ...................................................................................... 63 5.2 Sedimentation rate as a function of input suspended sediment concentration in the C18 canal, under a discharge of 1.7 m '/s ................................................................... 63 5.3 Sedimentation rate as a function of discharge in the C- 18 canal, with input suspended sediment concentration of 0.014 kg/m .................................................... 63 5.4 Schematic diagram of a suspended sediment particle subjected to constant flow velocity and settling velocity ................................................................................... 63 5.5 Historical flow record for C- 18 canal, from 03/01/81-01/18/91 ............................... 63 5.6 Assumed C- 18 canal flow record obtained by pro-rating the measured record for the Northwest Fork for the period 03/01/81-01/18/91 .................................................... 63 5.7 Cumulative deposition over ten-year period (03/01/81-01/18/91) for existing regulated versus assumed unregulated C- 18 canal discharge .................................. 63 5.8 Portion of the com putational grid . .......................................................................... 63 5.9 Removal ratio in the presence of trap as a function of C- 18 canal discharge ........... 63 5. 10 Schematic diagram of a particle passing over a trap at three different velocities ..... 63 5. 11 Removal ratio as a function of input suspended sediment concentration to the C- 18 can al ......................................................................................................................... 6 3 5.12 Difference between influent and effluent loads (trapped load) as a function of input suspended sediment concentration to the C- 18 canal .............................................. 63 5.13 Removal ratio as a function of organic content at a constant discharge of 1.7 in 3/S .63 5.14 Sedimentation (shoaling) rate in trap as a function of organic content at a constant discharge of 1.7 in 3/S assuming uniform consolidation .......................................... 63 5.15 Mass deposited in the C- 18 canal (upstream of the trap, Figure 5.8) as a function of organic content .......................................................................................................... 63 5.16 Influent (qi) and effluent (q,) loads vs. organic content, and the difference (qi-q,).. 63 6.1 Experim ental test pit configuration ........................................................................... 63 LIST OF SYMBOLS area C Co Cz D, D.x, Dxy, Dyx, Dyy H He H0 K KL, KT L M Oc P Pe Q Qd Qe Qf R sediment concentration (kg/m3) frictionless wave celerity related to Equation 4.3 Chdzy discharge coefficient horizontal dispersion coefficients depth (m) equilibrium bed elevation related to Equation 6.1 datum bed elevation related to Equation 6.1 sedimentation coefficient related to Equation 6.1 longitudinal and transverse dispersion constants, respectively channel length related to Equation 4.3 number of time steps in one ebb tidal period organic content (%) tidal prism (m3) Peclet number discharge (m3/s) depositional flux (kg/m2-s) erosional flux (kg/m2-s) freshwater discharge (m3/s) sediment removal ratio R 2 correlation coefficient Rave ebb-tide averaged removal ratio S sediment source/sink term Sa salinity (ppt) SR sedimentation rate (m/d) T tidal period (s) U depth-averaged, x-direction velocity (m/s) Ua,b,bt,c,ct flow velocity related to Figures 5.4 and 5.10 V depth-averaged, y-direction velocity (m/s) Ws settling velocity (m/s) WSf free settling velocity (m/s) a empirical coefficient related to Equation 2.16 an Fourier coefficients related to Equation 4.2 as empirical coefficient related to Equation 3.2 b empirical coefficient related to Equation 2.16 b, empirical coefficient related to Equation 3.2 g acceleration due to gravity (mis2) h water depth Ah deposit thickness ht trap depth related to Figure 5.10 k damped wave number ko frictionless wave number m empirical coefficient related to Equation 2.16 n Manning's flow resistance coefficient ns sediment bed porosity nw empirical coefficient related to Equation 2.16 p probability of deposition q sediment load (kg/s) qe influent sediment load (kg/s) qj effluent sediment load (kg/s) t time At time step Ub bottom, x-direction velocity Vb bottom, y-direction velocity WC sediment water content x horizontal coordinate xS pre-trap channel length related to Figure 5.10 Xt trap length related to Figure 5.10 y horizontal coordinate z vertical coordinate a empirical coefficient related to Equation 5.1 ats empirical coefficient related to Equation 2.13 13 empirical coefficient related to Equation 5.1 empirical coefficient related to Equation 2.13 7 bottom friction-dependent coefficient CN erosion rate constant (kg/m2-s) SNo limiting erosion rate constant (kg-N/s) Ti water surface elevation TIC water surface elevation correction related to Equation 4.1 rIHT water surface elevation at high tide related to Equation 4.1 11L water surface elevation at channel opening related to Equation 4.3 tILT water surface elevation at low tide related to Equation 4.1 X., empirical coefficient related to Equation 3.5 9t damping coefficient related to Equation 4.3 v eddy viscosity Pb sediment bulk density (kg/m3) Pd bottom sediment dry density (kg/m3) Ps sediment granular density (kg/m3) Pw water density (kg/m3) a wave frequency related to Equation 4.3 Tb bed shear stress (Pa) Td critical shear stress for deposition (Pa) "rs bed shear strength (Pa) Solids volume fraction (De limiting solids volume fraction xS empirical coefficient related to Equation 3.5 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science TRAPPING ORGANIC-RICH FINE SEDIMENT IN AN ESTUARY By Neil Kamal Ganju August 2001 Chairman: Ashish J. Mehta Major Department: Civil and Coastal Engineering Trench-traps are frequently implemented to capture incoming sediment before it can reach the main body of an estuary. Given the presence of organic matter in Florida's humnic estuarine environment, the effect of organic content on the efficiency of an estuarine trap scheme is the focus of this study. The candidate location, the Loxahatchee River estuary, is fed by tributaries which contribute organic-rich fine sediment. Flow and sediment transport models were utilized and calibrated using collected field and literature data. The calibrated models were first used to simulate historic sedimentation rates in the flow-regulated C-i18 canal, one of the main tributaries. A relation was developed for sedimentation rate as a function of discharge in this canal. This relation was applied to a ten-year flow record, to yield a total sedimentation of 0.15 mn. To determine what effect flow regulation has on sedimentation, a hypothetical unregulated C- 18 canal flow record was constructed using data from another feeder tributary. In this case the simulated sedimentation was 47% higher, due to less variable discharge conditions. A trap was incorporated in the C-i18 canal, 120 m upstream of the confluence of the canal and the central embayment of the estuary. Trap efficiency was calculated as a sediment removal ratio, or the percentage by which influent sediment load to the trap is reduced in the effluent load from the trap. Trap efficiency modeling was performed for varying C-i18 canal discharge, and a specific discharge (1.7 m 3/S) was found to maximize removal ratio. Trap efficiency simulations were also performed for varying input sediment concentration to the C-i18 canal, under a constant discharge. Removal ratio increased with increasing concentration at concentrations below 0.25 kg/in3, but remained constant above this value. The trapped load (difference between influent and effluent loads), however, increased with concentration below values of 7 kg/in3, but decreased above this value, due to the decreased settling velocity in this high-concentration regime. Simulations were performed for varying organic content, and removal ratio decreased with increasing organic content, due to decreasing settling velocity. Sedimentation in the trap increased with organic content, due to decreasing density. Influent load to the trap increased with organic content, since less sediment was able to deposit upstream of the trap. Future work should include characterizing the nature of organic-rich sediment more comprehensively, as well as developing a monitoring scheme to determine actual sedimentation rates in a test trap at this location. CHAPTER 1 INTRODUCTION 1.1 Problem Statement Sedimentation due to the influx of fine-grained particles is an issue affecting numerous waterways and coastal areas. Frequently, these particles originate far inland, and are transported into the coastal zone by runoff and streamflow (Rusnak, 1967). In the humic estuarine regime, inorganic sediment is often complemented by a measurable organic fraction. This fraction can be produced by either autochthonous sources (e.g., native phytoplankton, submerged vegetation) or allochthonous sources (e.g., river-borne phytoplankton, swamp vegetation, windblown material) (Darnell, 1967). The organic fraction is transported in the same fashion as inorganic sediment, but the lower density and therefore lower settling velocity renders the organic fraction highly susceptible to resuspension even under relatively mild flow conditions (Mehta et al., 1997). While the transport of inorganic fine fractions has been investigated, the effect of organic content in fines on sedimentation is largely unstudied. In estuarial muds, the organic fraction tends towards mixing with the other sediment types, thereby altering the transport behavior of the inorganic fraction. Given the presence of organic matter, any solution to the sedimentation problem in a productive estuary must take into account the organic content of the sediment and the associated transport behavior. One commonly employed solution to reduce sedimentation is the implementation of a trap scheme by trenching the submerged bottom. To create a trench-trap, the depth at the chosen location is increased by dredging. The increased depth results in a decreased flow velocity, thereby allowing incoming sediment to settle in the trap itself, instead of being carried further downstream. The sediment can then be removed from the trap, rather than dredging the otherwise distributed deposit from a broader area. Given this background, the objective of this study was to determine the role organic content plays in the trap efficiency of a selected trap design. By holding the trap depth and location constant and varying only the organic content of the sediment, the efficiency of a trap can be assessed for different organic contents and flow discharges. For the present purpose, efficiency will be determined by the sediment removal ratio, which is the percentage by which the effluent sediment load (leaving the trap) is reduced with respect to influent load (entering the trap). The candidate estuary for this study is the Loxahatchee River, located in Southeast Florida. Shoaling has occurred in the estuary in several spots, mainly at the confluence of major tributaries in the central embayment of the estuary, where velocities are typically low (Sonntag and McPherson, 1984). Several tributaries feed the estuary, carrying freshwater, nutrients, and sediment. Due to the biologically productive terrain upstream of the estuary, organic-rich sediment is present in the loads carried by the tributaries. To prevent this sediment from accumulating in the central embayment, a "preemptive" trap scheme is a viable option. For the present purpose, the trap scheme will be implemented in one area of the estuary where a flow-regulated tributary feeds the central embayment. The performance of this scheme will be evaluated with regard to the organic content of the sediment and the flow hydrograph, in order to determine what role organic content and discharge have on trap efficiency. 1.2 Problem Approach Several tasks must be undertaken to determine the efficiency of a trap scheme. These include: 1) Data collection from the field and from the existing literature to characterize the nature of the flow. This includes measuring tidal elevations and current velocities in the estuary, and obtaining strearnflow data for major tributaries from the literature. 2) Data collection to characterize the nature of the sediment. This includes collecting sediment samples and performing laboratory tests on the samples. Historical suspended sediment concentration data will also be examined. 3) Modeling the flow field via a hydrodynamic model, in order to determine the velocities as well as the water surface elevations. 4) Development of a sediment transport model to determine suspended sediment concentrations. This model will incorporate the sediment characteristics determined from the laboratory tests. 5) A one-trap scheme will be introduced to the calibrated flow model, and the output from that model will be applied to the calibrated sediment transport model. The removal ratio of the trap will be indicative of the efficiency of the trap scheme. 6) The influent and effluent sediment loads through the trap will be recorded in order to quantify trap efficiency. 1.3 Outline of Chapters Chapter 2 describes the modeling scheme used to evaluate trap efficiency. Chapter 3 contains the field and laboratory data collected for this study. Chapter 4 describes the calibration of the model, and Chapter 5 discusses the application of the model to predict sedimentation and trap efficiency. Conclusions are made in Chapter 6, followed by the bibliography and biographical sketch. CHAPTER 2 TRAP EFFICIENCY MODELING 2.1 Introduction Modeling sediment trap efficiency requires the use of flow and sediment transport models. A flow model provides water velocities and surface elevations, and this output is applied to the sediment transport model. These models and the method to calculate the trap efficiency are described next. 2.2 Flow Modeling 2.2.1 Governing Equations The Navier-Stokes equations govern the free surface flows of constant density and incompressible fluids (Pnueli and Gutfinger, 1992). Applying the hydrostatic pressure distribution assumption yields three-dimensional long-wave equations, and these can be vertically integrated to produce the following two-dimensional equations (Casulli, 1990), where x and y are horizontal direction coordinates: x-momentum: 8(HU) 8(HUU) +(HUV) gH 8 +U 8 a B U + + = -gH- +-vH-I+- vH -- yU t x -y ax x x ) y Oy (2.1) y-momentum: 8(HV) 8(HUV) +(HVV) + gH V yV x + + + gH + v +- -ay V at x Byy ax ax ay By (2.2) 5 continuity: o& 8(HU) a(HV)0 t x ay (2.3) where H is the water depth, U is the vertically-averaged horizontal x-direction velocity, V is the vertically-averaged horizontal y-direction velocity, t is time, g is the acceleration due to gravity, il is the water surface elevation measured from the undisturbed water surface, v is the eddy viscosity, and y is the bottom friction dependent coefficient defined as c2 g ub+vb C (2.4) where ub and vb are the horizontal x and y bottom velocity components respectively, and Cz is the Ch6zy discharge coefficient, which is related to Manning's n by (H + 1)1/3 z n (2.5) n Solving this system of three partial differential equations (Equations 2.1, 2.2, and 2.3) for the three unknowns (U, V, i) can be accomplished via a numerical method. The numerical algorithm used is based on the method developed by Casulli (1990). First, a characteristic analysis is performed on Equations 2.1-2.3, in order to determine which terms must be discretized implicitly, such as the water surface elevation (Eqs. 2.1, 2.2), and the velocity divergence (Equation 2.3). The advective terms are discretized explicitly using an upwind scheme, which is unconditionally stable when a Eulerian-Lagrangian method is used to discretize the terms. This method requires the solution of a 5-diagonal matrix at every time step. It is used in conjunction with an alternating-direction implicit (ADI) routine, which results in two simpler, linear tri-diagonal matrices (Casulli, 1990). 2.2.2 Model Operation The 2-D vertically averaged hydrodynamic model reported by Marvdn (2001) and used in this study is operated through the MATLAB computational application. The use of MATLAB allows for the generation of the necessary graphics and data output in a simple fashion, though computational effort is intensive, due to the necessity of large matrices. A rectangular grid with square elements is used, with numeric "ones' indicating the body of water, and "zeros" representing land boundaries. A similar grid is needed for the input bathymetry, with the depth at mean high water entered into each element. 2.2.3 Flow Boundary Conditions Flow boundaries are indicated by extending water cells to the grid edge. If freshwater inflow is desired, a permanent velocity can be imposed at the edge, corresponding to the desired flow condition. If a non-steady state inflow is desired, velocity as a function of time can be implemented. For a tidal flow boundary, a function specifying the water surface elevation at the boundary can be applied. If no velocity or elevation is specified at cells which terminate at the grid edge, they become no-flow boundaries in the algorithm. 2.2.4 Flow Model Input/Output Parameters The area and bathymetry grids described in Section 2.2.2 are required to specify the domain to be modeled. Other required inputs are the tidal forcing function at the seaward boundary, the calculation time step, the total simulation time, a file containing Manning's n coefficient values for each cell, and velocities at the tributary flow boundaries. The output is three matrices consisting of the water surface elevations, xdirection velocities, and y-direction velocities, for every time step in the simulation. 2.3 Sediment Transport Modeling 2.3.1 Governing Advection-Diffusion Equation Advection-diffusion is formulated using a finite-volume explicit method based on the quadratic upstream interpolation method (QUIKEST) method by Leonard (1977): aHC a(HUC) 8(HVC) a HC 8HC a 8HC 8HC + + Dxx +D y- + Dyx +Dyy = S at ax ay x x dy ay ax ly (2.6) where C is the depth-averaged suspended sediment concentration, and Dij are the dispersion coefficients calculated via Preston (1985) as follows: D IKLU2+ KTV2 H x =rH Cz~ U2 + V2 (2.7) KLV2+ KTrU2H Dyy = HCz U2 + V2 (2.8) (IKL KT)UV Dxy = D Hg Cz U2 + V2 (2.9) where KL and KT are the longitudinal and transverse dispersion constants, respectively. The quantity S is a source/sink term, which accounts for erosion and deposition as the algebraic sum of the upward and downward fluxes as follows: S= Qe +Qd (2.10) The erosion and deposition fluxes Qe and Qd are described in the following sections. 2.3.2 Erosion Flux The upward (erosional) flux at the bed is computed from: Qe = EN(b s) (2.11) where EN is the erosion rate constant, Tb is the bed shear stress, and sr is the bed shear strength with respect to erosion. The bed shear stress is computed as pwn 2u2 b = (H + f")A (2.12) where pw is the density of water. The shear strength of the bed is calculated via Mehta and Parchure (2001): T, = a,((D_ (D)0s (2.13) where cas is an empirical coefficient dependent on sediment type, (D is the solids volume fraction, 0e is the limiting solids volume fraction (value of D when c,=O), and Ps is an empirical coefficient. 2.3.3 Deposition Flux The depositional flux Qd is a function of probability, settling velocity, and concentration, defined as (Krone, 1962): Qd = -pWrC (2.14) where W, is the settling velocity, and p is the probability of deposition, expressed as r d(2.15) where Td is the critical shear stress for deposition. When the bottom shear stress is greater than or equal to Td, sediment is unable to deposit. This condition is prevented in the present analysis by setting -rd above the highest observed shear stress in the flow model output. In general, the settling velocity of fine sediment is dependent on concentration. As a result the settling velocity differs depending on three identifiable regimes: free settling, flocculation settling, and hindered settling. In the free settling range, relatively low concentrations permit the individual flocs to settle without interference from other flocs. The settling velocity in this range is a function of the drag coefficient and the submerged weight of the floc. As concentration increases, the collision frequency of flocs increases, resulting in the formation of larger flocs. These flocs are able to settle quicker due to their increased mass, and characterize the flocculation settling range. Eventually, the concentration in the water column reaches a point where a floc is unable to settle quickly due to significant interference from other flocs, and the limited pore space for the fluid. This interference reaches a maximum when the water column resembles a bed of mud with negligible settling (Mehta, 1994). Hwang (1989) formulated a fit of the flocculation and hindered settling ranges, relating settling velocity to concentration as follows: -aCflW W (C + b2)m (2.16) where a, b, mn, and nw are empirical constants. At free settling concentrations (C<0.25 k g/in3) a constant settling velocity (Wsf) is prescribed. Laboratory tests performed in a settling column are required to determine the site-specific constants. 2.3.4 Suspended Sediment Boundary Conditions The boundary conditions at the tributary connections can be expressed as steadystate concentrations, or sediment rating functions can be applied if unsteady tributary flows are desired. This also holds true at the tidal entrance, where incoming concentrations can be specified, varying with tidal stage and/or current velocity. 2.3.5 Sediment Model Input/Output Parameters The flow output is the primary input for the sediment transport model. The userselected inputs are time step, total simulation time, dispersion constants, bed dry density and granular density, fluid density, suspended sediment point sources, the coefficients for Equation 2.16 (for settling behavior), and the coefficients for Equation 2.13 (for erosional behavior). The area and bathymetry grids from the flow model are used as well. 2.4 Sedimentation, Sediment Trap, and Trap Efficiency 2.4.1 Sedimentation Sedimentation at any point in the estuary can be calculated from the deposit thickness Ahi given by ts Ahi At Qd.At i=1 Pd (2.17) where t, is the total simulation time, At is the time step, i is the time step index, Qdi is the deposition flux, and Pd is the deposit dry density. The sedimentation rate is then SR -Ah t' (2.18) where SR is the sedimentation rate. 2.4.2 Definition of Trap In this study, a sediment trap is defined as an area of the submerged bottom deepened to a depth greater than the surrounding bottom, in order to reduce flow velocity. The lower velocity should allow sediment to deposit in the trap rather than move past and deposit elsewhere. This in turn allows for maintenance dredging to be performed at a specific location (the trap) rather than over a broad submerged area. 2.4.3 Definition of Trap Efficiency Trap efficiency is defined as the percent by which effluent suspended sediment load is reduced with respect to the influent suspended sediment load (removal ratio). In a tidal situation, the seaward edge of the trap will be the influent side during flood tide, and the effluent side during ebb tide, and vice versa for the landward edge. 2.4.4 Calculation of Trap Efficiency At each time step in the sediment transport simulation the concentration, the velocity, and the water surface elevation will be calculated in each cell. The cells that border the trap and are flow-normal are also of interest. Sediment loads can be calculated for these border cells as follows: q = UCHAx (2.19) where q is the sediment load, U is the flow velocity, and Ax is the cell width. The sediment load on each side of the trap will be used to compute the sediment removal ratio as follows: qj -qe qj (2.20) where R is the removal ratio, qj is the influent sediment load, and qe is the effluent sediment load. The removal ratio will be averaged over a tidal cycle, using the removal ratio values from each time step. 2.4.5 Calculation of Trap Efficiency as a Function of Organic Content Simulations will be run for differing organic content of the sediment. The average removal ratio for the each organic content will be compared for a given flow discharge. The native organic content will be used as the benchmark case by which to assess the efficiency of the trap under the other organic content cases. The removal ratio as a function of organic content will be plotted to determine what effect organic content has on trap efficiency. CHAPTER 3 FIELD AND LABORATORY INFORMATION 3.1 Site Description The Loxahatchee River estuary is contained within Palm Beach and Martin counties in southeast Florida (Figure 3.1). / I ". I en 0 0 in The river emptis into the Atlntic Ocean viaJupiter ne.Tremitibais , P.' 01 191 2cw Tunr-s 'I 3opsno 4i Dolphin S-46 control structure 5 Marlin Figure 3.1 Loxahatchee River estuary and tributaries. The river empties into the Atlantic Ocean via Jupiter Inlet. Three main tributaries feed the estuary: the Northwest Fork, the North Fork, and the Southwest Fork. Jones Creek and Sims Creek, two lesser tributaries, also feed the estuary. The Southwest Fork's upstream reach is referred to as the C-18 canal, which was created in 1957/58 to lengthen the Southwest Fork and facilitate drainage of the westward swampland. Flow through the C-18 canal and the Southwest Fork is regulated by the S-46 automated sluice gate structure. The three forks converge on the estuary approximately 3 km west of the inlet, at the central embayment. The Intracoastal Waterway (ICWW) intersects the estuary in a dog-leg fashion, east of the Florida East Coast Railroad (FECRR) bridge. Five navigation/access canals exist on the south shore of the central embayment. Depths in the estuary range from under 1 m to over 5 m in some channel portions, with an average depth of just over 1 m. The navigation channel (maintained by the Jupiter Inlet District) runs westward from Jupiter Inlet, under the FECRR bridge, and through the central embayment, approximately 14 km upstream from the inlet. Flood shoals exist in the central embayment mainly due to the influx of sand from the ocean, and smaller shoals exist at the termini of the three main tributaries. Small islands are located west of the FECRR bridge, on both sides of the channel. While the Northwest Fork and North Fork are natural tributaries, as mentioned the Southwest Fork was lengthened westward in 1957/58 by the construction of the C-18 canal and S-46 control structure (Figure 3.1), in order to divert flow from the Northwest Fork to the Southwest Fork. A channel was then constructed to allow for the diversion of flow from the C-18 canal to the Northwest Fork. From this point on, the C- 18 canal will indicate the narrow channel section of the Southwest Fork, and the broader section will be referred to as the Southwest Fork (Figure 3.1). Dredging plans for the C-18 canal from 1956 are shown in Figure 3.2 (U.S. Army Corps of Engineers, 1956). The existing bottom was deepened up to 3 m at some locations to facilitate drainage. The datum (MSL) refers to the National Geodetic Vertical Datum of 1929 (NGVD). The Loxahatchee River estuary drains over 1,000 km2 of land through the three main tributaries, the ICWW, and several minor tributaries. The individual basins that comprise the watershed are shown in Figure 3.3 and listed in Table 3.1. The watershed occupies residential areas, agricultural areas, and uninhabited marsh and slough areas. Y+- Natural bottom (pre-1957) _-- O _ct) El .4 CC ogDredged canal bottom CI / (post-1 957) 0 500 1000 1500 2000 Distance from S-46 structure (m) Figure 3.2 Dredging plans for C-18 canal, 1956. The creation of the C-18 canal has increased the drainage area of the Southwest Fork. This canal drains the Loxahatchee Slough, a shallow swamp-like feature containing diverse flora and fauna. Upstream of the Northwest Fork is the Loxahatchee River proper, which meanders through typical South Florida swampland, all contained within the Jonathan Dickinson State Park (JDSP). The North Fork drains the east section of JDSP, which contains extensive swampland and scrubland. As a result of the biologically productive nature of the watershed, organic-rich sediment is present in the runoff which eventually reaches the estuary. The freshwater nature of these tributaries ends where seawater mainly from Jupiter Inlet intrudes. Estuarine conditions (Figure 3.3) persist for 8 km up the Southwest Fork/C- 18 canal, 9 km up the North Fork, and 16 km up the Northwest Fork (measured from the inlet) (Russell and McPherson, 1984). Salinities above 1 ppt have been observed during low-flow conditions in the Northwest Fork, more than 16 km from the inlet. Figure 3.3 Loxahatchee River es and central embayment. Table 3.1 Basin areas in the Loxahatchee River estuary watershed Basin Area (kmZ) Intracoastal 545 C-18 278 Jonathan Dickinson 155 South Indian River 65 Loxahatchee River 6 During high freshwater flow the estuarine boundary naturally moves seaward; during low-flow conditions the opposite is true. Figure 3.4 shows the salinity in the Northwest Fork normalized by the salinity at Jupiter Inlet (SaNwF/SajI), versus freshwater discharge to the Northwest Fork normalized by the maximum flood tide flow rate (QNWF/QJO). The flood tide flow rate is calculated as 71P T (3.1) where P is the tidal prism, and T is the (semi-diurnal) tidal period. The values used for salinity, tidal period (T), and tidal prism (P) at Jupiter Inlet are 35 ppt, 12.42 hr, and 2.93 x 108 in3, respectively (Russell and Goodwin, 1987). Salinity in the Northwest Fork was measured 11 kmn from Jupiter Inlet (Russell and McPherson, 1984). The trend in Figure 3.4 implies that salinity in the tributaries can vary greatly depending on the freshwater flow condition. This is especially relevant when the tributary flow is regulated (e.g., Southwest Fork), and salinity is influenced by management practices. At the turn of the century the Loxahatchee River estuary was a pristine ecosystem consisting of mangroves, salt marshes, and scrubland. Prior to World War 11 agricultural interests transformed the area into a rural landscape with citrus groves and vegetable farms. Significant residential development has occurred in the area since World War 11. In response to this development the estuary was designated an aquatic preserve in 1984. Nonetheless, the construction of homes along the shoreline continues. Currently, the entire estuarial shoreline in the central embayment as well as a significant portion of the tributary shorelines is residentially occupied. A chronology of noteworthy events 0.9 QjI 20,587 m /s 0.7 0.6 05 Z U) 0.4 0.3 0.2 0.1 0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 QNwF/QJI Figure 3.4 Normalized salinity in the Northwest Fork vs. normalized freshwater discharge to the Northwest Fork. influencing the hydrology of the Loxahatchee River during the 1928-1980 period is given in Table 3.2. Recreational boating is widely practiced in the estuary by local residents. Access is necessary to the upstream areas for recreational activities, and also to the open sea and the ICWW. Many of the natural and artificial access routes have shoaled in recent years (Antonini et al., 1998), leading to hazardous boating practices such as high-speed entry/exit to prevent grounding of the vessel. The canals adjacent to the south shore of the central embayment (Figure 3.1) are especially susceptible to shoaling (Sonntag and McPherson, 1984), directly affecting boaters who rely on these canals for access. Aside from boating, the ecological health of the estuary is also sensitive to shoaling. Seagrass plays an integral part in this environment (Mehta et al., 1990). Table 3.2 Chronology of hydrology-related events in the Loxahatchee River watershed, 1928-1980 Year Event 1928 Small ditch dredged to divert water from Loxahatchee Marsh to Southwest Fork 1947 Jupiter Inlet permanently stabilized for navigation 1957-1958 C-1 8 canal created to divert water from Northwest Fork to Southwest Fork 1970-1971 Severe drought throughout watershed 1974 C- 14 canal created to allow flow to be diverted from C- 18 to Northwest Fork 1976-1977 U.S. Army Corps of Engineers dredged lower estuary 1977-1978 Oyster bars near FECRR Bridge dredged to improve navigation and flushing in the central embayment 1978 Sewage treatment plant began discharging up to 2.5 m3/s to Northwest Fork 1980 Operation of S-46 structure modified to allow for more water storage in C- 18 canal 1980 Three channels dredged in central embayment for improved navigation Seagrass coverage maps (Jupiter Inlet District, 1999) indicate shifting and shrinking seagrass communities in the central embayment. 3.2 Tributary Flows Tributary flow data were obtained from USGS streamflow gage data, for all years available (1971-2000 N.W. Fork, 1980-1982 N. Fork, 1959-2000 S.W. Fork). Cumulative frequency distribution curves have been constructed (Figs. 3.5a-c) to designate the median and extreme flow events (Table 3.3). The Northwest Fork carries substantially more flow than the North Fork, while the regulated C- 18 canal/Southwest Fork carries more flow on average than both. Under storm conditions the Northwest Fork discharges greater amounts than the other tributaries. 0.9 ' 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10 20 30 40 50 60 Flow rate (m3Is) re 3.5 Cumulative frequency distribution of tributary flow a) Northwest Fork. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 1 0.2 0.1 0 0.2 0.4 8 1 1.2 Flow rate (m3/s) 1.4 1.6 1.8 2 Figu 0 .i ., 0 I '-I (U 0 b) North Fork. The criterion for opening the gates of the S-46 structure is based on water level behind the structure. When the level exceeds a predetermined mark, the sluice gates are 5 10 15 20 25 30 Flow rate (m3I/s) c) Southwest Fork. Table 3.3 Median, high, and maximum flows in three tributaries Tributary Median Flow High Flow Maximum Flow _____________(50%) (m3/s) (90%) (M3/s) (100%) (m3/s) Northwest Fork 7.0 x10-1 4.1 x100 6.1 x10! North Fork 1.0 x10-1 2.1 x I' 1.9 x100 Southwest Fork 1.3 x100 7.8 x100 3.2 x101 opened until the level recedes by 30 cm (Russell and McPherson, 1984), at which point the gates are closed. This flow regulation has resulted in a discontinuous flow record; there have been weeks when no flow has passed the structure, and days when storm flows have been released. The flows from the North and Northwest Forks are by contrast more continuous and more immediately responsive to the rainfall/runoff condition. During the normal wet season, the level behind the S-46 structure may not be sufficiently high enough to release flow, while the other tributaries are freely discharging to the estuary. Figure 3.6 illustrates this point, showing flow data for a one-month period from the three tributaries. 5 4.5 4 3.5 --NWF 2.5 -uNF -a-SWE M 2 .5 1 0.5 0 t :. . . . . . . 0 5 10 15 20 25 30 Time (d) Figure 3.6 Tributary flow over a one month period, 10/10/81-11/10/81. 3.3 Tides Ultrasonic water level gauges (Model #220, Infinities USA, Daytona Beach, FL) with stilling wells were installed to measure tidal elevations over more than a month's time. The locations were chosen so as to span a large reach of the estuary, and also to facilitate gauge placement and retrieval. Thus the eastern gauge was placed on a bridge pier, as was the gauge in the Southwest Fork. The Northwest Fork gauge was attached to a navigation post. The gauge locations are shown in Figure 3.7. Characteristic tidal ranges are given in Table 3.4, and sample records from the three gauges are shown in Figure 3.8. All tidal elevations use North American Vertical Datum 1988 (NAVD 88) as the datum. NAVD 88 is the most recent datum, and replaces NGVD. The tidal ranges indicate the total change in water surface elevation between high and low tide, while the phase lag indicates the difference in time between high/low tide at gauge UFG1 and the other gauges. The effect of bottom friction is manifested in reduced tidal range and lag between UFG1 and the other two gauges. Figure 3.7 Locations of tide gauges (UFG#), current transects (T#), grab samples (GS#), suspended sediment data locations (SSD). A= tide gauge, current transect, = grab sample, u = suspended sediment data location. Table 3.4 Spring/neap tidal ranges and phase lags for three gauges Phase lag from Gauge ID Spring tidal Neap tidal UFG1 (min) range (in) range (m) high tide low tide UFG1 0.90 0.66 0 0 UFG2 0.85 0.65 21 60 UFG3 0.86 0.64 28 60 3.4 Currents An Acoustic Doppler Current Profiler (Workhorse 1200kHz ADCP, RD Instruments, San Diego, CA) was used to profile current velocities at the transects shown in Figure 3.7. The water velocity was profiled over most of the depth, while data from the upper 72 cm were lost due to the need to submerge the device at all times. Simpson and Oltmann (1993) provide a method to interpolate velocity measurements throughout the water column using a power-law velocity profile, in which the velocity (u) is a function of elevation above bottom (z) to the 1/6th power (i.e., u-z /6). ---UFG1 -a-UFG2 -UFG3 Time (h) Figure 3.8 Sample records of tidal measurements at three locations (09/14/00-09/15/00). MSL datum is taken as NAVD 88. The upper 72 cm were interpolated using this profile equation across an incremental cross-sectional distance, and the resultant velocity profile was integrated vertically from bottom to surface to yield a mean velocity. With a known cross-sectional area, the discharge through the transect was then estimated. Table 3.5 contains the discharge through two transects (Figure 3.7), at times after high tide at gauge UFG1. These values are for ebb flow. 'A 0 10 35 3 4 Table 3.5 Selected transect discharges and times of discharge, 08/30/00 Transect Transect Transect maximum Time after high tide Discharge area (m2) depth (m) (gauge UFG1) (min) (m3/s) 3 472 4.2 233 416 4 398 3.8 260 326 3.5 Sedimentation With reference to sedimentation, the central embayment is influenced mainly by the daily flushing due to tide, while the upstream tributary locations are influenced primarily by riverine discharge and rainfall events. Estimates of the net accumulation of sediment have been made for three areas of the estuary. Sonntag and McPherson (1984) estimated shoaling rates in the south shore access canals (Figure 3.1) to be between 1.5-3.0 x 10-2 m/yr. They also estimated shoaling rates in the central embayment to be as low as 2.5 x 10-4 m/yr, suggesting that circulation and flushing in the embayment inhibit substantial accumulation. In the present study poling depths (obtained by pushing a graduated pole into the bottom until a hard substrate is reached) in the C-18 canal were determined to estimate sedimentation rates along the length of the canal. Since the bottom was dredged at the time of the construction of the canal in 1957/58, the bed thickness can be considered to represent the subsequent accumulation in the interim 42 year period. Figure 3.9 shows these thicknesses along the canal length. Table 3.6 compares the shoaling rates in the three areas. Sediment thickness increases with distance from the S-46 structure, possibly due to the large erosional forces near the structure (when flow is released), and the reduction of theses forces as the flow moves along the canal, allowing more sediment to deposit. Table 3.6 Shoaling rates in three locations of the estuary Location Shoaling rate (m/yr) C-18 canal 2.1 x 10.' Access canals 1.5-3.0 x 10" Central embayment 2.5 x 10. Z. 2 E U) 0.5 0 snMean valuefrom m 0.5 ... *480 m from S-46 structure (Section 5.1) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Distance from S-46 (in) Figure 3.9 Poling depth bed thicknesses in the C- 18 canal. Straight line indicates mean trend. 3.6 Sediment Rating Curves Sediment rating curves relating suspended sediment concentration to discharge were developed using data from three locations in the estuary (Figure 3.7). Discharge data from the three tributaries were compared to USGS suspended sediment data for the same tributaries. Sonntag and McPherson (1984) reported two values of suspended sediment concentration (0.059 kg/m3, 0.017 kg/m3) with corresponding flow data for the C-18 canal (31 m3/s, 28 m3/s) and a mean concentration value for the duration (1980-82) of their study (0.014 kg/m3). The median flow for the C-18 canal (1.3 m3/s) from Figure 3.5c was correlated to this mean value of concentration in the present study. For the Northwest Fork mean and maximum concentration values were reported for the study period without corresponding flows. The maximum flow during this period (11.2 m3/s) was recorded by a USGS streamflow gauge and that value was correlated with the maximum concentration (0.023 kg/m3), while the median flow for the entire flow record (0.7 m3/s) was correlated with the mean concentration (0.016 kg/m3). The same procedure was followed for the North Fork. The resulting points were connected to create sediment rating curves. A fit in the form of C = asQbs (3.2) was used (Miiller and F6rstner, 1968), where a, and b, are site-specific coefficients. The values used and the rating curve coefficients are shown in Table 3.7. Table 3.7 Median and high flow concentration data and coefficients for Equation 3.2 Median flow High flow (=99%) as b, Tributary concentration concentration coefficient coefficient (kg/m3) (kg/m3) Northwest Fork 0.011 0.023 0.012 0.27 North Fork 0.010 0.018 0.018 0.02 Southwest Fork 0.014 0.059 0.012 0.49 The flows that correlate with the high flow concentrations were of differing cumulative frequencies, but all were over 99%. Data for the upstream boundary of the North Fork (JDSP) were not available; values only existed for a location at the opening to the central embayment (Figure 3.7). The coefficient as is, in a sense, indicative of the erodibility of the upstream banks/bed. The North Fork data were obtained at a downstream location, so it is difficult to make comparisons with the other two tributaries. However, between the Northwest Fork and Southwest Fork one can infer that the degree of erodibility is equal, as manifested by the a, values. The exponent b, is indicative of the intensity of the erosional forces present in the river. These rating curves suggest that the erosional forces of the C-i18 canal/Southwest Fork are relatively higher than the Northwest Fork. The course of the Northwest Fork is far more meandering than the C- 18 canal/Southwest Fork, and the cross-section is wider as well. This would indicate a less hydraulically efficient Northwest Fork that is less capable of eroding and/or transporting sediment than the C- 18 canal/Southwest Fork. It is important to note that the transport of fine sediment is largely dependent on the supply of sediment, which indicates that the rating curves are sensitive to the availability of fine sediment. If the source of fine sediment for the C- 18 canal was to be depleted or enhanced, then the rating curve would be modified to represent, respectively, less or more suspended sediment concentration for the same discharge. 3.7 Sediment Composition 3.7.1 Organic Fraction Composition Possible sources of organic material in the Loxahatchee River range from simple organisms such as protozoa to complex organisms such as vertebrates. As these organic materials are degraded, they become mixed with the native inorganic sediment, especially silts and clays. While the specific sources of organic material and their relative contribution to the organic fraction are unknown, some of the likely sources are listed in Table 3.8 (Twenhofel, 1950). Table 3.8 Likely organisms in the Loxahatchee River and corresponding organic materials Organism Organic materials produced Protozoans calcite, chitin, acanthin Annelids calcite, phosphate, chitin Mollusks calcite, chitin Arthropods calcium carbonate, chitin Vertebrates keratin, collophane Plants calcium carbonate, cellulose, resins, fats, gums, waxes 3.7.2 Inorganic Fraction Composition Grab samples collected within the estuary were visually classified as sand, sand/mud mixture, and mud. Samples from the central embayment and the eastern reach of the estuary were largely sand and shell, while samples from the western reaches (Figure 3.7) were mainly mixtures of sand and mud. Samples from within the tributaries and along the banks contained mostly fine sediment. The inorganic sediment fraction was subjected to x-ray diffraction to determine the dominant minerals. Other than the quartz sand fraction, kaolinite, smectite, illite, pyrite, and rutile were present (in order of decreasing amounts). Wet sieve analyses (Ingram, 1971) of the finer samples from the western reach of the estuary were conducted to determine the percentage of fines (<74 microns). In order to determine the organic content (loss on ignition) of the sediment, the samples were dried at 550 C, ground in a mortar with a pestle, and heated at 5500 C. The difference in mass between before and after the high-temperature heating is the mass of the organic fraction of the sample (Gross, 1971). Those samples which contained over 59% fines and 10% organic content were combined as a composite sample representative of the western reach of the estuary. All of the samples combined happened to be collected upstream of the central embayment, suggesting that the finer sediments are present in the lower-energy locations of the estuary. Table 3.9 contains the individual sample information for the composite sample. A positive correlation between percentage of fines and organic content is suggested by these data. The composite sample was tested for bulk (in situ) and dry (0% water content) densities (Lewis and McConchie, 1994) (Table 3.10). Granular (or particle) density was then calculated via the mass balance PS PdP w, Pw +Pd -Pb (3.3) Additional relations are given to compute the porosity, ns, and the water content, wc. n. =1 Pd P, (3.4) nPw (-ns)p (3.5) Before the individual samples were combined, their mass was recorded (Table 3.8). The mass of each sample was then multiplied by the organic content. This value was summed for all four samples, and divided by the total composite sample mass. This yields the organic content for the composite sample (15%). Table 3.9 Percent fines and percent organic content for combined samples Sample Percent fines (<74 iim) Percent organic content Mass contributed to ID (by weight) (by weight) composite sample (kg) 1/2 59 13 0.98 3/4 63 13 0.92 5 69 18 0.76 6 87 19 0.72 Table 3.10 Density measurements of composite sample Bulk density Dry density Granular density (kg/m3) (kg/m3) (kg/m3) 1218 336 2559 1230 428 2038 1336 562 2367 3.8 Sediment Erodibility The erosion behavior of fine-grained sediment in the upper reaches of the estuary was determined via the Particle Entrainment Simulator (PES). The device, originally designed by Tsai and Lick (1986), consists of a cylindrical column that is filled with a slurry of the sediment. The slurry is allowed to settle and consolidate for a specified period of time (in the reported tests, three consolidation times were used: 24, 72 and 96 hours). Once the requisite consolidation time is achieved, the cylinder is loaded onto the apparatus, which consists of a perforated cylindrical disk that oscillates within the cylinder, above the sediment-water interface. The period of oscillation is measured with a digital tachometer, and converted to a shear stress value. Samples are taken from the overlying water at specified time intervals, and analyzed for suspended sediment concentration via gravimetric analysis. Tsai and Lick (1986) provide a description of the PES testing procedure. Once the time-concentration-shear stress data are obtained, plots of erosion rate or flux (kg/m-s) versus shear stress (Pa) can be developed (Figure 3.10). For each test, by extending the best-fit line to zero erosion rate, the shear strength of the bed (with respect to erosion), r,, can be estimated. The data in Figure 3.10 indicate that longer consolidation times result in a higher shear strength. The erosion rate constant, 6N, is the slope of the erosion rate vs. shear stress curve. An empirical relationship between erosion rate constant and shear strength in the form FN = ENO exp(S-) ( (3.6) 0.0007 0.0004 024 hr 0 072 hr I- a96 hr S0.0003 0.0002 -z3 0 A 0.0001 0 U 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Shear stress (Pa) Figure 3.10 Erosion rate vs. shear stress for beds with three pre-test consolidation times. Intersection of each mean trend line with the shear stress axis gives the shear strength. The slope of the line gives the erosion rate constant. can be inferred (Mehta and Parchure, 2001), where ENO is the limiting (Ts=O) erosion rate constant of 0.2 kg/N-s, and Xs and X, are sediment-specific coefficients. Equation 3.5 is plotted in Figure 3.11 along with the results from the PES. The coefficients X and 2, were found to be 14.0 and 0.44, respectively. Table 3.11 gives the parameters and results of the tests. The trend in Figure 3.11 implies that sediment beds with higher shear strengths have lower erosion fluxes than beds with lower shear strength for a given applied shear stress, as would be expected (Mehta and Parchure, 2001). a' 0.1 z U) Eq. 3.6 r 0.01 0 o -,PES (U 0 Co I- 0.001 0.0001 0 0.05 0.1 0.15 0.2 Shear strength (Pa) Figure 3.11 Erosion rate constant vs. shear strength. Table 3.11 PES test consolidation times, erosion rate constants, shear strengths Consolidation time Erosion rate constant cN Shear strength , (hr) (kg-N/s) (Pa) 24 0.0012 0.110 72 0.00062 0.125 96 0.00060 0.140 3.9 Settling Velocity The settling velocity can be modeled according to Equation 2.16, for which a settling column is used to obtain data for the settling velocity at different initial suspension concentrations. Accordingly, a slurry of native water and the composite fine sample was vigorously mixed and poured into a 2 m tall and 0.1 m diameter cylindrical settling column. Withdrawal tubes located at eight elevations allow for sampling of the slurry through time, and the samples were gravimetrically analyzed for concentration. The time-concentration-elevation data were entered into a MATLAB-based program which uses a routine developed by Ross (1988) to calculate the settling velocity at each elevation and time. The program presents a plot of settling velocity versus concentration, and a fit of the above equation is obtained by varying the a, b, mn, and nw coefficients in Equation 2.16. Hwang (1989) provides a detailed description of the procedure. The parameters of the testing performed here are given in Table 3.12. The data from all tests were combined to yield Figure 3.12. Table 3.12 Settling column testing parameters Initial Sampling time Sampling tube Concentration intervals elevations (kg/in3) (min) (mn from bottom) 18.33 0, 5, 15, 30, 60, 120, 180 0.05, 0.15, 0.3, 0.55, 0.8, 1.05, 1.3, 1.559.88 same as above same as above 3.40 same as above same as above The coefficients used to fit Equation 2.16 to Figure 3.12 were a7=0.189, b=6.4, m=1 .8, and n,=1 .8. At concentrations below 0.25 kg/rn3, a constant (free settling) velocity (Wsf) is specified. Above that concentration, and below concentrations of 7 kg/rn3, the flocculation settling zone is indicated, where particles collide, aggregate and form larger, faster settling flocs, with increasing concentration. Above 7 k g/rn3 the hindered settling zone occurs, where interference from other flocs reduces settling velocity with increasing concentration. 0.01 0.001 F .2 0.0001 0 E 0)Wsr=1.8 x 10-5 m/s 0.00001 Free settling zone Flocculation settling zone Hindered settling zone 0.000001 ., 0.01 0.1 1 10 1( Concentration (kglm3) Figure 3.12 Settling velocity vs. concentration for composite fine sample. CHAPTER 4 MODEL CALIBRATION 4.1 Introduction Calibrations of the flow and sediment transport models are described in this chapter. The development of the computational grid is addressed first, followed by the flow model, including the initial and boundary conditions, and model calibration. The final section describes the sediment transport model and its operation. The objective of this development, as noted in Chapter 1, was to evaluate sediment trap efficiency as a function of organic content. The C- 18 canal was chosen for the site of the trap, since this canal seemingly supplies much of the fine-grained deposit found in the central embayment. The function of the trap would be to intercept the incoming sediment before it reaches the wide region of the central embayment. Thus the focus in the simulations will be sediment transport from the C-i18 canal to the central embayment. Certain aspects of the estuary have been idealized in model formulation, in order to minimize computational time and to avoid potential errors. These idealizations are as follows: 1) Tidal variation in the ICWW is not considered, due to the complexity of implementing multiple tidal forcings in the model, in the absence of synchronous tidal data from the ICWW. 2) The north arm of the ICWW is extended to a distance of 420 m only, in order to minimize computational time. 3) The two lesser tributaries, Sims Creek and Jones Creek, are retained, but not considered as sources of freshwater input, which is likely to be minor. 4) The three islands west of the FECRR bridge (Figure 3.1) are excluded, since each is smaller in area than a single cell. It is deemed more accurate to exclude the islands rather than represent them in an areally disproportionate manner. 5) The C-i18 canal is "bent" to reduce total grid size, in order to reduce computational time. 4.2 Grid Development Due to the narrowness of the C- 18 canal, which is approximately 75 m wide at the junction with the Southwest Fork and less than 40 m wide at the S-46 structure, it was decided to represent it as a single cell channel, with a cell size of 60 x 60 m. As a single cell channel, the bending of the C-i 18 canal has no effect on computation. The same cell size was then conveniently extended to the rest of the model domain. A bathymetry file was created using available data (Mehta et al., 1990). Data from a 2000 survey (Cutcher, 2000) were compared to the bathymetry, and corrections were made for areas that had shoaled or eroded during the period between the two surveys. The input bathymetry is shown in Figure 4.1. In the computational grid (Figure 4.2), each land cell was assigned the number zero, while each water cell was assigned a one. Flow boundaries (black cells) were extended to the edges of the grid, such that "ones" were at the edges of the grid. The estuary entrance at Jupiter Inlet is a flow boundary, as are the three main tributaries, and 4.5 __ 4.0 3.5 ~3.0 2.5 2.0 , 1.5 1.0 0.5 0 meters Figure 4.1 Bathymetry of Loxahatchee River estuary, as used in the flow/sediment transport model. the two lesser tributaries. The south arm of the ICWW is also a flow boundary. The north arm of the ICWW was not extended to the grid edge because of the aforementioned reasons. Jupiter Inlet is at the bottom edge of the grid. The relative locations of the tide gauges and ADCP current measurement transects are also shown in Figure 4.2. Southwest Sims Creek E Gauge JonesCreek L Jupit I . I I Fork/C-18 can a UFG3 Gaug il I WW n0 - ADCP transe er Inlet NorthwestFork Gauge UFG2 --1 z ADCPtra e UFGi rth arm ct3 Figure 4.2 Computational grid, with flow boundaries in black cells, simulated tide gauge and current transect locations. 4.3 Flow Model Calibration 4.3.1 Initial and Boundary Conditions At the beginning of a simulation, the water surface elevation was chosen to be uniform, with all cells at high water. In reality the water surface is non-uniform, due to I FT77 I + T I V 1 I I I I I I L! North Fork -7-T-1 I I F-r-FTT-1 al nsect4 amplitude change and phase lag. Velocities throughout the domain were correspondingly set to zero at the start of each simulation. It was observed that a full tidal cycle was required to be simulated before the water surface elevations reached a quasi-steady state. This was verified by recording velocities and water surface elevations at the locations of the three gauges over multiple tidal periods. Since tidal forcing at the south arm of the ICWW was not considered, neither velocity nor water surface elevation was specified at the grid edge. If no specification is made at grid edge cells, the landward cell edge is treated as a wall in the model (i.e., a noflow boundary). The computational scheme uses velocity values from adjacent cells, but also imposes a zero velocity node at the cell edge. The closed boundary of the north arm of the ICWW (Figure 4.2) is a no-flow boundary as well, since land cells are adjacent. Tidal forcing at Jupiter Inlet (Figure 4.2) is perhaps the most important boundary condition in this system, because it is the mechanism by which the majority of the water flows through the estuary. The data obtained from the three gauges (Figure 3.7) were used to estimate this forcing. The raw data contained a trend in water surface elevation that was also observed at a station on the northeast Florida coast. The trends followed similar increases and decreases in mid-tide elevation, and it was hypothesized that onshore winds may have created increased elevations in the estuary. The wind record from two offshore sites (20 and 120 nin east of Cape Canaveral, Florida) was averaged and correlated with the mid-tide elevation (Figure 4.3). The data show a positive correlation between wind speed and mid-tide elevation. 0.3 0.2 0.1 0 8 o.1 2 =0.1958 4 (D 0 5D36 71 1'0 11 1 -0.1 -0.2 -0.3 Wind speed (m/s) Figure 4.3 Mid-tide elevation at UFG1 vs. average wind speed from two offshore buoys. To obtain a tidal record without the effect of this variation, filtering was performed. For each tidal cycle, the following calculation was made: 1=HT + TILT 2 (4.1) where rij is the mid-tide elevation, 1JHT is the water surface elevation at high tide, and iLT is the elevation at low tide. The mid-tide elevation was subtracted from each measured elevation within the same tidal cycle. The mio variation is also shown in Figure 4.4a. Figure 4.4b shows the tidal record obtained from the raw data in Figure 4.4a, after subtracting the mid-tide trend. Tidal elevations and discharge measurements were used to calibrate and validate the flow model. For the discharge data to be of use however, the tidal data must be synchronous. The ADCP current data were obtained while only one gauge (UFG1) was operating (08/30/00). Once all three gauges were functioning two weeks later (09/13/00), the UFG1 data during the ADCP measurements were compared with the UFG1 data from the fully functional period. An appropriately matching (i.e., equal tidal range) tidal record from the later period was assumed to be representative of the earlier period. A Fourier analysis (Ochi, 1990) of tidal representation of the form Ni cos(2rnt) +bnsin(27rnt I n=1 (. .Ndt) Ndt)) (4.2) was performed on the entire tidal record (09/13/00-10/13/00). In Equation 4.2, rj is the water surface elevation, a0 is the offset elevation, subscript n is the harmonic constituent index, an and bn are the harmonic coefficients, and dt is the time step. The resulting equation, carried to N=4, was used as the forcing at Jupiter Inlet. The derived coefficients are given in Table 4.1. Table 4.1 Fourier coefficients for tidal forcing at Jupiter Inlet n an (M) bn Wm 0 0.015 1 0.416 -0.024 2 -0.012 -0.022 3 0.010 -0.0036 4 (=N) -0.0053 -0.0068 E Raw data UFG1 o a ,4o - Mid-tide trend 0 -0.2 -0.4 -0.6 -0.8 Time (h) Figure 4.4 Tidal data from UFG1, 09/14/00-10/13/00. a) Raw data. Time origin is 12:00 am. 0.8 0.6 0.4 o : 0.2 o- 0 4 1 1 2 2 3 3 M4 4 0 0 CU-0.2 LU -0.4 -0.6 -0.8 Time (h) b) After mid-tide trend is removed. Time origin is 12:00 am. The tidal forcing was modified by an amplitude multiplier (1.17) and a phase correction (0.62 h) until the simulated tide at the UFG1 location matched the UFG1 measured data. This procedure was carried out so that the simulated tidal record closely matched the measured tidal record from the period of the ADCP current measurements. For tidal simulation, Manning's n was assumed to be 0.041 throughout the modeled domain as a first approximation (based on preliminary simulations). This coefficient is manifested in Equations 2.4 and 2.5, representing the effect of bottom friction in the vertically-integrated momentum equations (Eqs. 2.1-2.2). Chow (1959) provides qualitative descriptions of waterways and their corresponding n values. For major streams with irregular and rough sections, a minimum value of 0.035 and a maximum value of 0. 10 are prescribed for n. In order to correctly simulate the measured tides at the gauge locations UFG2 and UFG3, bottom friction had to be increased via Manning's n. First, the central embayment was assigned a higher value (0.052), in order to account for the increased presence of shoals and depressions in the central embayment. This increase in n enhanced agreement. of tidal elevations at gauge UFG2 (Northwest Fork), though the phase lag of the simulated tide at UFG3 was not large enough. To increase the phase lag, bottom friction was further increased by specifying an n value of 0.057 at the throat of the Southwest Fork, and throughout the C- 18 canal (Figure 4.5). The increased flow resistance caused by the constriction of the Southwest Fork into the C- 18 canal, as well as the presence of shoals in the area, were represented in the higher n value. The predicted tides are compared with those measured at the three gauge locations in Figures 4.6a-c. Agreement is best at UFG1, while the simulations at the other two n=O.OS2 " All other cells n=0.041 Figure 4.5 Selection of Manning's n throughout model domain. locations do not entirely agree in amplitude or phase. Also, the filtering process described earlier introduced some irregularities, which can be seen in the measured data for gauge UFG3 (Figure 4.6c). Overall, however, the model seems to perform reasonably well in regard to water level simulation. 4.3.2 Comparison of Measured and Simulated Discharges Once simulated tidal elevations were adjusted for at all three locations, simulated discharges through the transects indicated in Table 3.5 and Figure 3.7 were compared with the corresponding measurements. The transects used in the model domain are shown in Figure 4.2. At each transect, the discharge through each of the cells were summed to obtain the total discharge through the transect. The model results thus obtained are 0.5 0.4 0.3 0.2 0.1 E C 5 10 15 2 W -0.1 -0.2 -0.3 -0.4 -0.5 Time (h) Figure 4.6 Measured tide vs. model result, 09/20/00. a) UFG1 0.5 0.4 AU 0.3 0.2 U 0.1 C . 0 , . 5 1 15 2( W -0.1 -0.2 U -0.3 -0.4 -0.5 Time (h) b) UFG2. 10 .1 A Gauge UFG3 A AA a Model results A 5 15 20 25 W -0.1 oA -0.2 -0.3 -0.4- V_ A A A A -0.5 Time (h) c) UFG3. compared with the ADCP-derived data in Table 4.2. Differences between the two sets of discharges can be attributed to the idealized cross-section in the model, as well as error resulting from the interpolation process (for the upper 72 cm of water column) described in Section 3.4. Table 4.2 Comparison of measured (08/30/00) and simulated discharges at two transects Transect Time after high tide Measured Simulated % difference* at UFG1 (min) discharge (m3/s) discharge (m3/s) 3 233 416 455 +9 4 260 326 370 +14 *100% x (simulated-measured)/measured 4.3.3 Neap Tide Simulation In order to validate the model, a similar filtering was carried out for a neap tidal cycle, using the same amplitude multiplier and phase correction from the previous (spring tide) analysis. The Fourier coefficients are given in Table 4.3, and the computed tidal elevations are compared to the measurements (Figs. 4.7a-c). Though the simulated tides are not wholly in phase with the observed tides, the amplitudes are predicted reasonably well by the model. Table 4.3 Fourier coefficients for neap tidal forcing at Jupiter Inlet flow boundary n an (in) bn (in) 0 0.0155---1 0.3 14 -0.058 2 -0.0088 0.022 3 0.0195 -0.000085 4 0.0026 0.012 Time (h) Figure 4.7 Measured neap tide vs. model result, 10/02/00. a) UFG1. 48 0.5 0.4 U U 0.3 0.2 UI 0.1 C _ o* M 5 010 U > W -0.1 -0.2 -0.3 W U -0.4 -0.5 Time (h) b) UFG2. 0.5 0.4 0.3 0.2 "E 0, 0.1 C 0 A 5 10 A -0.1 AA -0.2 A A A A -0.3 A A -0.4 Time (h) c) UFG3. 4.3.4 Comparison with Analytical Solution for a Co-oscillating Tide In order to validate the predictive ability of the model, a scenario with a known analytic solution was examined. When a tidal wave propagates into a one-dimensional channel bounded by a wall at it's terminus (Figure 4.8), the wave is reflected back, producing a co-oscillating tide. The horizontal velocity at the wall must remain zero, while maximum velocity occurs at the open end of the channel. At a given location, maximum velocities occur at one-quarter tidal period after high tide, and one-quarter tidal period after low tide. Rfleeoting wall Tidal amplitude at channel entrance LML Total channel length I L \ a t Figure 4.8 Definition sketch for tide entering a channel with a reflecting wall. The analytical solution for velocity in a one-dimensional channel with frictional damping and a reflecting wall is (Ippen and Harleman, 1966): u =1 q- C0 k0 [e x cos(cyt kx) e x cos(ct + kx)] h 0 2 + k2 VF2(cos 2kL + cosh 2lL) (4.3) where u is the velocity, 71L is the mouth tidal amplitude, h is the mean water depth, Co is the frictionless tidal wave celerity, k0 is the frictionless wave number, k is the damped wave number, jt is the wave damping coefficient [=(k2-k02)112], cF is the wave frequency, x is the channel axis coordinate, and L is the channel length (Figure 4.8). The values used to solve Equation 4.3 are as follows: IlL=0.45 m, h=1.62 m, C0=4 m/s, k0=3.53 x 10-5 rad/m, V-=2.19 x 10-5 rad/m, k=4.15 x 10-5 rad/m, L=2200 m, and a=1.405 x 104 rad/s. The tidal amplitude at the mouth (7iL) was selected based on the observed tidal amplitude at the mouth of the C-18 canal. The water depth was the actual mean depth in the C- 18 canal, which was used to compute Co [=(gh)12] and k0 (=a/Co). The length of the channel was selected to be the actual length of the canal. The wave frequency corresponded to the semi-diurnal (M2) tidal period of 12.42 h. The damped wave number, k (and therefore t), was varied until the predicted velocities matched the simulation performed with the flow model. A measure of the damping is the ratio, k0/k. The selected value of this ratio was 0.85. For comparison, models of the Panama Canal have yielded damping ratios between 0.79 and 0.91 (Ippen and Harleman, 1966). Velocities through the channel were calculated at t=T/4. Model simulation was performed by specifying a zero-flow condition at the S-46 control structure (Figure 4.2). The tidal forcing developed in Section 4.3.1 was applied. The simulated velocities in the C- 18 canal were recorded one-quarter tidal period after high tide. The comparison between the analytical solution and simulated solution is shown in Figure 4.9. At the wall (Figure 4.8) there is no velocity, while the velocities in the canal between the wall and the entrance to the canal are slightly underestimated by the model. A lower damping ratio (i.e., more damping) would reduce the analytically solved velocities at the intermediate canal locations and improve agreement, though the velocity at the entrance would then be overestimated (in relation to the analytical solution). 0.1 0.09 0.08 0.07 0.06U 0.05 L________________ -Eq. 4.3 .Model 0 ts 0.04 0.03 0.02 0.01 0 0 500 1000 1500 2000 2500 Distance from S-46 structure (in) Figure 4.9 Comparison of Equation 4.3 and model results for C-i 8 canal. Overall, this comparison shows that the flow behavior in the C- 18 canal, under zero net discharge, closely follows the analytical solution. 4.3.5 Tributary Boundary Conditions The flow boundary conditions for the three main tributaries were formulated in an identical manner. For example, the historical Northwest Fork flow data were compiled and subjected to a frequency analysis, in order to develop a cumulative frequency distribution (Section 3.2). The discharge (0.7 m3/s) corresponding to the 50% cumulative frequency (median value) was converted to a velocity by dividing the discharge by the flow cross-sectional area (753 in 2) That velocity (0.00093 m/s) was then specified at the flow boundary, at each boundary cell. The same process was repeated for the North Fork and the Southwest Fork, with their respective 50% discharges. To obtain boundary conditions for high-flow scenarios, the same process was done using the 100% discharge (the highest observed value). Sims Creek and Jones Creek were treated as no-flow boundaries, since no velocity or elevation was imposed at the grid edge. This results in essentially a wall condition. The short lengths of these tributaries (300 m for Sims Creek, 900 m for Jones Creek) suggests that a wall condition may not be wholly inaccurate. 4.4 Sediment Transport Model Calibration 4.4.1 Sediment Bed Properties In order to meet the objective of this study, the density of the bed as a function of organic content was determined. Such a relation was developed for fine sediments from three sites in Florida (Rodriguez et al., 1997, Mehta et al., 1994), as well as from the Loxahatchee River. The three sites are the Lower Kissimmee River, the Taylor CreekNubbin Slough basins, and the Rodman Reservoir. All locations harbor organic-rich fine sediments mixed with sand, as does the Loxahatchee River. The granular density of sediment was found to vary with organic content as follows: PS = -16.5(Oc) + 2650 (4.4) yielding an appropriate density of 2,650 kg/m3 for a sediment with no organic content (Oc=0%). The bulk density was found to vary according to: Pb = 1568e-018(c) 0.9(Oc) + 1114 (4.5) The dry density was then computed via the mass balance Pd = (Pb P)P (P! Pw) (4.6) Equations 4.4, 4.5, and 4.6, and the data used to create them are shown in Figure 4.10, including the samples analyzed in the present study (Oc=15%). The granular, bulk, and dry densities decrease with increasing organic content, though the dry and bulk densities level off to near constant values (112 kg/m3 and 1,051 kg/m3, respectively) at an organic content greater than 70%. 3000 2500 2000 Eg Granular density 1500 I," e" . " Bulk density 1000 A Dry density + Loxahatchee River. 500 A A 0 10 20 30 40 50 60 70 Organic content (%) Figure 4.10 Variation of granular, bulk, and dry densities with organic content using data from three Florida locations and the Loxahatchee River. 4.4.2 Suspended Sediment Boundary Conditions To simulate the input of sediment into the estuary, suspended sediment concentrations must be specified at the appropriate boundary cells. At the Southwest Fork/C-18 canal flow boundary (Figure 4.2), Equation 3.2 with the appropriate coefficients (Table 3.7) was applied. At the Northwest Fork the same equation was similarly used. Sediment input from the North Fork was not considered, since the data used to obtain the rating curve were from a central embayment location (Figure 3.7). Due to the relatively low flow of the North Fork, it is reasonable to assume that the main source of suspended sediment at the data location was the inlet, and not an upstream source. Sediment inputs at the Jupiter Inlet/ICWW boundaries were not considered, since fine sand is the major component of the suspended sediment load at those locations (Sonntag and McPherson, 1984). Sims Creek and Jones Creek (Figures 3.1, 4.2) were assumed to contribute negligible fine sediment loads. Table 4.4 shows the locations where sediment inputs were implemented, and the corresponding suspended sediment concentrations for median and maximum flows. Table 4.4 Input sediment concentrations at the tributaries Tributary Median flow (50%) Maximum flow (100%) concentration (kg/m3) concentration (kg/m3) Northwest Fork 0.011 0.030 Southwest Fork 0.014 0.066 North Fork 0.000 0.000 Sims Creek 0.000 0.000 Jones Creek 0.000 0.000 4.4.3 Governing Transport Equation The governing advection-diffusion transport equation (Equation 2.6) requires values of the longitudinal and transverse dispersion constants, KL and KT. Marvdn (2001) selected values of 13 and 1.2, respectively, when modeling the Cedar/Ortega River system in northern Florida. These values were adopted in the present study, and a sensitivity analysis was performed by varying KL and simulating deposition in the C- 18 canal under identical flows and input suspended sediment concentrations. This analysis is described later in Section 4.4.5. 4.4.4 Erosion Function Calibration The bed shear strength (with respect to erosion) is calculated via Equation 2.13 (Mehta and Parchure, 2001), with the coefficients related to organic content. Note however that in what follows the erosion function has been disabled for all simulations, since the organic-rich fine sediment was only present in the upstream reaches of the estuary. 4.4.5 Deposition Function Calibration The probability of deposition, p (Equation 2.15), requires a value for the critical shear stress for deposition. This is set to the highest observed shear stress so that deposition is possible at all times. In these simulations, rd was set to 20 Pa. The settling velocity is characterized by Equation 2.16. The velocity scaling coefficient, a, is used to account for the variation of organic content, with higher organic content resulting in lower settling velocity. Using a-values from Lake Okeechobee (Hwang, 1989), the Ortega River (Marvn, 2001), and the Loxahatchee River, the variation of "a" with organic content (Oc in %) was formulated as follows: a = -1.3 x 10"7(Oc)4 + 7.1 x 10"6(Oc)3 1.7 x 10"4(Oc)2 + 6.6 x 10"4(Oc) + 0.2 (4.7) Equation 4.7 is applicable in the range of Oc between 0 and 44% and is plotted in Figure 4.11 a. Values for the other coefficients of Equation 2.16 were found to be b=6.4, m=1.8, and n,=1.8 (Section 3.9). The use of these coefficients in Equation 2.16 yields the settling velocity in m/s. Figure 4.1 lb illustrates the variation of this velocity (at a representative concentration C=0.5 kg/m3) with organic content. As expected, the settling 1 C 0 0.1 0 0.01 10 20 30 40 5 Organic content (%) Figure 4.11 Variation of settling velocity parameters with organic content. a) coefficient a 8.00E-05 7.00E-05 -6.00E-05 E 5.OOE-05 ____S4.00E-05 S3.00E-05 2 nn1-C5 0 5 10 15 20 25 Organic content (%) 30 35 40 45 - Eq. 4.7 1 Hwang (1989) * Marvan (2001) + Present study 1.00E-05 0.00E+00 _~WH~7 b) Settling velocity. velocity decreases with increasing organic content. For example, a two-fold increase in organic content, from 20% to 40%, yields a 56% decrease in settling velocity. 4.4.6 Sensitivity Analysis for Longitudinal Dispersion Constant The selection of the dispersion constants (Equations 2.7-2.9) was based on a sensitivity analysis to determine if the values used by Marvdn (2001) were reasonable for this study. In the C-18 canal (Figure 4.2), only longitudinal dispersion has an effect on the transport of sediment, because of the one-cell width of this canal. Sedimentation rate was chosen as the result of interest, since it is the primary focus in the canal. Sedimentation rate in the C-18 canal was calculated via Equations 2.17-2.18 for three different values of KL, and the calculated rate is shown in Figure 4.12. The plot shows that even with a 27-fold increase in KL, the sedimentation rate decreases only 7% at the location (60 m) of the greatest difference between the results. This implies that the results of a given simulation are not greatly affected by the value of KL, especially in this range of values (2>KL>55). Therefore the original values of KL and KT were retained (13 and 1.2, respectively). In order to explain the relatively minor differences in sedimentation rate with varying KL, the Peclet number can be calculated for these simulations as Pe = LU D,,x (4.8) where L is the channel length, U is the x-direction velocity, and Dx is the dispersion coefficient in the x-direction (Equation 2.7). This dimensionless number represents the ratio of advection to diffusion. Therefore, for Pe>l, advection is the dominant transport mechanism, and for Pe m, U=O.014 rn/s (median C-18 flow velocity), and the varying KL values to compute Dx,, 0.00012 0.0001 0.00008 o 0.00006 E M 0.00004 0.00002 0 0 200 400 600 800 1000 1200 Distance from S-46 structure (m) Figure 4.12 Sedimentation rate in C-18 canal as a function of longitudinal dispersion constant, KL. Pe varies from 24 to 672, indicating that advection is dominant, under these values of KL. Therefore the transport behavior is not greatly affected by KL. 4.4.7 Comparison with Analytical Solution for Advection-Diffusion In order to verify the performance of the advection-diffusion mechanism of the model, a comparison was made between an analytical solution and model prediction. The transport of a conservative substance in a 1-D channel is governed by the equation (Harleman, 1966): ac ac a at ax ax( a 49 where C is the concentration of the substance, U is the horizontal velocity, and D, is the x-direction turbulent diffusion coefficient. A relevant case is a channel separated by a barrier, with the upstream end containing a steady substance concentration Co, and the downstream end having no concentration (Figure 4.13). At time t=O the barrier is lifted and the motion of the substance in the downstream direction at a velocity U is tracked. The initial and boundary conditions are: C(,t) = CO t 0 C(x,O) = 0 x > 0 C(OO, t) = 0 t > 0 C=CO Barrier (at t--0) U C=O (at t--0) X=-0 +x Figure 4.13 Definition sketch for substance concentration in uniform 1 -D channel, with barrier separating zones of constant concentration and zero concentration at t=0. which indicate a constant concentration at x=0, at all times. When the barrier is lifted (at t=0), the solution for concentration at any distance and subsequent time is given by (Harleman, 1966): C(x' t) = C I eDx erfcL x +Dt + I erfc (4.10) Using CO=0.066 kg/m3, U=0.32 m/s, and Dx=30 m2/s, the concentrations at t=750 s and t=1,500 s were calculated for x=0 to 1,200 m. The concentration and velocity values correspond to the maximum flow condition in the C- 18 canal. The resulting concentration profiles are plotted in Figure 4.14. An analogous situation was simulated using the numerical model by eliminating tidal forcing, and specifying a constant discharge (and hence velocity) and input suspended sediment concentration at the S-46 structure. The deposition and erosion functions were disabled so that strictly transport was modeled. The discharge was maintained at 31 m3/s (100% flow), corresponding to a velocity of 0.32 m/s, and a constant sediment concentration input of 0.066 kg/m3 was imposed on the C-18 canal flow boundary, as computed via the sediment rating curve for the C-18 (Equation 3.2). The model was run for 1,500 s, and the concentrations in the C-18 canal were recorded. Figure 4.14 shows the comparison between the analytical solution and model prediction. The t=750 s comparison shows that the numerical model allows the concentration front to move quicker (0.08 m/s faster at C=0.007 kg/m3) than the analytical solution. The comparison at t=1,500 s shows better agreement for the concentration predictions (no difference at C=0.007 kg/m3). The discrepancy between the model versus analytical results might be explained by the numerical scheme, which causes oscillations in velocity, which deviate approximately 4% from mean (at 100% C-18 discharge), at a frequency of 0.3077 cycles/h. While the dispersion coefficients (Equations 2.7-2.9) in the model are functions of the Chdzy coefficient, velocity, depth, and the dispersion constants, the analytical solution requires only a constant dispersion coefficient. Therefore an oscillating velocity would also cause the dispersion coefficients to oscillate. Nevertheless, the dispersion constant KL from the numerical model was modified for this comparison so that D' (Equation 2.7) was equal to D,, from the analytical solution (30 M2 /s). 4.4.8 Comparison with Flume Data for Deposition Under Turbulent Flow The deposition algorithm of the model was used to compare the output with laboratory data for deposition in a flume under turbulent flow, in order to validate the algorithm. Deposition of fine cohesive sediment under turbulent flow was investigated by Krone (1962) in a re-circulating laboratory flume, using sediment from the San Francisco Bay. Under high flow conditions (no deposition) and a water depth of 0.3 mn, sediment was suspended throughout the flume at the beginning of the test, and then the velocity was reduced to a constant value so as to allow for deposition of the suspended material. The suspension was re-circulated so that the sediment concentration at the beginning of the flume was equal to the concentration at the end of the flume. Tests were conducted for times up to 200 h. The suspended sediment concentration was measured in the return flow through time, at five different flow velocities. At concentrations above 0.3 kg/in3, two distinct deposition phases were observed, corresponding to differing suspension concentrations. Each phase was characterized by a different deposition rate. Below 0.3 kg/in3 a linear relationship was found between deposition rate and bed shear stress (Tb). This trend was extended to zero shear stress, to yield a deposition rate that corresponded 0.07 0.06 0.05 0.04 -- Eq. 4.10, t=750 s .2 -- Eq. 4.10, t=1,500 -+- 2-D model, t=750 s - .03 ----2-D model, t=1,500 s 0 0.02 0.01 0 0 200 400 600 800 1000 1200 Distance (m) Figure 4.14 Comparison of analytical solution and numerical model prediction for concentration in a 1-D channel, at t=750 s and 1500 s. to a constant settling velocity, i.e., dC/dt -Ws/h. The sediment concentration through time in this regime (<0.3 kg/m3) was related to a W, as follows: C = CO exp- hPWs (4.11) where C is the instantaneous concentration, Co is the initial concentration, p is the probability of deposition (Equation 2.15), t is time, W, is the (constant) settling velocity, and h is the water depth. From data taken after concentrations had reached 0.3 kg/m3, the settling velocity was found to be 6.6 x 10.6 m/s, and the probability of deposition was found to be 1-(rb/0.06), where 0.06 Pa is the critical shear stress for deposition. One test was used for comparison in the present study. In that test the flow velocity was 0.134 mis, and a suspended sediment concentration of 0.3 k g/rn3 was observed after 43 h of the 117 h test. Therefore only the last 74 h were used in this comparison. To re-create the above laboratory conditions in the sediment transport model, the depth in the C- 18 canal was reduced to 0.3 m, the discharge was modified to produce a flow velocity of 0.134 mis, and initial concentration in the canal was selected to be 0.3 k g/rn3. The value Of Trd was changed from 20 Pa (Section 4.4.5) to 0.06 Pa (Equation 2.15, Section 2.3.3), and the erosion function was disabled. The value Of Tb (0.05 Pa) was determined via Equation 2.12. After the first time step, the re-circulating aspect of the flume was mimicked by using the concentration at the end of the canal as the input concentration at the beginning of the canal for every successive time step. As noted, only the constant settling velocity regime was modeled, by using the flume-derived value of 6.6 x 10-6 mis. Concentrations were recorded for 74 h, which corresponds to the duration of the flume test. The model result is plotted against flume data in Figure 4.15. In Figure 4.15, the model result follows the exponential decay observed in the flume tests, which should occur when a constant settling velocity is prescribed according to Equation 4.12. It should be noted that if a concentration or time-dependent settling velocity were introduced, the decay in sediment concentration would not be exponential. The comparison does show that the sediment transport model accurately predicts depositional behavior under turbulent flow, which is essential for the simulations described next in Chapter 5. Model result Flume data I 0 10 20 30 40 50 60 70 80 Time (h) Figure 4.15 Comparison of flume data (Krone, under turbulent flow. 1962) with model result for deposition CHAPTER 5 SEDIMENTATION AND TRAP EFFICIENCY 5.1 Historic Sedimentation Rates The calibrated flow and sediment transport models were applied to quantify the sedimentation rate as a function of discharge in the C- 18 canal. Ylow velocities and water elevations were obtained by running the flow model for various C- 18 discharges. These velocities and elevations were used in the sediment transport model to simulate sedimentation rates at a selected location in the canal. The sediment rating curve for the canal (Equation 3.2) was used to determine the input suspended sediment concentration at the S-46 boundary (Figure 4.2). The selected flows and concentrations are given in Table 5. L The Northwest Fork and the North Fork were maintained at their respective 50% flow conditions (Table 3.3) along with the corresponding input concentrations (Table 3.7). This was done because the S-46 structure frequently releases flows to the C18 canal that are not synchronous with the other tributaries (Figure 3.6). Table 5.1 C- 18 discharges and input concentrations for determination of sedimentation rate as a function of discharge C- 18 discharge C- 18 input suspended sediment (m 3/S) concentration (kg/M3) 1.5 0.012 10.5 0.038 19.0 0.051 37.0 0.070 The selected location to calculate the sedimentation rate (Equation 2.18) was 480 rn (8 grid cells) downstream of the S-46 structure. This site was selected because the poling depth data (Figure 3.9) contained a measurement (0.63 m) which fell near the mean poling depth trend (0.67 m) at this approximate location. The simulations for the eight discharges were run for 5 tidal cycles, and the sedimentation rate was calculated at the end of each simulation. An equation was fit to the result, with the form SR =c [1 exp(-3Qc18)] (5.1) where SR is the sedimentation rate in m/d, a and 3 are site-specific coefficients, and Qc-18 is the C-18 discharge in m3/s. Best-fit values of coefficients a and 3 were found to be 3.0 X 10-4 and 0.138, respectively. Figure 5.1 shows the model results and the best-fit Equation 5.1. 3.50E-04 3.OOE-04 2.50E-04 2.OOE-04 .- Model results .0 -Eq. 5.1 r 1.50E-04 E CO) 1.00E-04 5.OOE-05 0.OOE+00 0 5 10 15 20 25 30 35 40 C-18 discharge (m3/s) Figure 5.1 Sedimentation rate 480 m downstream of the S-46 structure in the C-18 canal as a function of canal discharge. The results in Figure 5.1 imply that as discharge increases the change in sedimentation rate decreases. For example, a doubling of flow from 2.5 to 5 m3/s results in a 71 % increase in sedimentation rate, while a similar two-fold increase from 10 to 20 In 3 /s results in a 25% increase in sedimentation rate. At lower flows, the sedimentation rate is much more sensitive to discharge than at higher flows. This is explained in the following analysis. In Figure 5.1, the trend of increasing sedimentation is evidently related to discharge; however, increasing discharge also increases concentration via the sediment rating curve (Equation 3.2). To separate the two effects, two scenarios were simulated. Using the same C-18 discharge (1.7 m 3/S) different input concentrations were implemented in the C-18 canal, and the sedimentation rate curve was plotted against concentration (Figure 5.2). As observed, the input concentration has a linear correlation with sedimentation rate, due to the linear increase in depositional flux resulting from increased concentration (Equation 2.14). Simulations were then performed with constant input concentration (0.014 kg/M3), under differing flows. The results are shown in Figure 5.3. These simulations show that at flows below 12 m 3/S, increasing the discharge increases the sedimentation rate, but above this discharge the sedimentation rate decreases. This trend can be explained by taking an individual suspended particle, and tracking it under different (constant) flow velocities (Figure 5.4). 1.20E-04 1.00E-04 C 0 8.00E-05 E . 600E-05 4.00E-05 2,OOE-05 O.OOE+00 0 0.01 0.02 0.03 0.04 0.05 0.06 Concentration (kglm3) Figure 5.2 Sedimentation rate as a function of input suspended sediment concentration in the C-18 canal, under a discharge of 1.7 m3/s. 9.00E-05 7.00E-05 6.00E-05 a) 5.00E-05 0 C 4.00E-05 E S3.00E-05 2.00E-05 1.00E-05 0.OOE+00 0 5 10 15 20 25 30 35 40 C-18 discharge (mI3/s) Figure 5.3 Sedimentation rate as a function of discharge in the C-18 canal, with input suspended sediment concentration of 0.014 kg/m3. Particle W$ x=O X=a \ x=b x=e Track of particle fUnder U=Ub] Figure 5.4 Schematic diagram of a suspended sediment particle subjected to constant flow velocity and settling velocity. As seen in Figure 5.4, as a particle at x=0 and suspended at the water surface settles at a rate equal to the settling velocity Ws, it is moved longitudinally by the water velocity U. Thus, for example, under a velocity Ua=0.051 m/s (corresponding to a C-18 discharge of 5 m3/s), a particle with settling velocity W,=1 x 10-5 m/s and at the water surface will deposit 8,262 m downstream from it's original location, given the canal water depth h=1.62 m. In contrast, under a velocity Uc=0.1 m/s (discharge=10 m3/s), the same particle will deposit 16,686 m downstream. Finally, under velocity Ub=0.075 m/s (discharge=7 m3/s), the particle will deposit 12,474 m downstream. Therefore if the sedimentation rate is measured at x=b, then one can expect that this rate will be maximum under a velocity of Ub. Equation 5.1 was applied to a historical flow record for the C-18 canal (03/01/8 101/18/91) using the daily discharge values (Qci 8) to determine the daily sedimentation rate (SR). The sum of daily sedimentation over ten years yields the ten-year sedimentation. The flow record used is shown in Figure 5.5. The regulation of the C-18 canal by the S-46 structure is manifested in the highfrequency of zero-discharge periods (54% of the days) and spikes. The deposition rate was found to be 0.15 mn over the ten-year period (0.015 mlyr). The deposition rate estimate made via poling depths in the C-18 canal (Section 3.5) was 0.021 mlyr (Table 3.6). The poling depth estimate accounted for the actual sediment bed thickness, which contained a mixture of sand and fine sediment. If the value is corrected to account for only fine sediment (using the average percent fines value from Table 3.8 of 70%), the 40___ 30 E 25 0 M 20 00 15 6 10 5 ki I~a A6i1ij 0 500 1000 1500 2000 2500 3000 3500 Time from 03/01/1981 (d) Figure 5.5 Historical flow record for C-18 canal, from 03/01/81-01/18/91. ten-year fine deposition thickness would be 0.147 m (0.0147 mlyr), which is within 3% of the model prediction. This procedure is based on the assumption that if only fine sediment was present in the estuary, it would deposit at a thickness proportional to it's mass fraction. This assumption does not account for the different bulk and dry densities of the sand and fine fraction, however. To compare sedimentation in a regulated tributary (C- 18) versus one that is hypothetically unregulated, the flow record for the Northwest Fork from the same period as Figure 5.5 was pro-rated so the total discharge over the ten-year period was the same as for the C-18 canal (Figure 5.6). This was done by summing the daily discharge over the ten-year period in the C- 18 canal (6,245 m 3 Is) and the Northwest Fork (7,217 M3/S), and multiplying each daily discharge value for the Northwest Fork by the ratio (0.865) of the ten-year cumulative discharges. As a result of this procedure, the ten-year cumulative discharge in the Northwest Fork becomes equal to the ten-year cumulative discharge in the C- 18 canal. This procedure creates a hypothetical unregulated C- 18 flow record, that contains a prevalent background discharge as only 4.5% of the days had zero flow, as compared to 54% for the existing (regulated) C- 18 flow record. Equation 5.1 was applied to the unregulated C- 18 canal flow record, resulting in a ten-year deposition thickness of 0.22 m (0.022 m/yr). This implies that episodic discharges from the C-18 canal actually result in lower sedimentation rates than if the flows were more evenly distributed, as in the Northwest Fork (Table 5.2). Figure 5.7 shows the cumulative deposition for the two flow records over the ten-year period. The deposition under the unregulated flow record is greater than it is under regulated flow. This is a consequence of the near-constant discharge present in the unregulated flow record. As Figure 5.1 shows, sedimentation rate increases greatly with discharge at lower values, but this increasing trend is attenuated at higher discharges. Therefore the higher occurrence of low flows in the unregulated C- 18 flow record allows for relatively higher deposition as compared to the existing regulated flow record. This can be illustrated by considering sedimentation over a sample period, such as two days. If the first day had an average flow rate of 25 m 3 Is, and the second day had no flow, the total two-day sedimentation would be 2.9 x 10 -4 m (Equation 5.1). If, however, the flow was divided evenly over the two days, resulting in 12.5 m3/s of flow each day, the total sedimentation would be 4.9 x 10-4 m, a 70% increase. aj25 20 15 6 10 5 0 500 1000 1500 2000 2500 3000 3500 Time from 03/01/1981 (d) Figure 5.6 Assumed C- 18 canal flow record obtained by pro-rating the measured record for the Northwest Fork for the period 03/01/81-01/18/91. Table 5.2 Sedimentation rate in the C-18 canal Flow record -Sedimentation rate (Eq. 5. 1) (Mlyr) Existing (regulated) 0.0 15 Hypothetical (unregulated) 0.022 5.2 Sediment Trap and Trap Efficiency Calculation Once the flow and sediment transport models were calibrated and tested (Chapter 4), a trap was incorporated in the C-18 canal (Figure 5.8). This location was chosen because it is near the area of greatest post-dredging deposit thickness, with a poling depth of approximately 1.2 m (Figure 3.9). A dredging depth of 3 m (from original bed depth), width of 60 m (one cell), and length 180 m (3 cells) were chosen as sufficient to reduce the velocity in the canal, and allow a measurable amount of sediment to settle. When 0.25 0.2 .0 0.15 0 C-18 CL unregulated *0 )-C-18 ____regulated _ 01 E ) 0.05 0 0 1 2 3 4 5 6 7 8 9 10 Time (yr) Figure 5.7 Cumulative deposition over ten-year period (03/01/81-01/18/91) for existing regulated versus assumed unregulated C-18 canal discharge. simulating a cumulative 50% flow magnitude (1.3 m3/s) and regular tidal forcing (Section 4.3.1) in the C-18 canal, the maximum velocity over the trap was found to be 0.04 m/s. Over the same area, with no trap in place, the maximum velocity was 0.12 m/s, which indicates a 67% decrease in velocity over the trap. In order to incorporate the trap, the bathymetry file was modified at the selected cells. The flow model was run with the trap in place, in order to generate the new velocities and water surface elevations. The output from the flow model was then applied to the sediment transport model. Sediment removal ratio, as defined in Equation 2.20, was calculated from the influent and effluent sediment loads in units of kg/s (Equation 2.19) at the cells adjacent to the trap on the landward and ocean-side edges of the trap (Figure 5.8). Freshwater flow with input concentration Flow direction on ebb tide E I - Influent cell -- Effluent cell C-18 canal Central embayment I f I I i I I I I ,-+-I. + *~ I I Figure 5.8 Portion of the computational grid. adjacent influent/effluent cells also shown. Three trap cells are shown in black. Trap- Influent and effluent sediment loads were calculated for each time step, and the removal ratio averaged over one ebb tidal cycle as follows: M Rave_ ~ M (5.2) where Rave is the ebb tide-averaged removal ratio, i is the index for each time step At, Ri is the removal ratio from a single time step, and M is the total number of time steps over an ebb tidal period, as follows: (5.3) 2At where T is the tidal period. Flood tidal data were not used to calculate the removal ratio because the effluent load (landward edge) was affected by the input concentration at the C-18 canal. In addition, the influent load (seaward edge) contained only the sediment which had escaped the trap on the previous ebb tide. It was observed that C-i 8 canal 100% flow (31 m3/s) was the only discharge that produced a constant seaward flow while the ocean tide was flooding. In this case the removal ratio was calculated for the entire tidal period. 5.2.1 Trap Efficiency as a Function of C-18 Canal Discharge If discharge through the S-46 control structure has an effect on trap efficiency, then flow management practice will affect trap efficiency as well. To explore this, simulations were performed using the sediment rating curves developed in Section 3.6, and applied to 8 flow cases. Table 5.3 gives the flows used and the corresponding sediment concentration. The organic content used was 15%, reflecting the mean organic content of the native sediment. Removal ratios were calculated only during periods of ebb flow through the trap (Section 5.2), and plotted against C- 18 canal discharge (Figure 5.9). Table 5.3 Flows and suspended sediment concentrations for trap efficiency as a function of C- 18 canal discharge C-i 18 flow (ma/s) C-i 18 suspended sediment concentration (kg/in3) 0.42 0.008 0.50 0.009 1.27 0.013 1.45 0.014 1.69 0.016 2.54 0.019 4.25 0.024 37.00 0.070 0.6 0.5 0.4 > 0.3 0 E 0.2 0.1 0 0.1 1 10 100 C-18 discharge (m3/s) Figure 5.9 Removal ratio in the presence of trap as a function of C-18 canal discharge. These simulations show that the removal ratio is maximum at a C-18 discharge of approximately 1.7 m3/s. At a higher discharge (and thus velocity), particles are transported past the trap. At a lower discharge, the same particles settle before the trap. To illustrate this behavior, Figure 5.10 shows the tracks of a particle under three different velocities U (with Ua m. At the trap the flow velocity would reduce to U~t0.011 m/s, but the particle would only fall another 0.34 m, which would leave it at a depth of 0.96 m when it left the trap, still suspended in the flow. Therefore for this trapping scheme and sediment type, a discharge of 1.7 mn3 /s results in the maximum removal ratio. Above this discharge particles are moving at a velocity such that more of them are able to pass the trap, and below this discharge more particles deposit before the trap. Particle tracks under different velocities particle U8 Ub UUb N Figure 5. 10 Schematic diagram of a particle passing over a trap at three different velocities. This hypothesis can be tested by moving the trap further upstream. The trap was moved 480 mn upstream (1260 mn from S-46 structure) from it's previous location, and the removal ratio was calculated for three C-i 18 canal discharges (0.42, 1.45, and 4.25 m3/s). Table 5.4 compares the removal ratios for the three discharges, for the two trap locations. The two discharges below 1.7 mn3/S, for which removal ratio is a maximum, had increased removal ratios when the trap was moved upstream. The discharge above 1.7 m 3/s had a decreased removal ratio at the new trap location. These observations confirm the mechanisms of Figure 5. 10. Table 5.4 Removal ratio for three C-i 18 discharges, with two different trap locations C-i 18 discharge (m3/s) Removal ratio with Removal ratio with trap ____________________ original trap location 480 mn further upstream 0.42 0.17 0.70 1.45 0.48 0.49 4.25 __0.35 0.30 5.2.2 Trap Efficiency as a Function of C-18 Canal Sediment Concentration The sediment rating curves developed in Section 3.6 were used in the previous simulation to determine input concentrations at the C-i18 canal. Note that all the concentrations in Tables 5.1 and 5.3 correspond to the free settling range, within which a constant settling velocity is prescribed (Section 3.9). In reality, high-concentration mud suspensions are common just above the sediment bed, with concentrations that may rise above 1 kg/in3 (Winterwerp, 1999). Under these conditions, settling would go beyond the free range, and thus trap efficiency would be affected by the settling regime, e.g., free settling versus flocculation settling. In order to quantitatively account for this effect using depth-averaged modeling (in which a vertical profile in concentration does not occur), concentration in the C- 18 canal was increased under a constant flow (1.7 mn3/S) and the removal ratio calculated. Table 5.5 shows the selected input concentrations and the resulting settling regime. Figure 5.11 shows the simulations. Table 5.5 Simulation parameters for trap efficiency as a function of input sediment concentration to the C-18 canal (Qc.18=1.7 m3/s) C-18 input sediment Settling zone concentration (kg/m3) 0.014 free settling 0.10 free settling 0.25 free settling 0.75-7 flocculation settling 7-25 hindered settling UAU 0.01 0.1 1 10 Concentration (kg/m3) Figure 5.11 Removal ratio as a function of input suspended sediment concentration to the C- 18 canal. The trend in Figure 5.11 implies that the removal ratio is not affected by concentration at values greater than 0.1 kg/m3. Note however that the formula to calculate removal ratio (Equation 2.20) normalizes the difference between influent and effluent load by the influent load. To eliminate the effect of normalizing the difference between influent and effluent loads, Figure 5.12 shows the non-normalized difference, qi-qe, p plotted against input concentration. As a result of not normalizing the load difference, observe that increasing input concentration does result in higher load being trapped. The rate of increase begins to decrease at concentrations above 5 k g/rn3, which is just below the hindered settling range (z7 k g/rn3 for this sediment type, Section 3.9). In this range a lower settling velocity decreases the amount of load that can be trapped. This simulation also serves as a sensitivity analysis for the settling velocity in the model. Since settling velocity is computed as a function of sediment concentration (Equation 2.16), Figure 5.12 also shows the variation of trapped load with settling velocity. 0.5 0.45 0.4 0.35 - 0.3 0 er 0.2 0.15 0.1 0.05 0 0.01 0.1 1 10 100 Concentration (kglM3) Figure 5.12 Difference between influent and effluent loads (trapped load) as a function of input suspended sediment concentration to the C- 18 canal. 5.2.3 Trap Efficiency as a Function of Organic Content To determine the effect of organic content on trap efficiency, simulations were performed at a C-i18 canal discharge of 1.7 m 3/S and at an input suspended sediment concentration of 1 k g/rn3. This value was selected because the removal ratio is independent of concentration in this range (Figure 5.11). Table 5.6 shows the a-values (settling velocity scaling coefficient in Equation 2.16), and the sediment dry and granular densities as functions of organic content. The results are shown in Figure 5.13. The trend in Figure 5.13 indicates that sediment with a high organic content (and therefore low density and settling velocity) is more difficult to remove from suspension than sediment with relatively low organic content. To examine the trend of the amount of sediment actually being trapped, sedimentation rate in the trap was calculated via Equation 2.18. Marvdin (2001) observed consolidation rates for an organic-rich Florida sediment, where self-weight consolidation of the sediment resulted in a 64% decrease in bed height after 200 h. This correction was applied to each sedimentation rate to account for consolidation of the sediment bed in the trap. The resulting sedimentation (shoaling) rate versus organic content plot is shown in Figure 5.14. Table 5.6 Values used for coefficient a (Eq. 2.16), dry density, and granular density, for simulation of removal ratio as a function of organic content Organic content a-value Dry density (Eq. 4.6) Granular density (Eq. 4.4) (%) (Eq. 4.7) (kg/in3) (kg/rn 0 0.2000 2650 2650 5 0.1998 1210 2568 10 0.1954 590 2485 15 0.1890 331 2403 20 0.1812 220 2320 25 0.1700 172 2238 30 0.1532 149 2155 35 0.1240 138 2073 40 0.0760 131 1990 1 0.9 0.8 0.7 .2 0.6 0.4 I-I 0.3 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 Organic content (%) Figure 5.13 Removal ratio as a function of organic content at a constant discharge of 1.7 m3/s. 1.00E-03 9.00E-04 8.00E-04 S7.00E-04 6 .00E-04 4 .00E-04 E 3.00E-04 2.00E-04 C .2 3.OOE-04 cc 2.OOE-04 1.00E-04 O.OOE+00 0% 5% 10% 15% 20% 25% 30% 35% 40% Organic content (%) Figure 5.14 Sedimentation (shoaling) rate in trap as a function of organic content at a constant discharge of 1.7 m Is, assuming uniform consolidation. 83 The trend in Figure 5.14 implies that sediment with higher organic content shoals at a higher rate than sediment with lower organic content. Two phenomena contribute to this trend. Firstly, the decrease in dry density with increasing organic content (Figure 4.9) leads to a greater deposition thickness (Equation 2.17). Secondly the influent load rises as organic content is increased (due to less deposition upstream of the trap via lower settling velocity), which increases the potential amount of sediment that can be trapped. The mass deposited upstream of the trap (in terms of mass) versus organic content is shown in Figure 5.15. As the trend shows, sediment with low organic content tends to deposit at a higher rate upstream of the trap, due to the high settling velocity (and therefore deposition flux, Equation 2.17). 35000 30000 S25000 .0 0) IM 20000 C) a) C) U) cu100005000 0 0 5 10 15 20 25 30 35 40 Organic content(% Figure 5.15 Mass deposited in the C- 18 canal (upstream of the trap, Figure 5.8) as a function of organic content. |