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Part II

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Title:
Part II
Series Title:
Hydrographic measurements at St. Andrew Bay entrance, Florida
Creator:
Jain, Mamta
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Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
Publication Date:
Language:
English

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University of Florida
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University of Florida
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UFL/COEL-2002/006

HYDROGRAPHIC MEASUREMENTS AT ST. ANDREWS BAY ENTRANCE AND EAST PASS, BAY COUNTY, FLORIDA PART II
by
Mamta Jain and
Ashish J. Mehta

Submitted to: Coastal Technology Corporation Destin, FL 32541

July 2002




UFLJCOEL-2002/006

HYDROGRAPHIC MEASUREMENTS AT ST. ANDREWS BAY ENTRANCE
AND EAST PASS, BAY COUNTY, FLORIDA, PART II By
Mamta Jain and Ashish J. Mehta

Submitted to:
Coastal Technology Corporation
Destin, FL 32541
Coastal and Oceanographic Engineering Program Department of Civil and Coastal Engineering University of Florida Gainesville, FL 32611

July 2002




SUMMARY
Hydrographic measurements were carried out on March 27-28, 2002 in two channels in Bay County, Florida: St. Andrews Bay Entrance (also known as Panama City Harbor Entrance) and the newly opened East Pass, both connecting the same bay waters to the Gulf of Mexico. This report covers the second set of measurements in the same two channels. The first set was carried out on December 18 and 19 of 2001.
The present measurements included two flow cross-sectional surveys, one being in St. Andrews Bay Entrance, where heavy vessel traffic on March 28 prevented collection of data at another chosen section between jetties. The second section was at East Pass, where data were obtained on the previous day (March 27). Vertical profiles of flow velocity were obtained across these cross-sections. These data were used to determine the corresponding time-variation of flow discharge in each channel. The discharge variation was in turn used to calculate the associated tidal prisms.
The following values were obtained. St. Andrews Bay Entrance: (flood) tidal prism 4.2 X 107 M3, cross-section (at mean tide) 6,330 M2 and peak flood (cross-sectional mean) velocity 0.42 m/s. East Pass: (flood) tidal prism 1. 9X 106 M3, cross-section 255 M2 and peak (flood) velocity 0.40 m/s.
At St. Andrews Bay Entrance, the tidal prism was compared with the prism obtained in September 2001, when East Pass was closed. No credible trend of the effect of East Pass opening on the tidal prism at St. Andrews Bay Entrance could be established from this comparison, because the prism at East Pass was an order of magnitude smaller than at St. Andrews Bay Entrance. Stability analysis provides some insight into the trend of instability of East Pass, which can be traced back as far as 1934.




TABLE OF CONTENTS
S U M M A R Y ........................................................................................... 2
TABLE OF CONTENTS ........................................................................... 3
L IST O F F IG U R E S ................................................................................. 5
L IST O F T A B L E S ................................................................................... 7
ACKNOWLEDGMENT ........................................................................... 8
SECTION A: ST ANDREWS BAY ENTRANCE ............................................ 9
A-] INTRODUCTION .......................................................................... 9
A-2 MEASUREMENTS ........................................................................ 12
A -2.1 C ross-S ections ........................................................................... 12
A -2.2 T ide L evel ................................................................................ 12
A-2.3 Current and Discharge ................................................................. 13
A -3 TID A L PR ISM .............................................................................. 16
A-3.1 Calculation of Tidal Prism ............................................................ 16
A-3.2 Comparison with O'Brien Relationship ............................................. 17
SECTION-B: EAST PASS ....................................................................... 18
B-1 INTRODUCTION ......................................................................... 18
B-2 MEASUREMENTS ........................................................................ 19
B -2.1 C ross-S ections ........................................................................... 19
B -2.2 T ide L evel ................................................................................ 20
B-2.3 Current and Discharge ................................................................. 20
B-3 TIDAL PRISM ............................................................................. 22
B-3.1 Calculation of Tidal Prism ............................................................ 22




B-3.2 Comparison with O'Brien Relationship ............................................. 22
CONCLUDING COMMENTS .................................................................. 22
R E F E R E N C E S ...................................................................................... 24
APPENDIX: INLET STABILITY ANALYSIS ............................................. 25
C .1 Introduction ............................................................................ 25
C.2 Linearized Lumped-Parameter Modelfor Two Inlets .......................... 25
C.3 Stability Calculation .................................................................. 28




LIST OF FIGURES

Fig A-1.1 St. Andrews Bay Entrance, Florida in 1993. Jetties are -430 mn apart ....... 10
Fig. A-1.2 St. Andrews Bay Entrance bathymetry and current measurement crosssections D. The tide level recorder was located northward of the area shown. Depths are in feet below MLLW. Measurements at cross-sections A and B were conducted in September 2001 and are reported by Jain and Mehta (2001). Measurements at crosssections A' B' and C' were conducted in December 2001 and are reported by Jain et al. (2002).............................................................................11I
Fig A-2. 1 Cross-section D measured and compared with 2000 bathymetry. Distance is measured from point D-1. The datum is mean tide level. Measured area 6,330 M ............................................................................ 12
Fig.A-2.2 NOS predicted tide at St. Andrews Bay Entrance on March 27-28, 2002. The datum is MLLW............................................. 13
Fig. A-2.3 Cross-sectional mean current variation at cross-section D on March 28, 2002 .....................................................................14
Fig.A-2.4 Discharge variation at cross-section D on March 28, 2002 ................. 14
Fig. A-2.5 Ebb velocity structure at cross-section D on March 28, 2002 at 16:49. Vertical axis represents current speed in mis. Depth and width axes are in meters. Origin of width is point D-1I............................................ 16
Fig B- 1.l1 East Pass channel in 1997 ..................................................18
Fig. B-1.2 Location of East Pass current measurement cross-section F on USGS topographic map: left portion 1994; right portion 1982............................... 19
Fig B-2.1I Cross-section F measured by ADCP. Distance is measured from
2
point F-i1. The datum is mean tide level. Area = 300 mn............................... 20
Fig. B-2.2 Cross-sectional mean current variation at East Pass March 27, 2002.......21
Fig. B-2.3 Discharge variation at East Pass on March 27, 2002....................... 21
Fig. C. 1 Schematic diagram of two-inlet stability regimes ........................... 28
Fig. C.2 Inlet stability diagram for 1934 ............................................. 29
Fig. C.3 Inlet stability diagram for 1946 ............................................. 30




Fig. CA Inlet stability diagram for 1983 ......................................................... 30
Fig. C.5 Inlet stability diagram for 2002 ......................................................... 30




LIST OF TABLES

Table A- 1. 1 Locations of St. Andrews Bay Entrance cross-sections ......................... 9
Table A-2.1 ADCP measurement sequence at St. Andrews Bay Entrance .................. 13
Table A-2.2 Characteristic peak velocities and discharges at cross-section D at St. A ndrew s B ay E ntrance ............................................................................. 15
Table A-2.3 Characteristic slack water time at cross-sections D at St. Andrews Bay E ntran ce .............................................................................................. 15
Table A-3.1 Tidal prism values for St. Andrews Bay Entrance ............................... 17
Table B 1. 1 Location of East Pass cross-section F ............................................... 19
Table B-2.1 ADCP measurement sequence at East Pass ....................................... 20
Table B-2.2 Characteristic peak velocity and discharge at East Pass cross-section F ...... 21 Table B-3.1 Flood and ebb tidal prisms at East Pass ........................................... 22
Table B-4.1 Comparison of prisms measured at St Andrews Bay Entrance ................ 23
Table C. I Selected parameters for inlet I and inlet ............................................. 29
Table C.2 Cross-sectional areas of inlets ......................................................... 29




ACKNOWLEDGMENT

This study was carried out for the Coastal Technology Corporation, Destin, Florida. Assistance provided by Michael Dombrowski of Coastal Tech is sincerely acknowledged. The field investigation was performed by Sidney Schofield and Vic Adams of the Department of Civil and Coastal Engineering, University of Florida.




HYDROGRAPHIC MEASUREMENTS AT ST. ANDREWS BAY ENTRANCE
AND EAST PASS, BAY COUNTY, FLORIDA
SECTION A: ST. ANDREWS BAY ENTRANCE A-i. INTRODUCTION
Hydrographic measurements were carried out on March 28-27, 2002 in two channels in Bay County, Florida: St. Andrews Bay Entrance (also known as Panama City Harbor Entrance) and the newly opened East Pass, both connecting the same bay waters to the Gulf of Mexico. This report covers the second set of measurements in the same two channels. (The first set was carried out on December 18 and 19 of 2001.) The measurements included: 1) one flow cross-sectional survey in St. Andrews Bay Entrance and the second at East Pass, and 2) vertical profiles of flow velocity across these crosssections. Unfortunately, at St. Andrews Bay Entrance heavy vessel traffic on March 28 prevented collection of data a second chosen section between jetties.
The data were used to determine the corresponding time-variation of flow discharge in each channel. The discharge variation was in turn used to calculate the associated tidal prisms.
Figure A- 1. 1 is an aerial view of the St. Andrews Bay Entrance channel and Fig. A- 1.2 is a bathymetric survey based largely on measurements carried out in 2000. Crosssection D is where currents were measured on 03/28/2002 with a vessel-mounted Acoustic Doppler Current Profiler, or ADCP (Workhorse 1200 kHz, RD Instruments, San Diego, CA). The coordinates of end-points D- 1, D-2 are given in Table A- 1.1. Table A- 1. 1 Locations of channel cross-sections Section Side Latitude Longitude Northing Easting
D D-1 3007.4220 -8543.3271 410714.20859 1613635.15158
D D-2 3007.6540 -8543.5844 412134.85378 1612294.58589




Fig A- 1. 1 St. Andrews Bay Entrance, Florida in 1993. Jetties are -430 m apart.
10




D-2 IB'

412000.00
\400\ 0
411000.00
.... n-1
410000.00 c"-'
1. %
A-I
409000.00 A'.1
550
1610000.00 1611000.00 1612000.00 1613000.00 1614000.00 16!5000.U0
Fig. A-1.2 St. Andrews Bay Entrance bathymetry and current measurement crosssections D. The tide level recorder was located northward of the area shown. Depths are in feet below MLLW. Measurements at cross-sections A and B were conducted in September 2001 and are reported by Jain and Mehta (2001). Measurements at crosssections A' B' and C' were conducted in December 2001 and are reported by Jain et al. (2002).




A-2. MEASUREMENTS
A-2.1 Cross-Sections
Cross-section D measured by the ADCP is shown in Figs. A-2.1. It has been compared with the bathymetric survey of 2000. The trends in the two sets of depths are qualitatively (although not entirely) comparable. As far the velocity measurements given later are concerned, the ADCP-based values must be treated as having a good degree of accuracy because they were measured at the precise times and locations of acoustic profiling for current data. On the other hand, the bathymetric data are likely to be less accurate, given that they were not synchronous.
Bottom Contours
D-1 D-2
0
o o o 0 0
" 0 0 0 0 0
-5 C\j C0 ICO (0
-~-10
a
- 15 -20 i
Distance (m) from D-1
----ADCP -u--Contours
Fig A-2.1 Cross-section D measured and compared with 2000 bathymetry. Distance is
2
measured from point D-1. The datum is MLLW. Measured area = 6,330 m2.
A-2.2 Tide Level
Tide-variation given in Fig. A-2.2 is the predicted National Ocean Service (NOS) tide at St Andrews Bay Entrance channel based on the reference station at Pensacola. The record indicates a range of 0.30 m on March 27-28, 2002, and 0.17 m on March 28.




Since measured tide data were not available for this station, Fig. A-2.2 should be treated as an approximation of the actual tide on 03/27-28/2002.
Tides on 27 and 28 March

CD 0 (C0
co, 0) Cr) co
03//27/02

0 C D to O O0 C .q ,. .q .. 'P 'P .- co (D co C5 CO r- 0
Time (hrs)
03/28/02

Fig.A-2.2 NOS predicted tide at St Andrews Bay Entrance on March 27-28, 2002. The datum is MLLW.
A-2.3 Current and Discharge
The sequence of ADCP measurements is as given in Table A-2.1.
Table A-2.1 ADCP measurement sequence
Cross Date Time Date Time No. of
Section starting starting ending ending transects
D 03/28/2002 06:44 03/28/2002 17:44 44

The time-variation of the cross-sectional mean current variation at D is plotted in Fig. A-2.3. The corresponding discharge is given in Fig. A-2.4.

0.35
0.3 0.25 0.2
0.15 0.1 0.05
0
-0.05

.0
N
N

- Tides




Fig. A-2.3 Cross-sectional mean current variation at D on March 28, 2002.

Fig. A-2.4 Discharge variation at cross-section D on March 28, 2002.

Velocity Profile
0.500 0.400 0.300 0.200
E0.100
C')
-0.100
. 0.000 .
0.100 S ~ 00 IOnL 0 IO 7t C, nN
7 -0.200 't o i o 0 00 ) ,C)
> -0.300 -" r- C a) oM .0 "
-0.400 -0.500 -0.600
Time(hrs)
Velocity Profile

C_ 0
a.

Discharge Profile
3000
S2000 E 1000
2 0
co N 00 U) U 0 O .o (D O (D LO 0 N 0
-1000 -4 4 6 6 6 6 6 f"
-3000
-4000
Time(hrs)
--*--Total Discharge




Based on the data in Figs. A-2.3, and A-2.4, Table A-2.2 provides characteristic velocity and discharge related times and magnitudes.
Table A-2.2 Characteristic peak velocity and discharge values at cross-sections D.
Quantity V Cross-section D
QuniyValue Time
Flood Velocity (m/s) 0.42 10:28:20
Ebb Velocity (m/s) 0.49 14:48:11
Flood Discharge (m3/s) 2509 10:28:20
Ebb Discharge (m3/s) 2777 14:48:11
Examples of measured flood velocity structure over cross-section D is shown in Figs. A-2.5, for illustrative purposes.
Table A-2.3 Slack water time at cross-section D, St. Andrews Bay Entrance
Cross-section D
Slack water time (h) 12:20
Ichiye and Jones (1961) reported 0.52 m/s peak flood velocity and and 0.61 m/s at peak ebb close to cross-section A'. Lillycrop et al. (1989) measured 0.68 m/s peak flood and 0.73 m/s at peak ebb. Note that during both of those studies East Pass was open. Jain and Mehta (2001) reported 0.63 m/s at flood and 0.62 m/s at ebb, respectively, when East Pass was closed in September 2001, while Jain et al. (2002) measured 0.68 m/s and 0.73 m/s in December 2001 soon after East Pass had been opened.




,1'

k 800
100
Fig. A-2. Flo6eoiysrcuea rs-eto nMrh2,20a0:9
Vertcalaxi reresets urrnt peedin is.Deph an with xesare n mter. Oigi
of with i poin D-2
Flow,-2. repctvly.d Wenit atclte dshrecvefrtat pus-ecinDnMros is, not2 avlbe the49 fllwingh fsomul yilsaDppoiaevau2fte.rsP
A-3 TIDAL PRISM




where Q.. is the peak discharge (Table A-2.2), T is the tidal period which is 25.82 h and the coefficient CK = 0.86 (Keulegan, 1967). The calculated values are given in Table A3.1.
Table A-3.1 Tidal prism values for St. Andrews Bay Entrance
Tidal stage Tidal prism
(m3)
Flood 8.6x 107
Ebb 9.4x 107
A-3.2 Comparison with O'Brien Relationship
The O'Brien (1969) relationship between the throat area Ac and the tidal prism P on the spring range for sandy inlets in equilibrium is:
Ac = apb (A-3.2)
For inlets with two jetties, a = 7.49x10-4 and b = 0.86 (Jarrett, 1976). Now, considering cross-section A' to represent the throat section, Ac = 5,210 m2 at mid-tide level (Jain et al., 2002). Thus, from Eq. A-3.1 we obtain P = 9.0x107m3, which may be compared with the measured (flood) value of 8.6x107m3. The latter value is only 5% less than the former.




SECTION-B: EAST PASS

B-i. INTRODUCTION
Hydrographic measurements were carried out at East Pass on 03/27/2002. The aim was dual: 1) to determine the tidal prism of this new cut as a record of its incipient stability, and 2) to examine the effect of this inlet on St Andrews Entrance, by comparing the measured prism with that at St. Andrews Bay Entrance. The measurements included a flow cross-sectional survey and vertical profiles of flow velocity that cross-section.
Figure B-i1.1 is an aerial view of the East Pass before it was opened along the designed configuration. Cross-section (F) where currents were measured is marked in Fig. B-l1.2. The coordinates of end-points F-lI and F-2 are given in Table B- 1. 1.

Fig B-1.1 East Pass channel in 1997.




Table B-I .1 Location of channel cross-section at East Pass Section End Latitude Longitude Northing Easting
F F-i 3003.7839 -85 37 0715 388325.55736 1646376.03172
F F-2 30037910 -85 37 1233 388371.26716 1646103.35534

k i.... "
t!NSUFtIC)FNT DA FA
'.o F-I F2'
E-Z
" Reopened East Pass
mouth

Fig. B-1.2 topographic

Location of East Pass current measurement cross-section F on USGS map: left portion 1994; right portion 1982.

B-2. MEASUREMENTS B-2.1 Cross-section
The bottom track of cross-section F obtained by the ADCP is shown in Fig. B-2. 1.




Fig B-2.1 Cross-section F measured by ADCP. Distance is measured from point F-1. The
2
datum is mean tide level. Area = 300 m2. B-2.2 Tide Level
Tidal variation in the channel on 03/27/02 was predicted NOS tide at St Andrew Bay channel (Fig.A-2.2). The record indicates a range of 0.30 m on March 27, 2002. B-2.3 Current and Discharge
The sequence of ADCP measurements is as given in Table B-2. 1.
Table B-2.1 ADCP measurement sequence at East Pass
Cross Date Time Date Time No. of
section starting Starting ending ending transects
F 03/27/2002 7:12 03/27/2002 17:47 92

The time-variation of the cross-sectional mean current at F is plotted in Figs. B2.2. The corresponding discharge variation is given in Fig. B-2.3.

Bottom Contour F-1 F-2
0 r I I I 1 1
-0.5 0 3.5 11 18.2 24 31.5 37 46.6 59 72.6 75 84.5
-1
E -1.5
_ -2 o -2.5
-3
-3.5
-4
Distance (m) from F1
- ADCP




Velocity Profile

Fig. B-2.2 Cross-sectional mean current variation at F on March 27, 2002.

Total Discharge(m3/s)

150.00
S100.00 CY)
E 50.00
) 0.00 CO
-50.00 o -5oo.oo
-100.00
-150.00 -

L C' CO 0 N CO CD C) ID
- . c. c c) o o n t
0 C IO OitC N&Ps
S CO C) 0 C ) 0 6 COJ (0) U CTehTimefhrs)

-Total Discharge(m3/s)
Fig. B-2.3 Discharge variation at cross-section F on March 27, 2002.
Based on the data in Figs. B-2.2 and B-2.3, Table B-2.2 provides characteristic velocity and discharge-related times and magnitudes. Table B-2.2 Characteristic peak velocity and discharge at East Pass cross-section F
t Cross-section F
Quantity Flood Time Ebb Time
Velocity (m/s) 0.43 10:04:30 0.38 14:23:23
Discharge (m3/s) 114 10:04:30 101 14:23:23

0.600 0.400 S0.200
E
000 -

0 ,,,,, ,,,,,,,,,,,,,,.,,,,,,,,,,,,,,,., O ,, CO ,, ,, ,,J q, ,, ,, ,r I S ' I ""0 )
-) -0.200. 0 .o. C' C' U) .u. -. U) .i. Q .o. U)
>U) o C') 0r- o'J U 04') Q Cf o CA o)U C'
-0.400 c 0 0 0 -- o
-0.600
lime(hrs)
- velocity(m/s)l

rl*"V,

rl-

rr




From Table B-2.2 we note that peak (cross-sectional mean) flood velocity is greater than ebb by 12 %. Likewise, the flood discharge was greater than ebb by 12%. B-3. TIDAL PRISM
B-3.1 Calculation of Tidal Prism
The flood and ebb tidal prisms were estimated as follows. In reference to Fig. B2.3, the flood tidal prism was estimated by extrapolation of the starting point of the discharge curve, as measurement did not run over the entire tidal cycle. This extrapolation was based on the assumption of a diurnal tide (see Fig. A-2.2) having a period of 25.82 h. Such an extrapolation was not necessary for calculating the ebb prism. The calculated flood and ebb prisms are given in Table B-3. 1.
Table B-3.1 Flood and ebb tidal prisms at East Pass Flow Prism
direction (M3)
Flood 3.9x 106
Ebb 3.5xlO'
B-3.2 Comparison with O'Brien Relationship
Relative to Eq. A-3. 1, for inlets with no jetty, a = 1.58x 10-4 and b = 0.95 (Jarrett,
2
1976). Now, considering cross-section F to represent the throat section, A, = 255 M at
6 3
mean tide level. Thus, from Eq. A-3.2 we obtain P = 3.6x 10 m CONCLUDING COMMENTS
From the collected data the following values are obtained. At St. Andrews Bay Entrance, the measurements indicate: tidal prism 4.2x 107 M3, cross-section (at mean tide) 6,330 m 2 and peak flood (cross-sectional mean) velocity 0.42 m/s. The corresponding




values for East Pass are: (flood) tidal prism 1.9x106 m 3, cross-section 255 m2 and peak (flood) velocity 0.43 m/s.
It is interesting to compare the flood/ebb tidal prisms at St. Andrews Bay Entrance measured in 09/01 (Jain and Mehta, 2001) and 12/01 (Jain et al., 2002) with those from the present study. This is done in Table B-4.1 based on the prism definition according to Eq. A-3.1.
Table B-4.1 Comparison of prisms measured at St Andrews Bay Entrance
Prism
(3)
(in3)
Flow Cross- Cross- Cross- Cross- Cross- Crossstage section section section section section section
A A' B B' C' D
(09/01) (12/01) (09/01) (12/01) (12/01) (03/02)
Flood 6.9x107 6.0x107 5.0x107 6.7x107 5.8x107 4.2x10'
Ebb 6.0x107 6.9x107 3.7x107 4.9x107 6.4x107 4.6x107
Since cross-sections A and A' are close to each other (Fig. A-1.2) and believed to be close to the channel throat, it is instructive to compare the values obtained there. Note that there is no discernible trend of the effect of East Pass, which was closed in September 2001, but open in March 2002. This lack of an identifiable effect is not surprising, especially considering that the flood/ebb prisms measured at East Pass in 12/01 were only 0.23x107 M3 and 0.40x107 M3, respectively, and 0.19x107 M3 and 0.17x107 M3, respectively, in 03/02. Stability analysis carried out in the Appendix provides some insight into the trend of instability of East Pass, which can be traced back as far as 1934.




REFERENCES

Aubrey, D. G., and Weishar, L.(eds), 1988. Hydrodynamics and Sediment Dynamics of Tidal Inlets. Lecture Notes on Coastal and Estuarine Studies, Vol. 29, Springer-Verlag, New York.
Ichiye, T., and Jones, M. L., 1961. On the hydrology of the St. Andrews Bay system, Florida. Limnology and Oceanography, 6(3), 302-311.
Jain, M., and Mehta, A. J., 2001. UFL-COEL-2001/O00, Department of Civil and Coastal Engineering, University of Florida, Gainesville, FL.
Jain, M., Paramygin, V. A., and Mehta, A. J., 2002. UFL/COEL-2002/014, Department of Civil and Coastal Engineering, University of Florida, Gainesville, FL.
Jarrett, J. T. Prism-inlet area relationships. G.LT.L Report No. 3, U.S. Army Engineering Coastal Engineering Research Center, Ft. Belvoir, VA.
Keulegan, G. H., 1967. Tidal flow in entrances: water level fluctuations of basins in communication with the seas, Technical Bulletin No. 14, Committee on Tidal Hydraulics, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
Lillycrop, W. J., Rosati, J. D., and McGehee, D. D., 1989. A study of sand waves in the Panama City, Florida, entrance channel. Technical Report CERC-89-7, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
O'Brien, M. P., 1969. Equilibrium flow areas of inlets on sandy coasts. Journal of the Waterways and Harbors Division of ASCE, 95(1), 43-52.
van de Kreeke, J., 1967. Water level fluctuations and flow in tidal inlets. Journal of Waterways and Harbors Division, ASCE, 93 (4), 97-106.
van de Kreeke, J., 1984. Stability of multiple inlets. Proceedings XIX International Conference on Coastal Engineering, Houston. ASCE, New York, 1360-1370.
van de Kreeke, J., 1988. Hydrodynamics of tidal inlets. In: Hydrodynamics and Sediment Dynamics of Tidal Inlets, (Aubrey, D.G. and Weishar, L., eds), Springer-Verlag, New York, 1-23.




APPENDIX: INLET STABILITYANALYSIS

C.1 Introduction
Here we will briefly examine the stability of St Andrews Bay Entrance channel and East Pass. In general, due to the longshore sediment transport due to waves and currents (Aubrey and Weishar, 1988), the cross-section of a sandy inlet keeps changing (van de Kreeke, 1985); sometimes the tidal current becomes so small that it is not able to flush the sediment out of the inlet and the inlet closes.
Due to the complex nature of sediment transportation by waves and current it is difficult to carry out an accurate analysis of the stability of the two-inlet system. We will therefore attempt to do an approximate analysis.
Stability of inlet deals with the equilibrium between inlet cross-section area and inlet hydrodynamics. The pertinent parameters are the actual maximum bottom shear stress rand the equilibrium shear stress 'rq. The equilibrium shear stress is defined as the bottom stress induced by the tidal currents required to flush out sediment carried into the inlet due to longshore currents. When r equals 'rq the inlet is considered to be in equilibrium. When ris larger than Teq the inlet is in the scouring mode. Finally, when r'is smaller 'rq the inlet is in the shoaling mode. C.2 Linearized Lumped-Parameter Model for Two Inlets
For two inlets the dynamics of the flow in the inlets are governed by the longitudinal pressure gradient and the bottom shear stress (van de Kreeke, 1967): S1 p r (C.1)
p ax ph




in which p is the pressure, p is the water density, h is the depth and 'Cis the bottom shear stress. This stress is related to the depth mean velocity u by
-r = pFu I uI (C.2)
where F is the friction coefficient. Assuming hydrostatic pressure and a uniform shear stress distribution along the wetted perimeter of the inlet cross-section accounting for the exit and entrance losses, integration of Eq. C. 1 (with respect to the x-coordinate) between the sea and the bay yields (van de Kreeke, 1988) uiluil= 2g]i (r/o-7b) (C.3)
miRi + 2FLi
In Eq. C.3, ui refers to the cross-sectional mean velocity of the ith inlet, g is the acceleration due to gravity, mi is the sum of exit and entrance losses, Ri is the hydraulic radius of the inlet, Li is the length of the inlet, q/o is the sea tide, and i7b is the bay tide. Current velocity is positive when going from sea to bay.
Assuming the bay surface area to fluctuate uniformly, the continuity can be expressed as
2 d/
uiA =A a (C.4)
dt
in which Ai is the cross-sectional area, Ab is the bay surface area and t is time.
Assuming ui to be a simple harmonic function of t, Eq. C.3 is linearized. This yields
8 2gRi
3-ruu = 2 L (77o -7b) (C.5)
3z' m.R + 2FLi
in which fii is the amplitude of the current velocity in the ith inlet. It follows from Eqs. C.4 and C.5 that for a simple harmonic sea tide




1,(t) = ,oe j'

and assuming Ai and Ab to be constant, Ui= ,e j(a+a) (C.7)
where the phase angle acr is considered to be the same for all inlets. Differentiating Eq. A.5 with respect to t, eliminating di/dt between Eqs. C.4 and C.5, and making use of the expression for ui and i, yields an equation for fii
2iA + -18 AbB, jao= AbAojOe-ja (C.8)
2g 3z
in which the dimensionless resistance factor Bi is defined by
Bi = [ Ri (C.9)
miR, + 2-4L,
where we note that Bi is the function of Ai. Now, equating the real and imaginary parts of Eq. C.8 and eliminating the phase angle a yields the equation []2 []2 [Aba]2 B2a4 [Aj]2r [ i]2(~0
2 i2o 2 /i 2 (C.10)
For equilibrium flow areas i = Ueqi, substituting this value Eq. C. 10 becomes: ]2 []2 Ab]2 Bi2a4 = 2 [ eqiA 2
- qi =[Abto(r]2- jeA(C. 11)
2g 3)ri=1
For equilibrium flow ?. = 'feqi. Using linearized version in Eq. C.5 and Eq. C.2, the equilibrium velocity can be written as ueqi= eqi (C.12)
For the inlets to be in equilibrium the following condition has to be satisfied:3rp
For the inlets to be in equilibrium the following condition has to be satisfied:

(C.6)




Ab,0>
2 3)r

Fl i ^5 5+ ( F2L2 ) ^5q ag g u q a29 g

(C.13)

where the coefficient ai is defined by

Two sets of equilibrium cross-sectional area are obtained by solving the following equation

^ 2 ]2 ]2 2
[eql FF2a +eq2 F 3 (Ab )2 IL 4 =0 eq a eq2 FLa, (3L aig eq

(C.15)

The equilibrium curve for Inlet 1 and Inlet 2 is calculated from Eq. C. 11 and Bi given by following equation

(C.16)

A typical stability curve shown in Fig. C.1 is meant to explain how the analysis
works.
1 When the point defined by the actual cross-sectional areas [A,, A2] is located in
the vertically hatched zone or anywhere outside the curves, (Zone-1), both inlets
close.
2 When the point is located in the crosshatched zone, (Zone-2), Inlet 1 will remain
open and Inlet 2 will close.
3 When the point is located in the diagonally hatched zone, (Zone-3), Inlet 1 will
close and Inlet 2 will remain open.
4 Finally, when the point is located in the blank zone, (Zone-4), one inlet will close
and the other will remain open. However, in this case which one closes depends
on the relative rates of scouring and or/shoaling.

Ri = ai,

(C.14)

B = Li
ai Ai




Zone-4
Inlet I
Zone- 1<- A1
Figure C. 1 Schematic diagram for two-inlet stability regimes.

C.3 Stability Calculation
For the analysis on St Andrews Bay Entrance channel (Inlet 1) and East Pass
(Inlet 2) in year 2002 the parameters in Table C. 1 are selected.
Table C. I Selected parameters for InletI and Inlet 2
Parameter Value Parameter Value
Ab 90 km2 0,, 0.26 m
ai ~ 0.4 m/s5
o"ql04 / 9.7 x10-5 rad s- I
U eq2 0.45 m/s
Li 1340 m L2 840 m
F1 4x10-3 F2 4x10-3
0.138 a2 0.202 (for a triangular
schematization of cross-section)

The inlet stability analysis was also extended to include past cross-sections (Table C.2). All other parameters remain unchanged. Results are displayed in Figs. C.2 through C.5.




Table C.2 Cross-sectional areas of the inlets
Year Area (m )
St Andrews By Entrance East Pass
1934 0 1,835 3,400
1946 3,530 2,146
1983 3,943 1,392
2002 5,210 255
Inlet Stability in 1934
7000 6000
E 5000
C\1
< 4000 *U~*.
,,,z 3000 was.&& ...
0
S2000 ., .: ..
0 1000 2000 3000 4000 5000 6000 7000
St. Andrew Entrance A1 (m2)
. East Pass m St Andrew Entrance

Figure C.2 Inlet stability diagram for 1934.

Figure C.3 Inlet stability diagram for 1946.

Inlet Stability in 1946
7000 6000
E 5000 ,,,.o.....
< 4000
) / Ion ***#*oo
I, W 3000
Lii
1000
0 1000 2000 3000 4000 5000 6000 7000
St Andrew Entrance Al (n2)
. East Pass a St Andrew Entrance




Inlet Stability curve in 1983

Figure C.4 Inlet stability diagram for 1983.
Inlet Stability in 2002

6000
'5000
E
, 4000
3000 Co)
a- 2000
U 1000
0

0 1000

2000 3000 4000
St Andrew Al (m2) St Andrew a East Pass

Figure C.5 Inlet stability diagram for 2002.
In each plot, the symbol 9 denotes the point [A,, A2] based on the actual areas in a given year. Note that in 1934 and 1946 [A1, A2] remained in the "blank" zone relative to Fig. C.A, implying that one of the two inlets would remain open and the other would close. Observe further that, moving in time from 1946 to 1983, [A,, A2] traveled to the zone-2 right and bottom, effectively towards the "cross-hatched" zone of Fig. C. 1. This

6000 5000
E oo *': :::mass 4000 ** 60200,
' 3000 **** mmmmm
2000
LU 1000 E" ol
0 U
0 1000 2000 3000 4000 5000 6000
St. Andrew Entrance Al (m2)
. East Pass x St. Andrew Entrance

5000




locus of [A,, A21 is consistent with the increased stability of St. Andrews Bay Entrance (Inlet 1) and closure of East Pass (Inlet 2) (in 1998). In that regard, the 2002 data from the newly opened small channel suggest a condition that implies that East Pass (in preference to St. Andrew Bay Entrance) may close because [A,, A21 lies in the equilibrium flow curve of St. Andrew Bay Entrance.