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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
UFJCOEL-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 x107 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 1.9x106 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
SUMMARY .............................................. .... ............................. .........
TABLE OF CONTENTS......................................................................... 3
L IST O F FIG U R E S ................. ...................................... .... ...... ............. .5
LIST OF TABLES................................................................ ............7
ACKNOWLEDGMENT....................... ........... ...............................8
SECTION A: ST ANDREWS BAY ENTRANCE.........................................9
A-i INTRODUCTION.......................................................................9
A-2 MEASUREMENTS.....................................................................12
A-2.1 Cross-Sections.......................................................................12
A -2.2 Tide Level....................................................................... ... ..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-i INTRODUCTION......................................................................18
B-2 MEASUREMENTS.............................................................. ....19
B-2.1 Cross-Sections......... ............................. ...... ............... ....19
B -2.2 Tide Level...................... ... ...... ........ .. ..... ........ .............. ..... ...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 COM M ENTS.................................................................22
REFERENCES ......................... ...... .............. ........................ 24
APPENDIX: INLET STABILITY ANALYSIS..........................................25
C.1 Introduction................................... .... ......... ..... ...... ........ 25
C.2 Linearized Lumped-Parameter Model for 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 m apart..........10
Fig. A-1.2 St. Andrews Bay Entrance bathymetry and current measurement cross-
sections 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 cross-
sections A' B' and C' were conducted in December 2001 and are reported by Jain et al.
(2002) .................. ................................... .................................. ... 11
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 ,3 3 0 m 2.......................................................... ..................................... 12
Fig.A-2.2 NOS predicted tide at St. Andrews Bay Entrance on
M arch 27-28, 2002. The datum is M LLW ....................................................... 13
Fig. A-2.3 Cross-sectional mean current variation at cross-section D on
M arch 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 m/s. Depth and width axes
are in meters. Origin of width is point D-1....................................................16
Fig B-1.1 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-2.1 Cross-section F measured by ADCP. Distance is measured from
2
point F-1. The datum is mean tide level. Area = 300 m2...................... ...........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. C.4 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......................
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.
Andrew s Bay Entrance.................................................... ............... ....15
Table A-2.3 Characteristic slack water time at cross-sections D at St. Andrews Bay
Entrance .............. ............... ... .............. ........... ................................... 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.1 Selected parameters for inlet 1 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-1. 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 cross-
sections. 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. Cross-
section 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 30 07.4220 -85 43.3271 410714.20859 1613635.15158
D D-2 3007.6540 -85 43. 5844 412134.85378 1612294.58589
.4.
Fig A-1.1 St. Andrews Bay Entrance, Florida in 1993. Jetties are -430 m apart.
10
L.
t\
D-2 '
412000.00 -
-45.0
411000.00
S5.' -.o
C'-1
1610000410000.00 1611000.00 1612000.00 161300000 1614000.00 161500
Fig. A-1.2 St. Andrews Bay Entrance bathymetry and current measurement cross-
sections 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 cross-
sections A' B' and C' were conducted in December 2001 and are reported by Jain et al.
40(2002).
-5.00 8
1610000.00 1611000.00 1612000.00 1613000.00 1614000.00 1615000.00
Fig. A-1.2 St. Andrews Bay Entrance bathymetry and current measurement cross-
sections 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 cross-
sections 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
-5 C\ M LO CD
-15
-20
Distance (m) from D-1
ADCP +- Contours
Fig A-2.1 Cross-section D measured and compared with 2000 bathymetry. Distance is
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
co LOco
C66 1U) C C*0*
0/c27
03/127/02
(0 0 (0 LO cmJ OD co (0
0 N. LO co) LO LO
Tine (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
N
C1
-- 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
C/ 0.100
S0.000
S-0.100 U ) S o O 0O
S-0.200 c i 6 0 C 0 )
> -0.300 40 r 6 c 6 0 0 C5 6j
-0.400
-0.500
-0.600
Time(hrs)
--Velocity Profile
CD
c'.J:
Lfl c'
Discharge Profile
3000
:- 2000 -
E 1000
a)
o -1000 uuui4 65 "o0 co o oo 0 )N- r-
0) 0
0 -. \- 0- 0 66 0 CO 0\ UO C-
H -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 Cross-section D
Value 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.
0t ... ,1
5, 800
10 600
5500
4800
15 \ 300
170
S200
100
20 0
Fig. A-2.5 Flood velocity structure at cross-section D on March 28, 2002 at 10:49.
Vertical axis represents current speed in m/s. Depth and width axes are in meters. Origin
of width is point D-2.
A-3. TIDAL PRISM
A-3.1 Calculation of Tidal Prism
In general, tidal prism over flood (which is the characteristic prism per definition)
or ebb is obtained by integrating the discharge curve, from slack to slack, for flood or ebb
flow, respectively. When a complete discharge curve for that purpose is not available, the
following formula yields an approximate value of the prism, P:
QmT
P= (A-3.1)
trCK
where Qm 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 A-
3.1.
Table A-3.1 Tidal prism values for St. Andrews Bay Entrance
Tidal stage Tidal prism
(m3)
Flood 8.6x 10
Ebb 9.4x107
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 = a Pb (A-3.2)
For inlets with two jetties, a = 7.49x104 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-1. 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-1.1 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-1.2. The coordinates of end-points F-1 and F-2 are given in Table B-1.1.
Fig B-1.1 East Pass channel in 1997.
Table B-1.1 Location of channel cross-section at East Pass
Section End Latitude Longitude Northing Easting
F F-1 30 03.7839 -85 37 0715 388325.55736 1646376.03172
F F-2 30037910 -85 37 1233 388371.26716 1646103.35534
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.
N
4F-I
S.- E-2
SEast Pass
.. mouth
i"
'N
Fig B-2.1 Cross-section F measured by ADCP. Distance is measured from point F-1. The
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. B-
2.2. The corresponding discharge variation is given in Fig. B-2.3.
Bottom Contour
F-1 F-2
0
-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 F'1
-- ADCP
Velocity Profile
Fig. B-2.2 Cross-sectional mean current variation at F on March 27, 2002.
Total Discharge(m3/s)
150.00 -
-100.00
E 50.00-
0 0.00
-50.00
o -100.00
-150.00 -
N CN UM W- Cl U0 Ln "t!-
- 0 co 0 0 0 .- i6 .r ) C .. LO n C -. ~
Time(hrs)
-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
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-
En
.nno
-0.400 t "o ,- e o - to -
-0.600
- velocity(m/s)l
1
i~
rl-",
rjxo
rl
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. B-
2.3, 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 3.9x106
Ebb 3.5x106
B-3.2 Comparison with O'Brien Relationship
Relative to Eq. A-3.1, for inlets with no jetty, a = 1.58x10-4 and b = 0.95 (Jarrett,
1976). Now, considering cross-section F to represent the throat section, Ac = 255 m2 at
mean tide level. Thus, from Eq. A-3.2 we obtain P = 3.6x106 m3.
CONCLUDING COMMENTS
From the collected data the following values are obtained. At St. Andrews Bay
Entrance, the measurements indicate: tidal prism 4.2x107 m3, cross-section (at mean tide)
6,330 m2 and peak flood (cross-sectional mean) velocity 0.42 m/s. The corresponding
values for East Pass are: (flood) tidal prism 1.9x106 m3, cross-section 255 m 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
(m3)
Flow Cross- Cross- Cross- Cross- Cross- Cross-
stage 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 4.2x107
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-2001/000, 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.I.T.I. 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 ofASCE, 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 Tq. 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 Trq the inlet is considered to be in
equilibrium. When ris larger than Teq the inlet is in the scouring mode. Finally, when ris
smaller eq 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):
O=- p (C.1)
p ax ph
in which p is the pressure, p is the water density, h is the depth and r is 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)
Ui IUi = Ri (r -r) (C.3)
m, R, + 2F L,
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, 77 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
UAui = Ab (C.4)
i=l 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
-Uu. = ('iR ib) (C.5)
3t '' m,R, + 2FL,
in which ii 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
(C.6)
and assuming Ai and Ab to be constant,
Ui = Uiej(a+a) (C.7)
where the phase angle a is considered to be the same for all inlets. Differentiating Eq.
A.5 with respect to t, eliminating dirbldt between Eqs. C.4 and C.5, and making use of the
expression for ui and 7o yields an equation for fii
2iAi +1 8 AB 2oja= oiae-ja (C.8)
;i= 2g 37r
in which the dimensionless resistance factor Bi is defined by
B,= mR, (C.9)
mR, + 2F L,
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 B2a =[ o 2 i[ 2 (C.10)
For equilibrium flow areas u, = Ueq,, substituting this value Eq. C.10 becomes:
]2 [ 8 [ ]2 A ]2- eqiA (C.11)
2g."8 3 )r3 '- i=1
For equilibrium flow fi = ,eqi. Using linearized version in Eq. C.5 and Eq. C.2, the
equilibrium velocity can be written as
U q8/3e (C.12)
For the inlets to be in equilibrium the following condition has to be satisfied:
For the inlets to be in equilibrium the following condition has to be satisfied:
rl (t) = 0oe"'
,c 3 ( 8 3 2
^2'3W
1'Ueq( 2 eq
a, g ae g g
(C.13)
(C.14)
where the coefficient ai is defined by
R, = aj
Two sets of equilibrium cross-sectional area are obtained by solving the following
equation
LL 2 ]_ 2_ ] 3 2 [)r 2
[a F24aj A.3 (4a`a2 A+ 8 (b) 2 i ] r,
"eql 'a "eq2 FjLa i -) ( ) a,g eq=0
(C.15)
The equilibrium curve for Inlet 1 and Inlet 2 is calculated from Eq. C. 11 and Bi given by
following equation
Fj Li
aiB
*~^4
(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 [A1, 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.
F1 S emac d am fr t t s y rimlet s
Zone-l<-- 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. 1 Selected parameters for Inletl and Inlet 2
Parameter Value Parameter Value
Ab 90 km2 70 0.26 m
iieqi 0.4 m/s
ea 9.7x10-5 rad s
i eq2 0.45 m/s
Li 1340 m L2 840 m
F1 4x10-3 F2 4x10-3
8 a2 0.202 (for a triangular
as 0.138 across-section)
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 (mz)
St Andrews By Entrance East Pass
1934 1,835 3,400
1946 3,530 2,146
1983 3,943 1,392
2002 5,210 255
Inlet Stability in 1934
7000
6000 **
S 5000 m-.r*i,.
5 4000 n "'
3000 nMa
C 2000
1000
0
0 1000 2000 3000 4000 5000 6000 7000
St. Andrew Entrance Al (r2)
SEast 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 ***
5000 n;
< 4000
O 3000
I 2000 s
1000
0
0 1000 2000 3000 4000 5000 6000 7000
St Andrew Entrance Al (n2)
* East Pass a St Andrew Entrance
6000
5000 among
5000 "
4000 ***..E ::-"mmm
& 3000 **."" ,m
2000 "ON
S1000 *, O.
0 o-n,
0 1000 2000 3000 4000 5000 6000
St. Andrew Entrance Al (m2)
East Pass St. Andrew Entrance
Figure C.4 Inlet stability diagram for 1983.
Inlet Stability in 2002
6000
c. 5000 mil:,,
E ME
4000 *m..*..
a .. ***u ;... .
u, 3000 ws2 20.
S3 Moons**-.
| St Andrew A East Pa
0L 2000 13
31000 a
0 1000 2000 3000 4000 5000 6000
St Andrew Al (m2)
St Andrew East Pass
Figure C.5 Inlet stability diagram for 2002.
In each plot, the symbol denotes the point [A,, A2] based on the actual areas in a
given year. Note that in 1934 and 1946 [A,, A2] remained in the "blank" zone relative to
Fig. C.1, 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, [Ai, A2] traveled to the
zone-2 right and bottom, effectively towards the "cross-hatched" zone of Fig. C.1. This
Inlet Stability curve in 1983
locus of [A1, A2] 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 [A1, A2] lies in the
equilibrium flow curve of St. Andrew Bay Entrance.
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