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INLET STABILITY AND ESCOFFIER CURVES

Dredging modifications to tidal inlets need to consider basic inlet stability issues to avoid developing an inlet design that could result in an inlet that requires frequent maintenance dredging. In a worst case scenario, a naturally stable inlet could be altered by dredging to yield an inlet that is unstable. The unstable inlet could require frequent dredging or could cause severe erosion in the area. The following note discusses inlet stability related to required velocities necessary to maintain a stable inlet.

The hydraulic stability of an inlet was first discussed in a classic paper of Escoffier (1940) where a physical rationale was provided for determining whether an existing inlet was more likely to stay open or close depending on its position on the "Escoffier" curve (a hydraulic relationship between the inlet cross sectional area and the velocity in the inlet channel).

Escoffier(1940) recognized how inlets behaved from a stability standpoint using the hydraulic relationship between the cross sectional area of an inlet (plotted on the ordinate axis) and the time maximum (spatially averaged across the cross section) velocity during the tidal cycle (plotted along the abscissa axis). An example of an Escoffier curve is given in Figure 1. In this characteristic plot, Escoffier(1940) noted that on the left side of the curve (i.e. left of the maximum velocity), as inlet cross sectional area gets smaller, the velocity also gets smaller, thus decreasing the ability of the inlet to flush itself of sediment and leading to eventual closure of the inlet. Conversely, Escoffier noted that on the right side of the "Escoffier" curve, as the inlet area gets smaller, the maximum inlet velocity increases allowing increased flushing of sediments from the inlet channel thus tending to improve the stability situation from a hydraulic standpoint (at least until the maxima of the velocity on the Escoffier curve is reached).

Others (O'Brien and Dean(1972) and Van de Kreeke(1992)) have shown that Escoffier's postulated curve coupled with an independent inlet sediment-velocity equilibrium type relationship or an "equilibrium" inlet cross section area with tidal prism relationship (i.e. see O'Brien (1931, 1966)), can provide additional quantitative and qualitative information on the stability or instability of a proposed inlet. Often (see for example Van de Kreeke(1992)) the equilibrium velocity in an inlet is assumed equal to 1 (m/sec).

The subject of inlet stability in general and the Escoffier curve in particular is discussed in both the Shore Protection Manual(1984) and the Coastal Engineering Manual(2002) as well as many other publications, where the hydraulics of the inlet is characterized by its width, depth, length of connecting channel between ocean and bay, bay surface area, ocean tide amplitude, tidal period, and frictional characteristics (friction coefficient and entrance/exit losses).

Various analytical approaches that can be utilized in establishing an Escoffier curve are contained within the coastal engineering literature. Numerous analytical models (Chapman (1923), Brown (1928), Keulegan(1967), Ozsoy(1978), Escoffier and Walton(1979), Walton and Escoffier(1981)) have addressed simplified inlet-bay system mass and momentum equations which when coupled with assumptions on inlet cross section geometry can be utilized to construct the Escoffier curve. Simple approaches (i.e. Brown(1928)) have assumed a sinusoidal ocean tide and linearized the momentum equation either explicitly or implicitly. More detailed solutions to the non-linear inlet-bay system problem (i.e. Keulegan (1967)) can also be utilized to construct an Escoffier curve, but still consider only elementary types of ocean forcing functions rather than a realistic suite of astronomical harmonic forcing functions. An analytical non-linear solution approach that can be used to construct the Escoffier curve for a two harmonic forcing tide is provided by DiLorenzo(1988) who also assumed constant connecting channel cross sectional area, bay surface area, channel length, channel depth, and friction coefficient. As noted above, DiLorenzo's(1988) solution provides for an ocean tide consisting of a primary sinusoidal component and its damped and lagged second harmonic overtide. A requirement of the ocean/bay system for all of the above methods is that the bay be sufficiently deep such that the tidal wave propagates across the bay instantaneously (i.e. see Keulegan (1967)). Although this requirement may not always be met in practice, the tide in many bays propagates sufficiently fast to make this assumption useful from an engineering standpoint. The fluctuating water level response in the bay (i.e. the bay tide) and the inlet velocity are the unknowns that are solved for in the above approaches via the governing mass and momentum equations.

For more complex tidal situations when the ocean tides consist of a sum of ocean sinusoidal components (with frequencies that are not harmonics of the primary frequency), numerical inlet-bay models (i.e. Van de Kreeke(1967), Seelig et al.(1977)) must be utilized to provide realistic Escoffier curves.

Two inlet geometry scenarios are provided here to show differences that can occur depending on the geometric characteristics of the inlet.

Figure 1 shows an Escoffier curve where the inlet width has been assumed constant (width = 300(m), and Figure 2 shows an Escoffier curve where the inlet width divided by the inlet depth is held constant (i.e. width/depth = 30).

Other parameter values used in the present comparison are as follows:
ocean tide amplitude = 0.5 (m);
inlet length = 1500 (m);
tidal period = 12.4 (hours);
bay surface area = 35,000,000(meters squared); and
Darcy-Weisbach friction coefficient = 0.16 (dimensionless).
Additionally, for simplicity, channel entrance and exit loss coefficients as described in Keulegan(1967)) are assumed zero. The above parameters were chosen as representative of a real inlet as determined from the range of data contained in O'Brien and Clark(1973).

Assuming an equilibrium velocity of 1 (m/sec) the Escoffier curve constructed using the Keulegan(1967) method with the assumption of constant width (see Figure 1) shows a stable cross sectional area of 2020(meters squared).

Assuming an equilibrium velocity of 1(m/sec) the Escoffier curve constructed using the Keulegan(1967) method with the assumption of constant width divided by depth (width/depth = 30) (see Figure 2) shows that a stable cross sectional area is not feasible as the tidal cycle maximum velocity every where on the Escoffier curve is below 1 (m/sec).

Should you have any questions concerning tidal inlet stability for your specific project needs call: Todd Walton, Ph.D., P.E. (850-644-2847).

REFERENCES:

Brown, E.I. 1928. "Inlets on Sandy Coasts," Proc. Amer. Society of Civil Engineers, LIV, 505-553.

Chapman, S. 1923. "A Note on the Fluctuation of Water Level in a Tidal Power Reservoir," Phil. Mag. and Jour. of Science, XLVI, 101-108.

DiLorenzo, J.L. 1988. "The Overtide and Filtering Response of Small Inlet-Bay Systems,"Hydrodynamics and Sediment Dynamics of Tidal Inlets", ed. D.G. Aubrey and L. Weishar, 24-53, Springer-Verlag Publishing, New York, N.Y.

Escoffier, F.F. 1940. "The Stability of Tidal Inlets," Shore and Beach, Vol. 8, No. 4, 114-115.

Escoffier, F.F. 1977. Hydraulics and Stability of Tidal Inlets, GITI Report No. 13, U.S. Army Corps of Engineers, Coastal Engineering Research Center, Ft. Belvoir, VA.

Escoffier, F.F. and Walton, T.L. Jr. 1979. "Inlet Stability Solutions for Tributary Inflow," Jour. Waterways and Harbors Division, WW4, 105, ASCE, 341-355.

Keulegan, G.H. 1967. Tidal Flow in Entrances: Water Level Fluctuations of Basins in Communication with the Seas, Committee on Tidal Hydraulics Technical Bulletin No.14, U.S. Army Engineers Waterways Experiment Station, Vicksburg, MS.

Lorentz, H.A. 1926. Report of the Government Zuiderzee Commission, The Hague, Netherlands.

O’Brien, M.P. 1931. "Estuary Tidal Prisms Related to Entrance Areas," Civil Engineering, 738-739.

O'Brien,M.P. 1966. "Equilibrium Flow Areas of Tidal Inlets on Sandy Coasts", Proceedings of the 10th Coastal Engineering Conference, Vol.1, 676-686.

O'Brien,M.P. and Dean,R.G. 1972. "Hydraulics and Sedimentary Stability of Coastal Inlets", Proceedings of the 13th Coastal Engineering Conference, ASCE, 761-780.

O'Brien,M.P. and Clark,R.R. 1973. Hydraulic Constants of Tidal Entrances I: Data from NOS Tide Tables, Current Tables, and Navigation Charts, UFL/COEL/TR-021, Coastal and Oceanographic Engineering Laboratory, University of Florida, Gainesville,FL.

Ozsoy,E. 1978. "notes published in Stability of Tidal Inlets by P.Bruun", Elsevier Science Publishing, New York, N.Y.

Seelig, W.N., Harris, D.L., and Herchenroder, B.E. 1977. "A Spatially Integrated Numerical Model of Inlet Hydraulics," GITI Report No. 14, U.S. Army Coastal Engineering Research Center, Fort Belvoir, VA.

U.S. Army Corps of Engineers 1984. Shore Protection Manual, Coastal Engineering Research Center, Ft. Belvoir, VA.

U.S.Army Corps of Engineers 2002. Coastal Engineering Manual, Engineering Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.

Van de Kreeke, J. 1967. "Water Level Fluctuations and Flow in Tidal Inlets," Jour. Waterways Harbors Division, WW4, ASCE, 97-106.

Van de Kreeke, J. 1992. "Stability of Tidal Inlets; Escoffier’s Analysis," Shore and Beach, Vol.60, No.l, 9-12.

Walton,T.L. Jr. and Escoffier, F.F. 1981. "Linearized Solution to the Inlet Equation with Inertia," Jour. Waterways and Harbors Division, WW3, ASCE, 191-195. BR>




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