reduce the cross-sectional area, the inlet flow will scour out any depositions that reduce the channel cross

section below its equilibrium value. This concept was first developed analytically by Escoffier (1940, 1977).

He proposed a diagram for inlet stability analysis in which two curves are initially plotted. The first is the

velocity versus the inlet's cross-sectional flow area *A*c. A single hydraulic stability curve represents changing

inlet conditions when ocean tide parameters and bay and inlet plan geometry remain relatively fixed. As area

approaches zero, velocity approaches zero due to increasing frictional forces, which are inversely proportional

to channel area. As channel area increases, friction forces are reduced but, on the far right side of the curve,

velocities decrease as the tidal prism has reached a maximum, and any area increases just decrease velocity

as determined by the continuity equation. This curve can be constructed by calculating velocity *V*m by

varying channel area *A*c. *V*m can be determined by an analytical or numerical model, remembering that, if

using Keulegan or King models, an average maximum velocity is determined. The continuity equation *V*avg

plotted as VE is a stability criterion curve such as O'Brien and Jarrett's tidal prism versus cross-section area

relationship. Escoffier (1940) originally proposed a constant critical velocity (e.g., 1 m/sec, which would plot

as a straight horizontal line. If a *P *versus *A*c relationship is used, the appropriate equation (Table II-6-3) can

be used to relate *V*m to tidal prism. The two curves are shown in Figure II-6-42. The possibilities of

intersection of the two curves could possibly intersect at two locations or one location (a tangent), or there

could be no intersection at all. In the first case, point b (see Figure II-6-42) is a stable root in that any

deviation in area returns movement along the stability curve to its starting point. If channel area increases

(move right on curve from point b) velocity will fall and more sediment can fill in the channel to bring it back

to "equilibrium." If area decreases, velocity will increase scouring back to the equilibrium point. Point c is

an unstable root, where if the area decreases, velocities decrease until the inlet closes. Moving to the right

of point c, as velocity increases, area increases until the velocity starts falling and the stable root at point b

is reached. If the stability curve falls tangent to or below the stability criterion curve, the inlet will close.

Thus, if the inlet area is to the right of the unstable equilibrium point, and a storm occurs that provides a large

sediment input to the inlet region, the inlet area could shift to the left of that point, and the inlet would close.

van de Kreeke (1992) presents useful commentary on application of Escoffier's analysis where he notes that

separation of stable and unstable inlets is not determined by the maximum in the maximum velocity curve

(sometimes called the closure curve) of Figure II-6-42, but point c of that curve. Van de Kreeke emphasizes

the integral use of O'Brien-type stability correlations with Esscofier's curve, rather than the use of stability

equations alone.

(2) Escoffier (1977) presented work similar to the above, except the Keulegan *K *value was determined

for the abscissa of the plot in place of the area. For a given set of parameters for a particular inlet, *A*c is varied

and *K *is determined to define the *V*m curve. Note: If King's curves are used, *K *is related to *K*1 and *K*2 by

Equation II-6-11. Figure II-6-43 shows an example diagram. The VE curve then is determined by selecting

an appropriate tidal-prism versus-area relationship and by determining *V*max for various *A *values .

(3) A technique by O'Brien and Dean (1972) has also been used to calculate the stability of an inlet

affected by deposition. The stability index is defined to represent the capacity of an inlet to resist closure

under conditions of deposition. It incorporates a buffer storage area available in the inlet cross section, prior

to deposition and includes the capability of the inlet to transport excess sand from its throat.

m

(*V*max&*V*T)3 dAc

β'

(II-6-33)

II-6-50

Hydrodynamics of Tidal Inlets

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