Escoffier (1940) analyzed closure conditions for a tidal inlet channel by
comparing possible cross-sectional areas of the inlet with those predicted by a
stability criterion such as given in Equation 6-2. As noted by Seabergh (2003),
equilibrium cross-sectional area predicted through an Escoffier analysis implies
that the amplitude of the water-surface elevation in the bay is close or equal to
the amplitude in the tidal body connected to the inlet.
Kraus (1998) derived the form of Equation 6-2 through a process-based
model that accounts for the dynamic balance between ebb-tidal sediment
transport and the longshore sediment transport produced by waves. The power of
n in Equation 6-2 was found to be 0.9, in agreement with values listed in
Table 6-2, and the coefficient C was determined to be of the form:
⎛ α π3nM WE4 / 3 ⎞
= nondimensional coefficient with value of order unity entering the inlet
sediment transport formula employed
= Manning's roughness coefficient squared, sec2/m2/3
Qg = annually gross longshore transport rate, cu m/year (converted to
T = dominant tidal period, which is 44,712 sec for a semidiurnal tide
Equation 6-4 does not explicitly account for a threshold of motion for
transport by the ebb-tidal current or by the longshore sediment transport rate. A
threshold could be significant for gravel and cobble beaches, both for transport
by the tidal current in the inlet and by waves at and adjacent to the inlet.
Equation 6-4 indicates that the value of C will increase if the gross longshore
transport rate decreases, all other factors being equal, giving a larger value of the
cross-sectional area AC in Equation 6-2 for the same tidal prism P.
Jarrett (1976) compiled information on the ratios of inlet width, W to depth,
D for the 108 inlets he studied. He found that inlets with smaller W/D ratios
(<100) tend to be hydraulically more efficient. This result is reasonable, because
small W/D values indicate relatively greater depth, hence weaker bottom friction.
A more hydraulically efficient channel implies a larger channel cross section for
the same tidal prism. The average W/D ratio for all the inlets studied by Jarrett
(1976) was 337, and the average W/D ratio for the 16 Atlantic coast dual-jettied
inlets was 67.
Byrne et al. (1980) compiled information on W/D for their 14 studied inlets
located in Chesapeake Bay and obtained an average W/D = 23. They conclude
that the cross section of smaller channels must, therefore, become more efficient
than that of larger channels to maintain stability. The observed departure in W/D
characteristics between large and small inlets occurs between approximately AC =
100 sq m to 500 sq m (1,076 sq ft to 5,082 sq ft).
Chapter 6 Inlet Morphology and Stability