subsides, the cross-barrier flow rate decreases, and longshore sediment transport
can partially or completely fill the breach. Kraus (1998) presents a
mathematical model for calculating inlet (or breach) cross-sectional area about
equilibrium in response to changes in discharge through the opening and
longshore sediment transport.
This paper describes a numerical model of incipient breaching of an alluvial
coastal barrier. The numerical model extends the analytical morphologic
models of Kraus (1998, 2003) by coupling a sediment transport equation driven
by one-dimensional (1-D) inlet flow equations to calculate breach growth under
an assumed rectangular geometry. The morphologic model is first reviewed and
then extended to include forcing by tidal hydrodynamics, longshore sediment
transport, and possibility of multiple breaches and inlets. The numerical model
is tested by comparison to published physical model data and to data from the
1980 breach adjacent to Moriches Inlet, Long Island, New York.
Review of Analytical Breaching Model
The model proceeds from the continuity equation expressed for an assumed
rectangular breach cross-sectional geometry. Because of the assumption of a
specified geometry, the model is termed a "morphologic model." In the original
model (Kraus 2003), the simple form of a rectangular barrier island was
specified, as depicted in Fig. 1. The rectangular barrier island has cross-shore
width L, and the breach has width x and depth z measured from the crest of the
barrier. A net transport rate at the bottom QB in short period of time ∆t erodes
a bottom layer of uniform thickness ∆z , and a transport rate QS on each side
erodes each side as a layer of uniform thickness ∆x .
For such a rectangular barrier island and rectangular breach, the continuity
equation for sediment volume on one side and on the bottom yields,
x0 > 0 ,
z0 > 0 ,
in which x0 and z0 are the initial width and depth of the region in the barrier
island where the breach forms. Eqs. (1) and (2) are two coupled first-order non-
linear differential equations governing breach width and depth, respectively.