Review of Analytical Breaching Model

Kraus_HayashiBreachingModel
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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,

respectively,

x0 > 0 ,

(1)

and

z0 > 0 ,

(2)

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.