January 13, 2004
14:37
WSPC/101CEJ
00097
518
N. C. Kraus
developed under the assumptions that: (a) sediment (sand) volume is conserved;
(b) the initial condition is known, (c) sediment transport can occur at the bottom
of the breach and at its sides; (d) the breach will approach equilibrium if external
forces do not intervene; and (e) longshore sediment transport is weak or can be
neglected. Assumptions (b) to (e) can be relaxed in extension of the present analytic
model or in a numerical model. Assumption (e), weak longshore transport relative to
the breaching process, limits this model to describing incipient breaching. Tanaka,
Takahashi, and Takahashi (1996) and Kraus (1998) present analytical models of
river mouth and inlet crosssectional areas formed under a balance of tidal action
that includes river discharge and longshore transport under waves. Those analytical
models that relate to the equilibrium condition of an inlet or river mouth would be
a next logical stage of the present model development.
Under the stated assumptions and by reference to Fig. 4, conservation of mass
yields the following equations,
^
Lz∆x = QS ∆t
(1)
for breach width, and,
^
Lx∆z = QB ∆t
(2)
for breach depth, where L is length of the breach through the coastal barrier, z and
^
^
x are depth and width of the breach, respectively, t is time, and QS and QB are
net transport rates along the sides (assumed to be equal on each side) and bottom
^
^
of the breach, respectively. In general, the sediment transport rates QS and QB are
functions of the acting hydrodynamic forces and breach configuration.
To proceed with an analytic solution, transport by surge, or by flood or ebb tide is
not distinguished in forming the net transport rate in a morphologic representation,
and the following functional relations are taken:
1
,
1
(
x
z
^
^
QS = QS
QB = QB
3)


xe
ze
where QS and QB are constant maximum transport rates that are not necessarily
equal, and xe and ze are values of the breach width and depth, respectively, if the
breach achieved equilibrium. The morphologic parameterization of the transport
rates by Eq. (3) makes them time dependent, with the net transport rates going
to zero as equilibrium is approached. The equilibrium values xe and ze could be
specified in at least three ways, as through: (1) experience with previous breaches
at or near the study site, (2) specification via an empirical formula such as given
by Mehta (1976), Graham and Mehta (1981), and Shigemura (1981), or (3) through
operation of a hydrodynamic model, by which the critical shear stress or similar
diagnostic quantity indicating cessation of transport can be calculated. The mor
phologic approach as taken in forming Eq. (3) is discussed by Kraus (2001) as a