January 13, 2004
14:37
WSPC/101-CEJ
00097
521
Analytical Model of Incipient Breaching of Coastal Barriers
indicates that breach growth is controlled by seven parameters: x0, z0, xe, ze, QS ,
QB , and L. Equations (11)(17) reveal morphologic functional dependencies that
is a characteristic morphologic time scale governing growth toward equilibrium for
a given maximum net transport rate of sediment removed from the breach. The
dimensions of the initial perturbation or pilot channel of the barrier island exert
great control on the time development of the breach and whether it will tend to
widen more than deepen at a greater rate, or vice versa, prior to approaching equi-
librium width and depth. Such properties of the solution are explored in the next
section.
Equations (11) and (12) indicate an exponential growth of a breach toward equi-
librium, giving a more rapid growth initially, followed by gradual increase in depth
and width to equilibrium. The time behavior of the morphologic model qualitatively
describes the growth of breaches observed in nature and in the laboratory, whether
induced by storm surge or by a difference in water level on the sides of the barrier
island.
The volume of the breach is V = xzL, with x and z given by numerical solution
of Eqs. (4) and (5), respectively, for a general situation, or by Eqs. (11) and (12) for
the special case QS = QB . The depth of the breach is measured from the top of the
barrier island in the morphologic breach model. For stable inlets, empirical formulas
are available for estimating channel cross-sectional area (e.g. Jarrett (1976) for large
tidal inlets; Byrne, Gammish, and Thomas (1980) for small tidal inlets). The depth
corresponding to this channel cross-sectional area is measured from mean sea level
to the bottom of the breach and not from the top of barrier island. Therefore, in
applications of predictive expressions for equilibrium breach area xeze, one must
account for the distance from the top of the barrier island to the elevation of mean
sea level.
3.3. Sensitivity tests of morphologic breach model
Equations (4) and (5) were solved numerically for general cases, after first confirming
the numerical solution with the analytical solution given by Eqs. (11) and (12).
Figures 57 plot calculations for QS = 500 m3/day, QB = 1, 000 m3/day, L = 300 m,
and equilibrium width xe = 300 m, and equilibrium depth ze = 5 m. These values are
considered representative of the many small breaches along the Texas and Louisiana
coasts, as determined in the literature review. Note that if the crest of the barrier
island lies, for example, 3 m above mean sea level, then the depth of the breach below
mean sea level is 2 meters. For these calculations, the width of the pilot channel or
low section in the barrier was specified as x0 = 10 m, correspondingly, say, to
walkway or blowout through the dunes, and results were plotted for initial depths
z0 = 0.1, 1, 2, and 3 m. Plots are normalized by the corresponding equilibrium value.
Volume of the breach is predicted to be relatively insensitive to initial breach depth
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