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

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,

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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