January 13, 2004
14:37
WSPC/101-CEJ
00097
523
Analytical Model of Incipient Breaching of Coastal Barriers
1
0.9
0.8
z0, m
0.7
0.1
0.6
0.5
L = 300 m
3
x0 = 10 m
0.4
3
QS = 500 m /day
0.3
3
QB = 1,000 m /day
ze = 5 m; xe = 300 m
0.2
3
Ve = 450,000 m
0.1
0
0
100
200
300
400
500
600
700
800
900
1000
Days after Start of Breach
Fig. 7. Growth of breach volume for fixed initial width and different initial depths corresponding
to Figs. 5 and 6.
Fig. 7. Growth of breach volume for fixed initial width and different initial depths
1
corresponding to Figs. 5 and 6.
0.9
100
0.8
50
0.7
0.6
10
0.5
L = 300 m
1
z0 = 1 m
0.4
3
QS = 500 m /day
x0, m
0.3
3
QB = 1,000 m /day
ze = 300 m, xe = 300 m
0.2
0.1
0
0
100
200
300
400
500
600
700
800
900
1000
Days after Start of Breach
ig. 8. Solution of Eq. (4) for breach width, different values of initial breach width.
Theig. 8.rphouoigin of Ed.e4 por dreashthadth,rdifcerenidthugsowsnftisterreachswidther ini-
F mo Sol l t o c moq l f rebictc wit b ea fh wt val er of i iaal b for mall .
tial depth. Of course, breach depth approaches equilibrium faster for greater initial
depth. Growth of the dimensions of a breach depends directly on the transport rates
QS and QB , and so general conclusions cannot be made. However, if these rates are
23
1
1
0.9
0.8
10
0.7
50
0.6
L = 300 m
.5
0
F
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