EXAMPLE PROBLEM II-4-2

Part-II-Chap4
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EM 1110-2-1100 (Part II)

31 July 2003

FIND:

Setup across the surf zone.

GIVEN:

A plane beach having a 1 on 100 slope, and normally incident waves with deepwater height of 2 m and

period of 10 sec (see Example Problem II-4-1).

SOLUTION:

The incipient breaker height and depth were determined in Example Problem II-4-1 as 2.7 m and 3.2 m,

respectively. The breaker index is 0.84, based on Equation II-4-5.

&b = - 1/16 γb2 db, (sinh 2πd/L . 2πd/L, and Hb = γb db), thus

Setdown at the breaker point is determined from Equation II-4-21. At breaking, Equation II-4-21 simplifies to

η b = -1/16 (0.84)2 (3.2) = - 0.14 m

Setup at the still-water shoreline is determined from Equation II-4-24

η s = -0.14 + (3.2 + 0.14) + 1/(1 + 8/(3 (.84)2)) = 0.56 m

The gradient in the setup is determined from Equation II-4-23 as

dη /dx = 1/(1 + 8/(3 (0.84)2))(1/100) = 0.0021

and from Equation II-4-25, ∆x = (0.56)/(1/100 - 0.0021) = 70.9 m, and

&max = 0.56 + 0.0021(64.6) = 0.65 m

For the simplified case of a plane beach with the assumption of linear wave height decay, the gradient in the

= η b + (d&/dx)(xb - x), where xb is the surf zone width and x = 0 at the shoreline (x is positive offshore).

setup is constant through the surf zone. Setup may be calculated anywhere in the surf zone from the relation η

x, m

h, m

η,m

334

3.3

-0.14

167

1.7

0.21

0.0

0.56

-71

-0.7

0.71

Setdown at breaking is - 0.14 m, net setup at the still-water shoreline is 0.56 m, the gradient in the setup is

0.0021 m/m, the mean shoreline is located 71 m shoreward of the still-water shoreline, and maximum setup is

0.71 m (Figure II-4-10).

Figure II-4-10. Example problem II-4-2

II-4-16

Surf Zone Hydrodynamics