EXAMPLE PROBLEM II-4-2

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 *H*b = γb db), thus

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

&

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

&

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

&

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

&

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

&

334

3.3

-0.14

167

1.7

0.21

0

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).

II-4-16

Surf Zone Hydrodynamics

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