1 *dS*xx

(II-4-20)

'&

ρ*gd dx*

where *S*xx is the cross-shore component of the cross-shore directed radiation stress, for longshore homoge-

neous waves and bathymetry (see Equations II-4-34 through II-4-36 for general equations). Radiation stress

both raises and lowers (*setdown*) the mean water level across shore in the nearshore region (Figure II-4-7).

waves from the integration of Equation II-4-20 as

2π

1

η'&

(II-4-21)

8

4π

sinh

assuming linear wave theory, normally incident waves, and & = 0 in deep water. The maximum lowering of

the water level, setdown, occurs near the break point &b.

assuming linear theory (Sxx = 3/16 ρ g H2), is given by

3

1

(II-4-22)

'&

16 *h *% η * dx*

of & depends on wave decay through the surf zone. Applying the saturated breaker assumption of linear wave

where the shallow-water value of *S*xx = 3/16 ρ g d H2 has been substituted into Equation II-4-20. The value

height decay on a plane beach, Equation II-4-22 reduces to

1

tanβ

(II-4-23)

'

8

1%

2

3 γb

Combining Equations II-4-21 and II-4-23, setup at the still-water shoreline &s is given by

Surf Zone Hydrodynamics

II-4-13

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