EXAMPLE PROBLEM II-4-1

EM 1110-2-1100 (Part II)

31 July 2003

FIND:

Wave height and water depth at incipient breaking.

GIVEN:

A beach with a 1 on 100 slope, deepwater wave height Ho = 2 m, and period T = 10 sec. Assume

that a refraction analysis (Part II-3) gives a refraction coefficient KR = 1.05 at the point where

breaking is expected to occur.

SOLUTION:

The equivalent unrefracted deepwater wave height Ho& can be found from the refraction

coefficient (see Part II-3, Equation II-3-14)

Ho& = KR Ho = 1.05 (2.0) = 2.1 m

and the deepwater wavelength Lo is given by (Part II-1)

Lo = g T 2/(2π) = 9.81 (102)/(2π) = 156 m

Estimate the breaker height from Equation II-4-8

Ωb = 0.56 (Ho&/Lo)-1/5 = 0.56 (2.1/156.)-1/5 = 1.3

Hb (estimated) = Ωb H0& = 2.7 m

From Equations II-4-6 and II-4-7, determine a and b used in Equation II-4-5, tan β = 1/100

a = 43.8(1 - e-19 (1/100)) = 7.58

b = 1.56 / (1 + e-19.5 (1/100)) = 0.86

γb = b - a Hb / (gT 2) = 0.86 - 7.58 (2.7)/(9.81 102) = 0.84

db = Hb / γb = 2.7/0.84 = 3.2 m

Breaker height is approximately 2.7 m and breaker depth is 3.2 m. The initial value selected for the

refraction coefficient would now be checked to determine if it is correct for the actual breaker

location. If necessary, a corrected refraction coefficient should be used to recompute breaker height

and depth.

(2) Energy flux method.

(a) A more general method for predicting wave height through the surf zone for a long, straight coast

is to solve the steady-state energy balance equation

d (E Cg )

' &δ

(II-4-13)

dx

II-4-6

Surf Zone Hydrodynamics