equation gives the following equation to solve with the water depth at breaking as the

unknown,

5/ 2

2

*h*b

cos arcsin 2π sin θo

=

(9)

2

*L*o

height to water depth at incipient breaking (taken to be 0.78). This equation shows that

employed to quickly obtain *h*b from known input wave properties. Once *h*b is obtained, the

other quantities at the break point may be calculated directly. Fig. 2 illustrates the variation

of *h*b/*H*o with *H*o/*L*o and θo (solid lines).

Fig. 2. Normalized depth at breaking as a function of wave steepness and angle in deep water

(exact and approximate solutions).

If the wave angle at breaking is small, cos θb ≅ 1.0, and *h*b can be calculated explicitly

from:

2/5

2

=

(10)

*L*o γb 2 2π

2

Fig. 2 also includes solutions for this approximate expression (broken lines), indicating that

θo (calculations showed that the error is maximum 10% for all angles and steepnesses).

The wave angle at the break point is calculated from Snell's law:

Larson, Kraus, and Hanson

5

Integrated Publishing, Inc. |