γb ' *b *& *a*

(II-4-5)

2

for tan *β *# 0.1 and *H*o&/Lo # 0.06, where *T *is wave period, *g *is gravitational acceleration, and *H*o& is equivalent

unrefracted deepwater wave height. The parameters *a *and *b *are empirically determined functions of beach

slope, given by

(II-4-6)

and

1.56

(II-4-7)

1 % *e * &19.5 tanβ

(c) The breaking wave height *H*b is contained on both sides of Equation II-4-5, so the equation must be

solved iteratively. Figure II-4-2 shows how the breaker depth index depends on wave steepness and bottom

slope. For low steepness waves, the breaker index (Equation II-4-5) is bounded by the theoretical value of

0.78, as the beach slope approaches zero, and twice the theoretical value (sum of the incident and perfectly

reflected component), or 1.56, as the beach slope approaches infinity. For nonuniform beach slopes, the

average bottom slope from the break point to a point one wavelength offshore should be used.

(d) Komar and Gaughan (1973) derived a semi-empirical relationship for the breaker height index from

linear wave theory

1

&

5

Ωb ' 0.56

(II-4-8)

(e) The coefficient 0.56 was determined empirically from laboratory and field data.

(4) Irregular waves. In irregular seas (see Part II-1 for a general discussion of irregular waves), incipient

breaking may occur over a wide zone as individual waves of different heights and periods reach their

steepness limits. In the *saturated *breaking zone for irregular waves (the zone where essentially all waves are

breaking), wave height may be related to the local depth *d *as

(II-4-9)

for root-mean-square (rms) wave height (Thornton and Guza 1983) or, approximately,

(II-4-10)

for zero-moment wave height (see Part II-1). Some variability in *H*rms,b and *H*mo,b with wave steepness and

beach slope is expected; however, no definitive study has been performed. The numerical spectral wave

transformation model STWAVE (Smith et al. 2001) uses a modified Miche Criterion (Miche 1951).

(II-4-11)

to represent both depth- and steepness-induced wave breaking.

II-4-4

Surf Zone Hydrodynamics

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