EM 1110-2-1100 (Part II)
31 July 2003
Hb
γb ' b & a
(II-4-5)
2
gT
for tan β # 0.1 and Ho&/Lo # 0.06, where T is wave period, g is gravitational acceleration, and Ho& is equivalent
unrefracted deepwater wave height. The parameters a and b are empirically determined functions of beach
slope, given by
a ' 43.8 1 & e &19 tanβ
(II-4-6)
and
1.56
b'
(II-4-7)
1 % e &19.5 tanβ
(c) The breaking wave height Hb 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
Ho&
&
5
Ωb ' 0.56
(II-4-8)
Lo
(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
Hrms,b ' 0.42 d
(II-4-9)
for root-mean-square (rms) wave height (Thornton and Guza 1983) or, approximately,
Hmo ,b ' 0.6 d
(II-4-10)
for zero-moment wave height (see Part II-1). Some variability in Hrms,b and Hmo,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).
Hmo,b = 0.1 L tan h kd
(II-4-11)
to represent both depth- and steepness-induced wave breaking.
II-4-4
Surf Zone Hydrodynamics
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