EM 1110-2-1100 (Part II)
30 Apr 02
applications where wind waves are jointly present with swells in deep water, Goda and Suzuki (1976)
proposed the following values for smax : 10 for wind waves, and 25 for swells present with wind waves of
relatively large steepness, and 75 for swells with wind waves of small steepness. Under simple wind wave
conditions, the spreading function may be approximated by the equations provided. They are typical of
deepwater wind seas for which the wind has been constant. If the wind has shifted in direction, if there is
significant swell, or if the waves are in shallow water, the directional distribution may be different than the
shape functions presented.
(8) Wave groups and groupiness factors.
(a) Measurements of waves usually show a tendency of grouping between waves that is; high waves;
often seem to be grouped together. Examination of the sea surface profile records indicates that wave heights
are not uniform and they occur in successive groups of higher or lower waves. The interest in wave groups
is stimulated by the fact that wave grouping and associated nonlinear effects play an important role in the
long-period oscillation of moored vessels (Demirbilek 1988, 1989; Faltinsen and Demirbilek 1989), surf
beats, irregular wave runup, resonant interaction between structures (Demirbilek and Halvorsen 1985;
Demirbilek, Moe, and Yttervoil 1987;), and other irregular fluctuations of the mean water level nearshore
(Goda 1985b; 1987). Unfortunately there is no way to predict grouping.
(b) Wave grouping is an important research topic and there are several ways to quantify wave grouping.
These include the smoothed instantaneous wave energy history analysis (Funke and Mansard 1980), the
concept of the run of wave heights (Goda 1976), and the Hilbert transform. A short exposition of the wave
grouping analysis is provided here.
(c) The length of wave grouping can be described by counting the number of waves exceeding a
specified value of the wave height which could be the significant, mean, or other wave height. The
succession of high wave heights is called a run or a run length with an associated wave number j1. The
definition sketch for two wave groups is shown in Figure II-1-41 with the threshold wave height limit set at
H = Hc. The recurrence interval or repetition length above the threshold value of wave height is called the
total run denoted by j2.
(d) The group occurrence for N waves with k number of lags between waves in a sequence in a record
may be defined in terms of a correlation coefficient. The correlation coefficient RH so defined will describe
the correlation between wave heights as a function of the mean and standard deviation σ and is given by
j (Hi & )(Hi%k & )
N&k
1
1
RH '
σ0 N&k i'1
(II-1-169)
j (Hi & )
N
1
2
σ0 '
N i'1
then RH v 0 as N v 4. Real wave data indicate that RH(1) . 0.20 to 0.40 while RH(k) . 0 for k > 1.
(e) Thus, RH varies with the number of lags k between waves. If the succeeding waves are uncorrelated,
Furthermore, a positive value of RH suggests that large waves tend to be succeeded by large waves, and small
waves by other small waves.
Water Wave Mechanics
II-1-95
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