applications where wind waves are jointly present with swells in deep water, Goda and Suzuki (1976)

proposed the following values for *s*max : 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 *j*1. The

definition sketch for two wave groups is shown in Figure II-1-41 with the threshold wave height limit set at

(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 *R*H so defined will describe

the correlation between wave heights as a function of the mean * *and standard deviation *σ *and is given by

j (*H*i & )(*H*i%*k *& )

1

1

σ0 N&*k *i'1

(II-1-169)

j (*H*i & )

1

2

σ0 '

then *R*H v 0 as *N *v 4. Real wave data indicate that *R*H(1) . 0.20 to 0.40 while *R*H(k) . 0 for *k *> 1.

(e) Thus, *R*H varies with the number of lags *k *between waves. If the succeeding waves are uncorrelated,

Furthermore, a positive value of *R*H suggests that large waves tend to be succeeded by large waves, and small

waves by other small waves.

Water Wave Mechanics

II-1-95

Integrated Publishing, Inc. |