spectral peakedness is the correlation coefficient of the wave envelope, relating wave height variation

between successive wave heights. This coefficient *R*HH may be calculated as (Tayfun 1983)

π

&

2

4

π

1&

4

(II-1-173)

1

2

2

λ(*T*) '

m0

m0

4

4

;

(h) By further assuming that Rayleigh distribution is suitable for the consecutive wave heights, the joint

probability density function *p(H*1, H2) for two successive wave heights *H*1 and *H*2 in the wave group may then

be established. See Tayfun (1983) for details.

(i) The correlation coefficient *R*HH takes a value of about 0.2 for wind waves and 0.6 or greater for

swells (Goda 1976), a clear indication that wind waves rarely develop significant grouping of high waves.

Su (1984) has shown that the wave group containing the highest wave in a record is often longer than the

ordinary groups of high waves, and that the extreme wave usually consists of three high waves with the

highest greater than the significant wave height. Wave groups and their characteristics have been investigated

by analyzing the successive wave groups (Goda 1976 and Kimura 1980).

(j) Wave grouping and its consequences are of significant concern, but there is little guidance and few

practical formulae for use in practical engineering. The engineer needs to be aware of its existence and, for

designs that would be sensitive to grouping-related phenomena, attempt to evaluate its importance to the

problem of concern. This may involve performing numerical simulations or physical model simulations in

which a wide variety of wave conditions are tested and are designed to include those with high levels of

groupiness. The procedures for this lie beyond the scope of the CEM.

(9) Random wave simulation.

(a) Given a one-dimensional parametric spectrum model or an actual wave energy density spectrum,

it is sometimes necessary to use these quantities to calculate the height, period, and phase angle of a wave

at a particular frequency. Such an approach for simulating random waves from a known wave spectra is

sometimes termed the *deterministic spectral amplitude method*, since individual wave components in this

superposition method are deterministic (Borgman 1967). The method is also called the *random phase method*

because the phases of individual components are randomly chosen (Borgman 1969). Random waves

simulated by this approach may not satisfy the condition of a Gaussian sea unless N 6 4 in the limit. In

practice, for 200 # N # 1200 components, the spectrum can be duplicated accurately.

(b) The wave profile generated by simulation methods is used in a number of engineering applications

in spite of requiring a large number of components and considerable computer time. For example, random

wave simulation is frequently used during modeling studies in a wave tank for duplicating a required target

wave energy density spectrum. Random wave profiles are also extensively used in numerical models for

calculating structural loads and responses due to a random sea. The simulation method permits direct

prediction of the wave particle kinematics at any location in a specified water depth for given wave height-

period pair and random phase angle. The ARMA algorithms (Spanos 1983) and digital simulation methods

Water Wave Mechanics

II-1-97

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