EM 1110-2-1100 (Part II)
30 Apr 02
spectral peakedness is the correlation coefficient of the wave envelope, relating wave height variation
between successive wave heights. This coefficient RHH may be calculated as (Tayfun 1983)
K(λ)
π
E(λ) & (1&λ2)
&
2
4
RHH '
π
1&
4
(II-1-173)
1
2
2
λ(T) '
A %B
m0
m0
m0
4
4
A'
E(f) cos 2 π f T df
;
B'
E(f) sin 2 π f T df
(h) By further assuming that Rayleigh distribution is suitable for the consecutive wave heights, the joint
probability density function p(H1, H2) for two successive wave heights H1 and H2 in the wave group may then
be established. See Tayfun (1983) for details.
(i) The correlation coefficient RHH 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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