7.6. IRREGULAR (2-D) WAVE GENERATION
403
and
Q(r)
Q(r)
1 - \r\/Tp
0
: kl < Tp
■ M > Tp
(7.190)
TP
»?(<)
J
peak spectral wave period
sea surface elevation time series
time
convolution time lag
triangular data window
The function E(t) provides “...a uniform, running average of the squared
water surface displacement over the interval, Tp”, and it may be thought
of as a convolution of the data window, Q, with the function, T]1 2(t) (Funke
and Mansard 1980).
1 fTn
È=^
E(t)dt = /
1n Jo
Jo
where È is the time-averaged value of E(t), Tn is the duration of the wave
record, and f is frequency (Mase, Kita, and Iwagaki 1983).
Funke and Mansard (1980) listed the requirements for calculating a
SIWEH as:
• The one-sided target spectrum, S^Çf)
• The Fourier transform, £(/), of the SIWEH function, E(t)
• A groupiness factor, based on the SIWEH activity, defined
as
The SIWEH is related to the one sided energy spectrum, S^f), by the
expression
(7.191)
GF =
(£)
(7.192)
• The recycling period, Tn, of the wave train.
Step-by-step details for calculating a SIWEH and synthesizing a corresponding time series realization are given by Fun e an
an®a ,
1980) and by Mase, Kita, and Iwagaki (1983), and ^^^^^nrovided
consult these references. In addition, Funke and Mansar
ctwEH
summary arguments and examples illustrating the use u ness o