The wave energy in the JONSWAP spectrum is concentrated within a nar-
rower band of frequencies and is more peaked than that given by the
Pierson–Moskowitz spectrum. Significant wave height Hsis related to Hrms
in the next section.
JONSWAP spectrum given by equation (14.50) is for fetch-limited
conditions of deep seas. If waves generated are duration-limited, then an
effective fetch Feff, is calculated as
Feff
6g
8T
.8
w
U
1.5
(14.51)If a given fetch FFeff, then the waves are fetch-limited. If FFeff, the
waves are duration-limited; then Feffis substituted for Fin the calculation
of wave height and peak frequency.
Coastal Engineering Manual(US Army, 2002) recommends slightly
modified forms for JONSWAP spectrum.
In shallow water, both friction and percolation act to modify wave
growth.Coastal Engineering Manual(US Army, 2002) suggests that wave
growth formulas of deep water may be used with the restriction that no
wave with period exceeding 9.78(d/g)0.5exists.
14.10 Wave statistics
Wave records at a particular site are usually collected over a time period
ranging from 15 min to 1 h, spaced at about 3 h intervals. Each record is a
sample that provides the short-term statistics. For a narrow band of fre-
quencies over which the wave energy is concentrated, the record may be
described by the Rayleigh distribution. If P(H) is the probability that a
wave height will exceed H, then
P(H)exp[ (H/Hrms)^2 ]. (14.52)Hrmsis the root-mean-square value of the wave heights, defined as
H^2 rms
Ni 1H^2 i (14.53)whereNis the number of values of Hin the data. Note that P(H)1 for
H0 and 0 for Htending to infinity. Using the Rayleigh distribution, it is
now possible to estimate the average of the highest nth of the waves. For
example, for n3, the average is the significant wave height Hs
Hs 2
Hrms. (14.54)1
N 1