238
5 Wave Evolution in Non-uniform Currents in Deep Water
al., 1977; Sudolsky & Teplov, 1982; Pokazeyev et al., 1986) and in other countries (Francis & Dudgeon, 1967; Kato et al., 1976, 1978, 1981; Plate & Trawle,
1970; Tsuruya et al., 1987).
The detailed measurements of wind waves in a current under laboratory
conditions have been made by Japanese researchers in the wind-water flume
at the Hydrodynamic Laboratory of the Institute of Ports in Simonoseki
(Kato et al., 1976, 1978, 1981; Tsuruya et al., 1987). The wind-water flume
has an operating length of 28.5 m, a width of 1.5 m and a depth of 1.3 m.
Waves are measured at seven stations along the fetch. Both mean wave parameters and spectral densities of wave energy are determined. The experiments were performed at wind speeds from 5.6 to 11.3 ms- 1 and current
velocities from 0 to 29.9 cms- 1 for a fair current and from 0 to 14.4 em s- 1
for a countercurrent. Later, the corresponding current velocity range was
increased to 67.2 cms- 1 (Tsuruya et al., 1987). The ratio of the current velocity V to the wind speed U is up to 0.6, corresponding to strong countercurrents.
The Japanese researchers used an effective fetch notion in analysing the
experimental data. This notion is different from the traditional one, meaning
the usual distance from the shore, along which the wind blows. The time
of wind interaction with the water surface is considered to be a decisive
wave development characteristic. It is quite clear that the interaction time is
different within one fetch, depending on the presence or absence of a current.
The effective wave fetch in a current Xeff is defined as the distance at which
waves are developed to the same age as in the absence of current. Equal time
periods of wave interaction with wind in the absence and in the presence of
a current are defined as:
Xeff
X
Cgo
cg + V'
(5.138)
where Xeff is the effective fetch length; Cgo is the wave group velocity in
the absence of a current; and Cg = cg + V is the absolute wave velocity in
a current. When the wave parameters are changed due to wind effect along
the fetch, the formula for estimating the effective fetch length can be written
in the integral form:
X
J dx/Cg (x)
0
X
J dx/Cgo (x)
0
(5.139)
where the group velocities are referred to the wave frequency JP = Wmax/2n
of the spectral maximum and are dependent on the fetch x.
Using data from the measurements of Mitsuyasu & Rikiishi (1975), the
following formulas for waves in a current have been proposed (Kato et al.,
1981):
5 Wave Evolution in Non-uniform Currents in Deep Water
al., 1977; Sudolsky & Teplov, 1982; Pokazeyev et al., 1986) and in other countries (Francis & Dudgeon, 1967; Kato et al., 1976, 1978, 1981; Plate & Trawle,
1970; Tsuruya et al., 1987).
The detailed measurements of wind waves in a current under laboratory
conditions have been made by Japanese researchers in the wind-water flume
at the Hydrodynamic Laboratory of the Institute of Ports in Simonoseki
(Kato et al., 1976, 1978, 1981; Tsuruya et al., 1987). The wind-water flume
has an operating length of 28.5 m, a width of 1.5 m and a depth of 1.3 m.
Waves are measured at seven stations along the fetch. Both mean wave parameters and spectral densities of wave energy are determined. The experiments were performed at wind speeds from 5.6 to 11.3 ms- 1 and current
velocities from 0 to 29.9 cms- 1 for a fair current and from 0 to 14.4 em s- 1
for a countercurrent. Later, the corresponding current velocity range was
increased to 67.2 cms- 1 (Tsuruya et al., 1987). The ratio of the current velocity V to the wind speed U is up to 0.6, corresponding to strong countercurrents.
The Japanese researchers used an effective fetch notion in analysing the
experimental data. This notion is different from the traditional one, meaning
the usual distance from the shore, along which the wind blows. The time
of wind interaction with the water surface is considered to be a decisive
wave development characteristic. It is quite clear that the interaction time is
different within one fetch, depending on the presence or absence of a current.
The effective wave fetch in a current Xeff is defined as the distance at which
waves are developed to the same age as in the absence of current. Equal time
periods of wave interaction with wind in the absence and in the presence of
a current are defined as:
Xeff
X
Cgo
cg + V'
(5.138)
where Xeff is the effective fetch length; Cgo is the wave group velocity in
the absence of a current; and Cg = cg + V is the absolute wave velocity in
a current. When the wave parameters are changed due to wind effect along
the fetch, the formula for estimating the effective fetch length can be written
in the integral form:
X
J dx/Cg (x)
0
X
J dx/Cgo (x)
0
(5.139)
where the group velocities are referred to the wave frequency JP = Wmax/2n
of the spectral maximum and are dependent on the fetch x.
Using data from the measurements of Mitsuyasu & Rikiishi (1975), the
following formulas for waves in a current have been proposed (Kato et al.,
1981):