174
5 Wave Evolution in Non-uniform Currents in Deep Water
it is necessary to take a much greater value q instead of q = 2, which is
typically connected with the quadratic energy dissipation in wind wave models. Thus, the dissipation effect becomes greater for q = 10 in the model (see
Fig. 5.7b). The spectrum excess over the equilibrium interval is no more than
25 per cent. The second spectrum maximum is decreased compared with the
previous case, and its frequency is slightly displaced to the low-frequency
area.
Physical explanation of rips. Taking into consideration the aforementioned results, the following explanation of the origin of rips could be suggested. Waves propagating in the horizontally non-uniform current are increased in height and decreased in length. The blocking process begins for
the shorter and, later on, for longer waves. At the same time reverse waves
appear, and they are carried back and down stream. The free surface presents
a superposition of two systems: straight and reverse waves. The height of the
reverse waves is sharply increased while their length is decreased. The wave
action density is preserved and the energy and the a frequency are increased
before breaking occurs. The crest wave breaks after the wave steepness has
exceeded a definite ultimate value. The wave amplitude is sharply decreased,
and the wave itself is carried away by the current with its height increasing
and the length decreasing until the next breaking.
The balance can take place in the spectrum at a larger spectral density
level compared to ordinary wind waves due to the efficient current influence
on waves. It should be recalled that the mean steepness of wind waves is 1/36,
while the ultimate wave steepness can exceed 1/7. The number of waves with
a steepness near to the critical one is much larger in the spectrum of rips,
resulting in strong water surface instability. In this case, the water surface
presents itself as a whirlpool, i.e. a large quantity of relatively short steep
waves subjected to intensive breaking.
In conclusion, it should be noted that the main feature of the evolution
of the wave spectrum Eh, propagating in the increasing countercurrent, is
the appearance of a second spectral maximum, its rapid growth and shift of
the maximum frequency to the low-frequency area. This second maximum is
caused by reverse waves, appearing as a result of the straight wave blocking
in a current. The wind intensity increase would result in smoothing over
the described effects. It would be due to two reasons: firstly, due to the
decrease of the spectral maximum frequency a max, i.e. decreasing the current
non-dimensional speed Vm and, secondly, increasing the energy level in the
spectral maximum and in the range of high frequencies. This leads to an
increase in the parameter 80 (see Fig. 5.6).
There is not only qualitative, but also quantitative agreement between the
obtained theoretical solution with full-scale rip spectral observations (Barenblatt et al., 1985; Leykin & Monin, 1985). At the same time it is possible
to describe with the help of the model a wave evolution not observed in the
experiment due to a relatively small maximum current speed. This refers, pri-
5 Wave Evolution in Non-uniform Currents in Deep Water
it is necessary to take a much greater value q instead of q = 2, which is
typically connected with the quadratic energy dissipation in wind wave models. Thus, the dissipation effect becomes greater for q = 10 in the model (see
Fig. 5.7b). The spectrum excess over the equilibrium interval is no more than
25 per cent. The second spectrum maximum is decreased compared with the
previous case, and its frequency is slightly displaced to the low-frequency
area.
Physical explanation of rips. Taking into consideration the aforementioned results, the following explanation of the origin of rips could be suggested. Waves propagating in the horizontally non-uniform current are increased in height and decreased in length. The blocking process begins for
the shorter and, later on, for longer waves. At the same time reverse waves
appear, and they are carried back and down stream. The free surface presents
a superposition of two systems: straight and reverse waves. The height of the
reverse waves is sharply increased while their length is decreased. The wave
action density is preserved and the energy and the a frequency are increased
before breaking occurs. The crest wave breaks after the wave steepness has
exceeded a definite ultimate value. The wave amplitude is sharply decreased,
and the wave itself is carried away by the current with its height increasing
and the length decreasing until the next breaking.
The balance can take place in the spectrum at a larger spectral density
level compared to ordinary wind waves due to the efficient current influence
on waves. It should be recalled that the mean steepness of wind waves is 1/36,
while the ultimate wave steepness can exceed 1/7. The number of waves with
a steepness near to the critical one is much larger in the spectrum of rips,
resulting in strong water surface instability. In this case, the water surface
presents itself as a whirlpool, i.e. a large quantity of relatively short steep
waves subjected to intensive breaking.
In conclusion, it should be noted that the main feature of the evolution
of the wave spectrum Eh, propagating in the increasing countercurrent, is
the appearance of a second spectral maximum, its rapid growth and shift of
the maximum frequency to the low-frequency area. This second maximum is
caused by reverse waves, appearing as a result of the straight wave blocking
in a current. The wind intensity increase would result in smoothing over
the described effects. It would be due to two reasons: firstly, due to the
decrease of the spectral maximum frequency a max, i.e. decreasing the current
non-dimensional speed Vm and, secondly, increasing the energy level in the
spectral maximum and in the range of high frequencies. This leads to an
increase in the parameter 80 (see Fig. 5.6).
There is not only qualitative, but also quantitative agreement between the
obtained theoretical solution with full-scale rip spectral observations (Barenblatt et al., 1985; Leykin & Monin, 1985). At the same time it is possible
to describe with the help of the model a wave evolution not observed in the
experiment due to a relatively small maximum current speed. This refers, pri-