īefore formulating the final conclusion, we would like to discuss implications of the results for the spectral modelling of wave energy dissipation. Interesting also is behaviour of ν at low wave steepnesses, when the waves do not break, e.g. In the course of the breaking, their height was considerably reduced, downshifting of the carrier frequency has occurred, i.e.,, but the modulational properties still maintain to conform well with the general trend. 4) correspond to waves which have broken between the first probe where their ε 0 was recorded and the probe where the bandwidth readings were taken. And finally, the two most distant points ( a 0 k 0 > 0. Third and very interesting, the wind-forced points (filled circles), and the forcing varies very broadly as U / c = 0–11 (see Figure 4 below), grouped together with other points. Secondly, it covers the range where three-dimensional instabilities become essential (i.e., a 0 k 0 > 0. 44 is the Stokes limit at which the waves break ). First of all, the wave steepness ranges from gentle to extremely steep ( a 0 k 0 = 0. We should note that the set of conditions in which the modulation naturally developed is very diverse. While the scatter is considerable, there is some systematic behaviour of the steep data points around these lines. 5 × a 0 k 0, the outcome of the small-amplitude theory of for the fastest-growing instability is shown with dashed lines, and the high-order-non-linearity theory of with thin solid lines (following ). Here, c is wave phase speed.įor reference, the dash-doted lines indicates the trend ν = 0. Values of wind speed U = U 10 employed in this paper will be those extrapolated to 10 m height, and the wind-forcing conditions imposed ranged from no wind to extreme ( U / c = 11). This fan was used to impose wind forcing over mechanically generated waves, and in the present study records of the forced waves will be used to investigate the wind effect on the modulation. ASIST has a programmable fan capable of generating centreline wind speeds in the range of 0 to 30 m/s. Such cases will be noted in the figures below. The experiment was dedicated to wave breaking, and some waves would break between the probes, which may or may not bring about implications for the present study of the natural modulation. ![]() ![]() 24 m, surface elevations were recorded at 4.55 m, 10.53 m, 11.59 m and 12. 6 Hz, 1.8 Hz and 2.0 Hz are analysed here). 4 m thus providing deep-water conditions for the wave frequencies involved (wave trains with initial frequencies of 1. In the experiment, monochromatic deep-water two-dimensional wave trains were generated by the wave paddle.
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