Evolutions of Modulated Surface Gravity Water Waves in Currents.

摘要

A detailed experimental study has been carried out to study wave-wave interactions and wave-wave-current interaction. Experiments were conducted to investigate (1) Weakly nonlinear modulated wave evolution and wave instability; (2) Monochromic wave interaction with non-uniform current; (3) Weak nonlinear modulated wave interaction with non-uniform current;;The Experiments on the evolution of modulated surface waves of different initial strengths of modulation were conducted in a wave channel. Surface displacements were measured, and wave amplitude, frequency, wavenumber and phase speed in time and space were deducted from the displacement data by using fast Fourier transform (FFT) Hilbert-Huang transform (HHT) techniques. The experimental results of different initial amplitude ratios of sidebands to carrier waves at 0.0, 0.15, 0.20, 0.29 and 0.39 cover a complete cycle of sideband instability, corresponding respectively to (a) uniform wave trains of carrier wave, (b) symmetric grow of sidebands of Benjamin-Feir type, (c) asymmetric grow with higher growth rate of lower sideband than that of lower sideband, (d) inception of downshift of dominant wave frequency from carrier wave to lower sideband, and (e) resuming uniform wave trains at lower sideband with the diminished original carrier wave and higher sideband. The experimental results of the time-space dependent wavenumber, wave frequency and phase speed are in good agreement with those obtained from the theoretical dispersion relation. It is found that the frequency downshifting is incepted locally near the node point of modulation, with very large local variations in wavenumber, frequency and phase speed at the inception region. In addition, the wave frequency, wavenumber and phase speed should evolve gradually and continuously.;The results of monochromic wave interaction with current show that the adverse-current will shorten the wave length and enhance the wave amplitude. Therefore, the wave slope will be greatly increased by the adverse current; this can lead to wave breaking. The co-current has the opposite effect on waves as that of the adverse-current, but weaker. Hence, the wave interactions with adverse- and co-currents are asymmetrical even when the currents are symmetrical. After propagating through the symmetric adverse- and co-currents, the waves exhibit a constant phase shift. This constant phase shift is not predicted by theory.;For a modulated wave with lower initial side-band strength interacting with non-uniform current, most of the current energy is transferred to the upper and lower sidebands. For a higher modulated wave amplitude ratio, most of the current energy is transferred to the lower sidebands. Furthermore, a shorter downshift position is obtained by increasing the wave steepness or current flow rate. The downshift process occurred when two waves merging occur at the points of local amplitude minima. For wave merging, the process has to pass through a singularity point or phase reversal at the origin in a complex amplitude plot.