No abstract

The perturbation of pre-existing surface gravity waves caused by the presence of an internal wave was studied both experimentally and analytically. An extensive series of experiments was performed, and quantitative results were obtained for the one-dimensional monochromatic interaction of internal waves and surface gravity waves. Internal wave-induced surface slope, amplitude and wavenumber modulations were measured for a wide range of interaction conditions. A complementary theoretical analysis, based on the conservation approach of Whitham (1962) and Longuet-Higgins & Stewart (1960,1961), was performed and a closed form solution obtained for the one-dimensional wave interaction. Both the theory and the experiment demonstrate that the effect increases with interaction distance. The maximum interaction effect is found to occur when the phase speed of the internal wave and the group velocity of the surface wave are matched. The phase of the internal wave at which maximum surface-wave modulation occurs is found to be a sensitive and continuous function of the relative wave speeds. The experimental data are in good agreement with the present theoretical analysis.

The interaction of weakly nonlinear, long internal gravity waves in neighboring pycnoclines is studied. Two coupled equations which describe the evolution of the wave amplitudes are derived. These equations are shown to possess three conserved quantities. The numerical results demonstrate the existence of two types of periodic nonlinear wave solutions when mode-two waves propagate along each pycnocline with nearly equal speeds. The energy transfer between these resonant waves is discussed for two pycnocline separations.

This study is concerned with long internal gravity waves in a stratified fluid contained between rigid horizontal boundaries. For a general stratification, long waves of finite amplitude will tend to distort, and no permanent wave shape will result. In certain important cases, however, steady waveforms are found to be possible. The properties of such waves are investigated, and their relationship to the solutions provided by the weakly nonlinear theory is studied.