The subharmonic resonance of interval waves by progressive surface waves.

摘要

An experimental and theoretical investigation into the generation of internal gravity waves by monochromatic progressive surface waves is presented. Using the method of nonlinear resonant interactions, a triad consisting of a single surface wave and two oblique internal waves is considered. Expansion of the boundary value problem in a power series of a small parameter allows for solution at successive orders. A multiple time scale is adopted and the internal wave amplitudes are assumed to be slowly varying functions of time.; The analysis is initially pursued for an inviscid two-layer model. At the leading order, the linear solutions for the fundamental harmonics are obtained and the conditions for resonance are determined. At the second order, nonlinear effects are retained and provide inhomogeneous forcing at the boundaries. Evolution equations for the internal wave amplitudes are obtained and the exponential growth rates are determined. Experimental evidence is presented and demonstrates good quantitative agreement with the theoretical predictions.; Viscosity is then introduced into the problem through use of a solenoidal velocity correction and a boundary layer approximation. The effects of viscosity are found to be a reduction in the rate of growth of the internal waves as well as the requirement of a minimum surface wave amplitude for growth. Results are presented for the two limiting cases in which one of the fluid layers is much more viscous than the other.; Finally, the theoretical analysis is generalized to account for the continuous variation of density. A model of constant buoyancy frequency is adopted and it is shown that inhomogeneous forcing now exists in the governing equation as well as the boundary conditions. Specific attention is directed towards determining the role of this mechanism in generating and maintaining the internal wave spectrum in the ocean. Analysis shows that a direct energy transfer from the semi-diurnal barotropic tide to near-inertial baroclinic modes is possible. Existing observational spectra are then discussed in light of this finding.