Parametric instabilities of internal gravity waves in boussinesq fluids with large reynolds numbers

Abstract

Abstract Previous studies of parametric instabilities of a finite-amplitude internal gravity wave in dissipationless Boussinesq fluids predict the largest growth rates for perturbations with vanishingly small wavelengths, leading to the practical question of which perturbations are most unstable in the presence of molecular dissipation. At high Reynolds numbers, the amplitude of the gravity wave decays on spatial and temporal scales which are large compared to the wavelength and period respectively. Therefore, the interaction equations describing the growth or decay of small perturbations can be solved by a conventional expansion procedure yielding a leading term in the form of a Floquet solution. Numerical calculations show that the competitive processes of parametric growth and viscous decay produce instabilities with maximum growth rates at wavelengths which may be similar or even longer than the wavelength of the basic gravity wave. Two transformations leading to a significant reduction of computation...