EXCITATION AND BREAKING OF INTERNAL GRAVITY-WAVES BY PARAMETRIC-INSTABILITY

We study the dynamics of internal gravity waves excited by parametric instability in a stably stratified medium, either at the interface bet ween a water and a kerosene layer, or in brine with a uniform gradient of salinity. The tank has a rectangular section, and is narrow to fav our standing waves with motion in the vertical plane. The fluid contai ner undergoes vertical oscillations, and the resulting modulation of t he apparent gravity excites the internal waves by parametric instabili ty. Each internal wave mode is amplified for an excitation frequency c lose to twice its natural frequency, when the excitation amplitude is sufficient to overcome viscous damping (these conditions define an 'in stability tongue' in the parameter space frequency-amplitude). In the interfacial case, each mode is well separated from the others in frequ ency, and behaves like a simple pendulum. The case of a continuous str atification is more complex as different modes have overlapping instab ility tongues. In both cases, the growth rates and saturation amplitud es behave as predicted by the theory of parametric instability for an oscillator. However, complex friction effects are observed, probably o wing to the development of boundary-layer instabilities. In the unifor mly stratified case, the excited standing wave is unstable via;a secon dary parametric instability: a wave packet with small wavelength and h alf the primary wave frequency develops in the vertical plane. This en ergy transfer toward a smaller scale increases the maximum slope of th e iso-density surfaces, leading to local turning and rapid growth of t hree-dimensional instabilities and wave breaking. These results illust rate earlier stability analyses and numerical studies. The combined ef fect of the primary excitation mechanism and wave breaking leads to a remarkable intermittent behaviour, with successive phases of growth an d decay for the primary wave over long timescales.