Biharmonic Attractors of Internal Gravity Waves

Abstract

Abstract— The hydrodynamic system that admits the development of internal wave attractors under biharmonic forcing is investigated. It is shown that in the case of low amplitude of external forcing the wave pattern consists of two attractors that interact between themselves only slightly: the total energy of the system is equal to the sum of energies of the components with high accuracy. In the nonlinear case the attractors interact in the more complex way which leads to the development of a cascade of triad interactions generating a rich set of time scales. In the case of closely adjacent frequencies of the components of a biharmonic perturbation, the nonlinear “beating” regime develops, namely, the mean energy of the system of coupled attractors performs oscillations at a large time scale that corresponds to the beating period. It is found that the high-frequency energy fluctuations corresponding to the same mean energy can differ by an order of magnitude depending on whether the envelope of the mean value increases or decreases.