Oscillatory nature and dissipation of of the internal waves energy spectrum in the deep ocean

Abstract

In this paper the new approach is proposed to consider a large number of resonantly interacting internal waves in order to investigate the evolution of the energy spectrum in the ocean. The approach is based on a new method for deriving and solving the system of coupled differential equations that govern the evolution of the waves on the interaction time scale. All previous analytical models are based on studying of three resonant internal waves and under hydrostatic approximation. The case of eight resonant waves has been studied experimentally in [J. Fluid Mech. 30, 723 (1967)]. To study the oceanic energy spectrum, only statistical models has been used which are not precise enough to provide estimates of energy exchange in the ocean. The model reported in this paper, provides an illustrative example involving 140 000 resonant internal waves. In this model we don't need to assume the hydrostatic approximation. So our model involves internal waves with frequencies spanning the range of possible frequencies, i.e., between a maximum of the buoyancy frequency N to a minimum of the inertial frequency f . Periodic nature of the spectrum (which has never been reported in previous studies) is investigated. The possible application of this model to investigation of internal waves energy dissipation is discussed.