The spectral energy transfer from surface waves to internal waves

Abstract

The generation of internal waves by resonantly interacting surface waves is examined in the framework of spectral scattering theory in the random-phase approximation. Coupling coefficients are derived from Euler's equation of motion for arbitrary stratification. The spectral energy transfer is discussed for deep-water surface waves and a simple three-layer model of the stability frequency. Analytical and numerical evaluation of the transfer integral leads to a parametrization in terms of the basic model parameters. These are the depth, thickness and stability frequency of the thermocline and the scale parameters and bandwidth of the surface wave spectrum. Strong dependence on some of these parameters, in particular the surface wave energy and the ratio of surface and internal wave frequencies, indicates a large spatial and temporal variability of the transfer rate. The transfer to the internal wave field in the oceanic main thermocline is found to be negligible compared with the effect of other processes. High frequency waves in the seasonal thermocline may be generated very efficiently.