A Dissipation Function for the Internal Wave Radiative Balance Equation

The radiative balance equation describes the evolution of the internal wave action density spectrum n (k) in response to propagation, generation, nonlinear transfer, dissipation, and other processes. Dissipation is assumed to be due primarily to wave breaking, either by shear or gravitational instability. As part of the Internal Wave Action Model (IWAM) modeling effort, a family of dissipation functions is studied that is to account for this dissipation by wave breaking in the radiative balance equation. The dissipation function is of the quasi-linear form Sdiss = −γ (k, Ri−1) n(k), where the dissipation coefficient γ depends on wavenumber k and inverse Richardson number Ri−1. It is based on the dissipation model of Garrett and Gilbert (1988) and contains three free adjustable parameters: c0, p, and q. To gain insight into the role that each of the free parameters plays in the dissipative decay of the wave spectrum, we first consider simple examples that can be solved analytically: the response to homogeneous and stationary forcing, the free temporal decay of a Garrett and Munk spectrum, and the spatial decay of a monochromatic and bichromatic spectrum. Then the more complex problem of the reflection of an incoming Garrett and Munk spectrum off a linear slope is solved numerically. In these examples, the parameter c0 determines how rapidly the spectrum decays in space or time, p the form or shape of this decay, and q the relative decay of different wavenumbers. These dependencies are sufficiently strong to suggest that the free parameters can eventually be calibrated by comparing solutions of the radiative balance equation with observations, using inverse techniques.