Particle dispersion by nonlinearly damped random waves

We present a theoretical study of the dispersion of particles along quasi-horizontal stratification surfaces induced by small-amplitude internal gravity waves that are forced by white noise and dissipated by linear or nonlinear damping. This extends previous studies in which only linear damping was considered. The damping itself is a toy model for the nonlinear processes that would attenuate a wave mode in a broad spectrum of internal waves such as the Garrett-Munk spectrum for ocean internal waves. We compute the velocity covariance using an eigenfunction expansion of the Kolmogorov backward equation and investigate how the degree of nonlinearity affects the scaling of diffusivity with wave amplitude. We find a simple new expression for the diffusivity that is valid in both the linear and nonlinear cases, and we consider the likely quantitative importance of these process in the context of data from field experiments on small-scale ocean tracer dispersion.