| The ocean is filled with fast, small-scale motions called internal waves, which are too small to be resolved by numerical models, yet which are energetic motions in the ocean's interior. Can they contribute to the larger-scale circulation? This thesis develops stochastic models to investigate how the waves might enhance small-scale mixing, a process which ultimately controls the large-scale energy transport.;First, we consider how a small-amplitude random wave field can disperse particles vertically, by modelling breaking regions as excursion sets of a Gaussian random field and relating this to a coefficient of vertical dispersion. We apply this to the Garrett-Munk spectrum for the background wave field in the ocean to estimate the diffusivity in the abyssal ocean, and obtain results consistent with observations.;Next, we consider how the same field can contribute to horizontal particle dispersion even without wave-breaking, through a combination of nonlinear wave-wave interactions and correlations between the waves' Eulerian velocity field and the particles' Lagrangian trajectories. We compare solutions for the shallow-water and the Boussinesq equations with a heuristic model based on pseudomomentum.;Finally, we consider a mechanism for how wave energy might cascade to the small scales at which it can contribute to mixing, by investigating how random topography scatters the large-scale internal waves generated by tidal forcing. We derive an analytic formula for the scattering efficiency based on a diffusion approximation to the governing equations, and apply our results to an empirical spectrum for topography in the Pacific basin to estimate the e-folding scale of the internal tide. |
