Horizontal particle dispersion by random internal waves

Observations indicate that horizontal diffusion in the ocean on scales of 1-10km is on the order of 1m²/s. On these scales vortical motions are small, and internal gravity waves carry much of the energy. We investigate the horizontal diffusion which can be induced purely through random wave-wave interactions. We begin with the rotating shallow-water equations, and obtain an analytic expression which lets us define a scale-dependent diffusivity as a function of the Coriolis parameter. We analyze this diffusivity for low, intermediate, and strong rotation, and test our expression against Monte Carlo simulations. Next, we investigate the Boussinesq equations with rotation, which are more directly applicable to the ocean. By plugging in the Garrett--Munk spectrum, we obtain a numerical value for diffusivity which can be compared to measurements.