Lateral diffusivity from linear and nonlinear internal waves

Measurements of lateral diffusivity at scales $O(1)-O(10)$ km consistently show spreading rates of $O(1)$ m$^2$/s---a value much greater than expected from the classic internal wave shear dispersion calculation. While alternative hypotheses have been proposed, the physical mechanisms governing these $O(1)$ m$^2$/s spreading rates continue to be debated.

Here we consider the lateral diffusivity from a Garrett-Munk internal wave field in a bounded vertical domain, with both linear and nonlinear dynamics. Using a wave-vortex decomposition suitable for bounded domains, we project the nonlinear solution onto the linear solution at each time in the simulation. We then assess the degree of nonlinearity of the wave field, and show that most scales in the wave field remain linear in steady-state conditions. The scales showing the largest degree of nonlinearity are high horizontal wavenumber, low vertical mode.

Starting from steady-state conditions, we run both linear and nonlinear Boussinesq numerical simulations with passive tracers and particles. Our results show that the lateral diffusivity of $O(1)$ m$^2$/s is largely explained by linear dynamics at the fully resolved horizontal scales of $O(2.5)$ km and greater. While nonlinear interactions are necessary to maintain steady-state in these forced-dissipative simulations, nonlinear corrections to the velocity field do not appear to be necessary to explain the observed diffusivity.