### Quasigeostrophic and stratified boussinesq turbulence

Bartello, P *(McGill)*

Tuesday 09 December 2008, 10:00-10:30

Seminar Room 1, Newton Institute

#### Abstract

Turbulence generated by random isotropic i.c.'s in the strongly stratified and rapidly rotating environment that characterises large-scale atmosphere/ocean flows, leads to nonlinear geostrophic adjustment via a downscale cascade of wave energy and a first-order decoupling of geostrophic modes from linear wave modes. The march toward ever higher resolution in "realistic" models has renewed the community's interest in smaller-scale stratified turbulence with weak rotation, where this large-scale decoupling is reduced. Proceeding to even smaller scales, i.e. L~H~U/N, where L and H are the horizontal and vertical length scales and N is the Brunt-Vaissalla frequency, 3-d overturning may occur (Thorpe 1977).
Our recent non-rotating simulations of stratified flow show that, if the Reynolds number is sufficiently high, then the characteristic vertical scale decreases until the usual Froude number (U/NH) reaches order unity from below, where it saturates. Increasing the stratification decreases the Froude number based on the horizontal scale. Rescaling the equations in this way yields hydrostatic flow where the vertical advection term is not small. On the other hand, if the vertical scale of the flow is set by viscosity, weak rotation or, for some period of time, by the initial conditions, the classical quasi-horizontal layered flow of Riley, Metcalfe & Weissman (1981) is recovered. We also simulated how this picture changes with the addition of varying rotation rates in order to observe the transition from stratified to quasigeostrophic (QG) turbulence.
Throughout this work we examined the statistics of linear wave and vortical (PV) modes separately. It was shown that, although they form a complete basis, they can only be expected to have dynamical relevence when U/NH<<1. While this is the case in QG flow, and for strongly-stratified decay of isotropic i.c.'s, its application must be restricted to the buoyancy range in stratified turbulence without rotation. In the QG limit, we removed the omega-equation contribution to the vertical velocity from the total field, to study the degree of balance obtained at various Rossby numbers. Finally, with parameterisation of "wave drag" in balanced models in mind, we explicitly calculated the energy drain on the linear vortical modes exerted by the linear wave modes as a tentative preliminary step. Predictability, as a function of Rossby and Froude numbers is an ongoing focus.

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