Dissipation of synoptic-scale flow by small-scale turbulence
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K. Ngan, P. Bartello & D.N. Straub
McGill University
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The parameterisation of unresolved waves is an important problem in
atmospheric and oceanic dynamics. While the feedback of the unbalanced
motion on the balanced flow vanishes in quasi-geostrophic theory, it
cannot be neglected in general.
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In this work we examine the parameterisation problem in the context of
rotating stratified turbulence. Using a Boussinesq model, we study the
growth of ageostrophic perturbations to quasi-geostrophic flow.  For
weak stratification, there are analogies with the
three-dimensionalization of decaying 2-D turbulence: the growth rate
of the ageostrophic perturbation follows a ``pressureless'' estimate,
geostrophic energy is extracted from the base flow, and the associated
eddy viscosity is strongly peaked at large horizontal scales.  For
strong stratification, the transfer spectra and eddy viscosities
maintain this structure if there is synoptic-scale motion. This has
been confirmed for Rossby and Froude numbers of O(0.1). Implications
for atmospheric and oceanic modelling are discussed.