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Parameterisation of small-scale random forcing in β-plane turbulence

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ADI - Anti-diffusive dynamics: from sub-cellular to astrophysical scales

In two-dimensional turbulent flows subject to small-scale random forcing and dissipation, it is sometimes possible to make successful predictions for the structure of emergent large-scale coherent structures, or condensates, using a relatively simple closure for the eddy-driven momentum fluxes. In the case of the classical problem of zonal jet formation on a beta-plane, however, such an approach has hitherto had limited success. Here a closure approach suggested by Srinivasan and Young is developed and investigated with a view to understanding what is required for a successful resolution of the beta-plane problem. The key missing ingredient is found to be that distinct secondary instabilities develop on both the eastward and westward jets, and these lead to the growth and equilibration of  waves on the jet scale. Momentum fluxes due to these secondary waves then play a key role in the momentum balance of the equilibrated jets. Parameterised calculations in which the random forcing is replaced by a deterministic forcing based on Srinivasan-Young are shown to result in near-identical jet structures to numerical calculations of the full problem. A limitation, however, is that the parameterised calculations must themselves be eddy-permitting (i.e. not purely zonal) in order that secondary instabilities can develop.

This talk is part of the Isaac Newton Institute Seminar Series series.

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