JP1.8 Parameterization of baroclinic eddies in a channel model

Monday, 8 June 2009
Stowe Room (Stoweflake Resort and Confernce Center)
Gavin Esler, University College London, London, United Kingdom

How does the statistically steady state, or `climate', of a simple model of an extratropical tropospheric jet depend on its controlling parameters, such as the degree of supercriticality of the radiative equilibrium jet, the width of the baroclinic zone, the rate of radiative relaxation and the surface Ekman friction? The answer to this question requires a `turbulent closure' or parameterization that relates eddy fluxes to the mean climate. One suggestion for such a closure is to represent the eddy fluxes by a downgradient diffusivity acting on the potential vorticity field. Analysis of the momentum and energy budgets for such a closure, however, reveals that care must be taken with this approach. A spatially homogeneous diffusivity, for example, is highly unlikely to conserve total zonal momentum - a global invariant for the system.

A new variational principle to parameterize the eddy fluxes is suggested. It based on the downgradient diffusion of potential vorticity but leads naturally to a spatially inhomogeneous diffusivity profile. Momentum conservation and a physically realizable energy budget are enforced using Lagrange multipliers. The new parameterization is used to predict the `climate' of the Phillips' two-layer model across a range of parameter settings. The results are compared with numerical simulations and a detailed assessment of the parameterization is given.

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