The quasi-linear equilibration of a thermally maintained, stochastically excited jet in a quasigeostrophic model

Abstract

A theory for quasigeostrophic turbulence in baroclinic jets is examined in which interaction between the mean flow and the perturbations is explicitly modeled by the nonnormal operator obtained by linearization about the mean flow, while the eddy-eddy interactions are parameterized by a combination of stochastic excitation and effective dissipation. The quasi-linear equilibrium is the stationary state in dynamical balance between the mean flow forcing and eddy forcing produced by the linear stochastic model. The turbulence model depends on two parameters that specify the magnitude of the effective dissipation and stochastic excitation. The quasi-linear model produces heat fluxes (upgradient), momentum fluxes, and mean zonal winds, which are remarkably consistent with those produced by the nonlinear model over a wide range of parameter values despite energy and enstrophy imbalances associated with the parameterization for eddy-eddy interactions. The quasi-linear equilibrium also appears consistent with most aspects of the energy cycle, with baroclinic adjustment (though the adjustment is accomplished in a fundamentally different manner), and with the negative correlation between transient eddy transport and other transports observed in the atmosphere. The model overestimates the equilibrium eddy kinetic energy in cases in which it achieves correct eddy fluxes and energy balance. Understanding the role of forcing orthogonal functions rationalizes this behavior and provides the basis for addressing the role of transient eddies in climate.