This study investigates the parameter dependence of eddy heat flux in a homogeneous quasigeostrophic two-layer model on a β-plane with imposed environmental vertical wind shear and quadratic frictional drag. We examine the extent to which the results can be explained by a recently proposed diffusivity theory for passive tracers in two-dimensional turbulence. To account for the differences between two-layer and two-dimensional models, we modify the two-dimensional theory according to our two-layer f -plane analyses reported in an earlier study. Specifically, we replace the classic Kolmogorovian spectral slope, −5/3, assumed to predict eddy kinetic energy spectrum in the former with a larger slope, −7/3, suggested by a heuristic argument and fit to the model results in the latter. It is found that the modified theory provides a reasonable estimate within the regime where both β˜=βkd−2U−1 and the strength of the frictional drag, c˜D=cDkd−1, are much smaller than unity (here, cD is the nondimensional drag coefficient divided by the depth of the layer, kd is the wavenumber of deformation radius, and U is the imposed background vertical wind shear). For values of β˜ and c˜D that are closer to one, the theory works only if the full spectrum shape of the eddy kinetic energy is given. Despite the qualitative, fitting nature of this approach and its failure to explain the full parameter range, we believe its documentation here remains useful as a reference for the future attempt in pursuing a better theory.
Although classical theories of midlatitude momentum fluxes focus on the wave-mean flow interaction, wave-wave interactions may be important for generating long waves. It is shown in this study that this nonlinear generation has implications for eddy momentum fluxes in some regimes. Using a two-layer quasi-geostrophic model of a baroclinic jet on a β-plane, statistically steady states are explored in which the vertically integrated eddy momentum flux is divergent at the center of the jet, rather than convergent as in Earth-like climates. One moves towards this less familiar climate from more Earth-like settings by reducing either β, frictional drag, or the width of the baroclinic zone, or by increasing the upper bound of resolvable wavelengths by lengthening the zonal channel. Even in Earth-like settings, long waves diverge momentum from the jet, but they are too weak to compete with short unstable waves that converge momentum. We argue that long waves are generated by breaking of short unstable waves near their critical latitudes, where long waves converge momentum while diverging momentum at the center of the jet. Quasi-linear models with no wave-wave interaction can qualitatively capture the Earth-like regime but not the regime with momentum flux divergence at the center of the jet, because the nonlinear wave breaking and long wave generation processes are missing. Therefore, a more comprehensive theory of atmospheric eddy momentum fluxes should take into account the nonlinear dynamics of long waves.
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