This study uses the barotropic point jet to investigate the modification of eddy-mean flow interaction due to variations in resolution. This model study is motivated by the uncertainty as to whether the stability characteristics of eddies in two-level baroclinic models are modified by the extreme truncation of the model.
Linear stability analyses with varying resolution demonstrate that the growth rates of the unstable waves and the most unstable wavenumbers decrease as the resolution of the model is reduced. This study shows that if a model's resolution is adequate to resolve the analytic linear growth rate of the most unstable wave, then the integrated wave enstrophy needed to stabilize the flow is conserved. Since an increase in resolution increases the jump in the potential vorticity gradients at the jet point, the magnitude of the wave enstrophy at the jet in the quasi-linear neutral state also increases with increased resolution. Therefore, a low resolution model of the barotropic point jet may still be used to study the integrated wave enstrophy of the flow even though the structure is poorly resolved.
If a model's resolution is inadequate to resolve the analytic linear growth rate of the most unstable wave, then the potential vorticity fluxes and wave enstrophy in the quasi-linear neutral state will be underestimated by the model. Lindzen et al (1983) demonstrated that the barotropic point jet was mathematically homomorphic to the linearized Boussinesq Charney problem, therefore the results of the linear stability analysis can also be applied to the baroclinic problem. For values of the zonal mean wind on the order of observations, it is found that the two-level model can not resolve the analytic linear growth rates. Based on the results of the quasi-linear studies, this suggests that the potential vorticity fluxes and wave enstrophy in the neutral state will be underestimated.
Lindzen, R.S., A.J. Rosenthal, and B. F. Farrell, 1983: Charney's problem for baroclinic instability applied to barotropic instability. J. Atmos. Sci., 40, 1029-1034.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics