Indications of Stratified Turbulence in a Mechanistic GCM

Abstract

Abstract The horizontal kinetic energy spectrum and its budget are analyzed on the basis of a general circulation model with simplistic parameterizations of radiative and latent heating. A spectral truncation at total wavenumber 330 is combined with a level spacing of either ~200 m or ~1.5 km from the midtroposphere to the lower stratosphere. The subgrid-scale parameterization consists of a Smagorinsky-type anisotropic diffusion scheme that is scaled by a Richardson criterion for dynamic instability and combined with a stress-tensor-based hyperdiffusion that acts only on the very smallest resolved scales. Simulations with both vertical resolutions show a transition from the synoptic −3 to the mesoscale slope in the upper-tropospheric kinetic energy spectrum. Analysis of the spectral budget indicates that the mesoscale slope can be interpreted as stratified turbulence, as has been proposed in recent works of Lindborg and others, only when a high vertical resolution is applied. In this case, the mesoscale kinetic energy around 300–150 hPa is dominated by the nonrotational flow, and the forward horizontal energy cascade is accompanied by an equally strong forward spectral flux due to adiabatic conversion. This adiabatic conversion mainly results from a vertical potential energy flux that originates in the midtroposphere, where the mesoscale adiabatic conversion is negative. For a conventionally coarse vertical resolution, however, the mesoscale slope in the troposphere is dominated by the rotational flow, and the spectral flux due to adiabatic conversion is not comparable to that associated with horizontal advection.