Indications of upper tropospheric stratified turbulence in a high-resolution mechanistic general circulation model

The horizontal kinetic energy spectrum and its budget are analyzed on the basis of a mechanistic general circulation model that is run at high spatial resolution (spectral truncation at total wavenumber 330 and a level spacing of less than 250 m from the lower troposphere to the lower stratosphere). The mechanistic character of the model is due to simplistic parameterizations of radiative and latent heating. The only subgrid-scale parameterization is a Smagorinsky-type anisotropic diffusion scheme which 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. This setup allows to simulate the transition from the synoptic -3 to the mesoscale -5/3 slope of the upper tropospheric kinetic energy spectrum. We present indications that the -5/3 range can be interpreted as stratified macro-turbulence, as has been proposed in recent works of E. Lindborg and others. In particular, the model shows a forward horizontal energy cascade in the mesoscales around 300-150 hPa that is accompanied by an equally strong forward spectral flux due to adiabatic conversion. The latter results from a vertical energy exchange analogous to that by mesoscale gravity waves. Within the troposphere, the source of the associated vertical potential energy flux (assuming pressure as vertical coordinate) is located in the mid troposphere, where the enstrophy and energy cascades maintained by baroclinic Rossby waves are strongest. A second region of stratified turbulence is identified for the lower troposphere where mesoscale energy from the mid troposphere is deposited too.

In a sensitivity experiment with a conventional vertical resolution (level spacing larger than 1 km above the boundary layer) and identical model parameters otherwise, the mesoscale -5/3 slope develops even more clearly. It is dominated by the rotational flow and does not fulfill the scaling criterion for stratified turbulence with regard to the spectral fluxes due to horizontal advection and adiabatic conversion. Since the scaling criterion for stratified turbulence is also fulfilled if the forward cascades of kinetic energy and available potential energy are comparable, a complete interpretation of the macro-turbulence in a high-resolution circulation model would require to analyze both spectral budgets.