The<i>k</i>⁻³and<i>k</i>^−5/3Energy Spectrum of Atmospheric Turbulence: Quasigeostrophic Two-Level Model Simulation

Abstract

The Nastrom-Gage energy spectrum of atmospheric turbulence as a function of wavelength is simulated here with a two-level quasigeostrophic (QG) model. This simple model has no topography, no direct wave forcing, and no small-scale forcing, nor any kind of gravity wave generation. The two-level model does, however, allow for the simple mechanism of baroclinic energy injection at the large (synoptic) scales as the model atmosphere relaxes to a specified north-south ''radiative equilibrium'' temperature gradient. It also has a small sink of energy at the small scales due to subgrid hyperdiffusion; this attempts to model the small-scale sink not resolved by the two-level QG model, in particular, enhanced viscous dissipation in atmospheric fronts. The magnitude and shape of the observed energy spectrum, with its characteristic k 3 power-law behavior in the synoptic and subsynoptic scales (from several thousand to about eight hundred kilometers) and the characteristic k 5/3 behavior in the mesoscales (less than about six hundred kilometers), are reproduced convincingly in the model.