On the role of non-uniform stratification and short-wave instabilities in three-layer quasi-geostrophic turbulence

The role of short-wave instabilities on geostrophic turbulence is studied in a simplified model consisting of three layers in the quasi-geostrophic approximation. The linear stability analysis shows that short-wave instabilities are created by the interplay between the shear in the upper and lower layers. If the stratification is non-uniform, in particular surface intensified, the linear growth rate is larger for short-wave instabilities than for long-wave instabilities and the layers are essentially decoupled, with the small scales growing independently. The fully developed homogeneous turbulence is studied in a number of numerical experiments. Results show that in both the case of equal layer depths and surface intensified stratification an inverse cascade in kinetic energy is observed. The modal kinetic energy spectra for the case with surface intensified stratification show higher energy for higher baroclinic numbers at small scales, due to the decoupling of the layers. As a result, while the case with equal layer depths shows large barotropic instabilities with large scale gradients of potential temperature, the surface intensified stratification is characterized by a transition from surface dynamics, characterized by a patchy distribution of vorticity, to interior dynamics, characterized by vorticity filamentation. The effect of the short-wave instabilities can be seen in the probability distribution functions of the potential vorticity anomaly, which reduces to a Gaussian distribution when the growth rate of the short-wave instabilities is larger than the growth rate for the long-wave instabilities. The surface intensified stratification also alters the vertical structure of the potential vorticity fluxes and shows deviations of the fluxes from a scaling obtained assuming that the turbulence acts as a downgradient diffusion. Experiments with a passive tracer shows a dominance of the coherent structures at large scales, and of filamentation at smaller scales, in the tracer dispersion. (C) 2014 AIP Publishing LLC.