Spectral evolution of two-layer weak geostrophic turbulence. Part I: Typical scenarios

Abstract. Long-time evolution of large-scale geophysical flows is considered in a β-plane approximation. Motions in an infinite 2-layer model ocean are treated as a system of weakly nonlinear Rossby waves (weak geostrophic turbulence). The evolution of the energy spectrum of the barotropic and the baroclinic modes is investigated on the basis of numerical experiments with the kinetic equation for baroclinic Rossby waves.
The basic features of free (nonforced inviscid) spectral evolution of baroclinic flows are similar to those of the barotropic motions. A portion of the energy is transferred to a sharp spectral peak while the rest of it is isotropically distributed. The peak corresponds to an intensive nearly zonal barotropic flow. Typically, this well-defined barotropic zonal anisotropy inhibits the reinforcement of its baroclinic analogy. For a certain set of initial conditions (in particular, if the barotropic zonal flow is not present initially), a zonal anisotropy of both modes is generated. The interplay between the multimodal nearly zonal flow components leads to the excitation of large-scale (several times exceeding the scale of the initial state), mostly meridional, baroclinic motions at the expense of the barotropic nearly zonal flow. The underlying mechanism is explained on the level of elementary mixed-triad interaction. The whole wave field retains its essentially baroclinic as well as spectrally broad nature. It evidently tends towards a thermodynamically equilibrated final state, consisting of the superposition of a (usually barotropic, but occasionally multimodal) zonal flow and a wave system with a Raleigh-Jeans spectrum. This evolution takes place as a multi-staged process, with fast convergence of the modal spectra to a local equilibrium followed by a more gradual adjustment of the energy balance between the modes.