Wave turbulence in the two-layer ocean model

This paper looks at the two-layer ocean model from a wave-turbulence (WT) perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical variables, allowing the turbulent cascade of energy between the barotropic and baroclinic modes to be studied. It is already well known that in two-layers, energy is transferred via triad interactions from the large-scale baroclinic modes to the baroclinic and barotropic modes at the Rossby deformation scale, where barotropization takes place, and from there to the large-scale barotropic modes via an inverse transfer. However, by applying WT theory, we find that energy is transferred via dominant $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\{+--\}$ triads with one barotropic component and two baroclinic components, and that the direct transfer of energy is local and the inverse energy transfer is non-local. We study this non-locality using scale separation and obtain a system of coupled equations for the small-scale baroclinic component and the large-scale barotropic component. Since the total energy of the small-scale component is not conserved, but the total barotropic plus baroclinic energy is conserved, the baroclinic energy loss at small scales will be compensated by the growth of the barotropic energy at large scales. Using the frequency resonance condition, we show that in the presence of the beta-effect this transfer is mostly anisotropic and mostly to the zonal component.