Nonlinear energy and enstrophy transfers in a realistically stratified ocean

We discuss the nonlinear transfers possible in a quasigeostrophic fluid with a basic stratification taken from oceanic data. The energy and enstrophy conservation laws imply a cascade of energy to larger total scale (including both the horizontal scale, defined as wavelength/2π, and the deformation radius of the vertical mode). The triplet interactions among components with various horizontal scales and vertical structures, represented by the vertical mode numbers, are considered in detail for exchanges involving the barotropic and first three baroclinic modes. The initial transfer rates from one component into the other two are estimated and the most rapid transfers described as a function of the initial scale and mode number. These results suggest that barotropic motions will cascade to larger-scale barotropic motions, first baroclinic small-scale motions will transfer to first baroclinic larger scales, and first baroclinic large-scale motions will cascade to barotropic and first baroclinic motions at the deformation scale. Second and third mode motions prefer to transfer energy into small-scale (second or third mode deformation radius) first and third baroclinic mode motions.We also show the relationship of these triplet interactions to Rossby wave instabilities and resonant triads. For the latter motions, the weakness of the nonlinearity adds additional constraints which impty that the motions will tend to become zonal.