A closure for eddy-mean flow effects based on the Rossby wave energy equation

•Baroclinic instability is dynamically equivalent to wave drag by gravity waves.•A closure for meso-scale uxes is developed based on the Rossby wave energy equation and the IDEMIX concept.•The closure is validated in an idealized model of baroclinic instability and compared to other closures.

The concept of IDEMIX was recently developed to simulate and parameterize the effect of gravity waves on the large-scale circulation. It is applied here to Rossby waves. Since gravity wave drag is formally identical to baroclinic instability it appears possible to parameterize the effect of baroclinic and barotropic instability on the large-scale circulation following the IDEMIX concept which is based here on the Rossby wave energy equation in physical and phase space. The dimensions of that equation are reduced by assuming a fixed shape of the energy spectrum with respect to horizontal wave number. The result is a set of coupled conservation equations for Rossby wave energy compartments resolved in horizontal direction and wave vector angle. Using simple parameterisations for wave-wave interaction, the performance of the closure is tested in an idealized model of baroclinic and barotropic instability where the Rossby waves are assumed to contain the subgrid-scale energy.