Interactions Between Mean Flow and Finite-Amplitude Mesoscale Eddies in a Barotropic Ocean

For the purpose of deriving an analytical parametrization, oceanic mesoscale eddies are represented as a horizontally propagating wave field in a non-uniform environment. The mathematical analysis rests upon the assumption of scale disparity between a short eddy scale and a long mean-flow scale. The novelty resides in the treatment of finite-amplitude eddies, which, moreover, form either a band-like or a cell-like pattern. A barotropic ocean is chosen as a first step to illustrate the mathematical analysis, but dissipation is included. The main result is an analytical derivation of a mesoscale-eddy parametrization: the mean-flow equation contains Reynolds-stress terms which are computed from parameters of the eddy field, which, in turn, are predicted by separate evolution equations. Due to restrictive assumptions (barotropy, orthogonal waves,…), the parametrization established here should be viewed only as a first step toward the design of a more practical parameterization for large-scale modelling.