Reduced-Order Quasilinear Dynamics of Ocean Surface Boundary-Layer Flows

In an effort to develop new physically-based sub-grid representations of unresolved processes in global climate models, the combined effectiveness of quasilinear approximations and model reduction at reproducing oceanic surface boundary-layer turbulence is studied. Two different averaging operations are tested (horizontal and ensemble). Dimensional reduction is achieved with a Galerkin projection of the quasilinear equations of motion onto an energetically optimized subset of modes as determined by proper orthogonal decomposition. Test problems of horizontally homogeneous surface-forced thermal convection and Langmuir turbulence are examined. A reduced quasilinear model that employs the horizontal mean is able to reproduce vertical profiles of certain energetically important turbulent transports and energies to within 30% error with less than 0.2% of modes retained. Statistical descriptions based upon second-order closures that correspond to the quasilinear approximations are investigated.