Balanced and unbalanced flow in a two-layer shallow water model forced by a wind-driven slab layer

We consider forced-dissipative simulations in a two layer shallow water model. Simulations for which wind forcing is applied to a slab model embedded in the upper layer are compared to simulations for which it is applied as a body force distributed over the upper layer. The slab layer equations add time dependence to the so-called nonlinear Ekman equations (e.g., Wenegrat and Thomas, 2017) and produce pumping velocities that include fast and slow components. In a version of the slab model that includes self-advection of slab-layer momentum, inertial oscillations are seen to grow in regions of large scale anticyclonic forcing. Note this is different from inertial instabily, which occurs is strongly anticyclonic flow. For simulations using steady forcing, equilibrium solutions are not strongly sensitive to which representation of the stress is used. Time dependent forcing, however, leads to large differences –especially in the level and nature of the unbalanced portion of the flow.