A generalized slab model

Abstract

We construct a generalized slab model to calculate the ocean’s linear response to an arbitrary, depth-variable forcing stress profile. To introduce a first-order improvement to the linear stress profile of the traditional slab model, a nonlinear stress profile which allows momentum to penetrate into the transition layer (TL) is used (denoted ‘mixed layer/transition layer,’ or MLTL stress profile). The MLTL stress profile induces a two-fold reduction in power input to inertial motions relative to the traditional slab approximation. The primary reduction arises as the TL allows momentum to be deposited over a greater depth range, reducing surface currents. The secondary reduction results from the production of turbulent kinetic energy (TKE) beneath the mixed layer (ML) related to interactions between shear stress and velocity shear. Direct comparison between observations in the Iceland Basin, the traditional slab model, the generalized slab model with the MLTL stress profile, and the Price-Weller-Pinkel (PWP) model suggest that the generalized slab model offers improved performance over a traditional slab model. In the Iceland Basin, modeled TKE production in the TL is consistent with observations of turbulent dissipation. Extension to global results via analysis of Argo profiling float data suggests that on the global, annual-mean, ∼ 30% of the total power input to near-inertial motions is allocated to TKE production. We apply this result to the latest global, annual-mean estimates for near-inertial power input (0.27 TW) to estimate that 0.08 ± 0.01 TW of the total near-inertial power input are diverted to TKE production.