Revisiting Near-Inertial Wind Work: Slab Models, Relative Stress, and Mixed Layer Deepening

Abstract

The wind generation of near-inertial waves is revisited through use of the Pollard–Rhines–Thompson theory, the Price–Weller–Pinkel (PWP) mixed layer model, and KPP simulations of resonant forcing by Crawford and Large. An Argo mixed layer climatology and 0.6° MERRA-2 reanalysis winds are used to compute global totals and explore hypotheses. First, slab models overestimate wind work by factors of 2–4 when the mixed layer is shallow relative to the scaling H* ≡ u*/(Nf)1/2, but are accurate for deeper mixed layers, giving overestimation of global totals by a factor of 1.23 ± 0.03 compared to PWP. Using wind stress relative to the ocean currents further reduces the wind work by an additional 13 ± 0.3%, for a global total wind work of 0.26 TW. Second, the potential energy increase ΔPE due to wind-driven mixed layer deepening is examined and compared to ΔPE computed from Argo and ERA-Interim heat flux climatology. Argo-derived ΔPE closely matches cooling, confirming that cooling sets the seasonal cycle of mixed layer depth and providing a new constraint on observational estimates of convective buoyancy flux at the mixed layer base. Locally and in fall, wind-driven deepening is comparable in importance to cooling. Globally, wind-driven ΔPE is about 11% of wind work, implying that >50% of wind work goes to turbulence and thus not into propagating inertial motions. The fraction into this “modified wind work” is imperfectly estimated in two ways, but we conclude that more research is needed into mixed layer and transition-layer physics. The power available for propagating near-inertial waves is therefore still uncertain, but appears lower than previously thought.