Scaling Surface Mixing/Mixed Layer Depth under Stabilizing Buoyancy Flux

Abstract

This study concerns the combined effects of Earth’s rotation and stabilizing surface buoyancy flux upon the wind-induced turbulent mixing in the surface layer. Two different length scales, the Garwood scale and Zilitinkevich scale, have been proposed for the stabilized mixing layer depth under Earth’s rotation. Here, this study analyzes observed mixed layer depth plus surface momentum and buoyancy fluxes obtained from Argo floats and satellites, finding that the Zilitinkevich scale is more suited for observed mixed layer depths than the Garwood scale. Large-eddy simulations (LESs) reproduce this observed feature, except under a weak stabilizing flux where the mixed layer depth could not be identified with the buoyancy threshold method (because of insufficient buoyancy difference across the mixed layer base). LESs, however, show that the mixed layer depth if defined with buoyancy ratio relative to its surface value follows the Zilitinkevich scale even under such a weak stabilizing flux. LESs also show that the mixing layer depth is in good agreement with the Zilitinkevich scale. These findings will contribute to better understanding of the response of stabilized mixing/mixed layer depth to surface forcings and hence better estimation/prediction of several processes related to stabilized mixing/mixed layer depth such as air–sea interaction, subduction of surface mixed layer water, and spring blooming of phytoplankton biomass.