Assessing a Turbulent Mixing Scheme in Diurnal Warm Layers considering Langmuir Turbulence

Abstract This study investigates how Langmuir turbulence (LT) driven by Stokes drift shear affects the heated ocean surface boundary layer (OSBL) based on turbulence-resolving large-eddy simulations (LES) and assesses an analytic vertical mixing parameterization based on a simplified second-moment closure (SMC) approach. Diurnal solar heating forces OSBL shoaling to generate a diurnal warm layer (DWL) in which heat and momentum are trapped. Without LT, relatively weak turbulent mixing results in a near-surface jet that is associated with enhanced turbulent kinetic energy (TKE) production of shear-driven turbulence (ST), which approximately balances TKE dissipation rates. Conversely, LT maintains strong mixing, delaying the DWL formation and preventing the TKE dissipation enhancement by generating a less sheared jet. However, sufficiently strong heating destroys TKE to ultimately reduce mixing and to create more sheared jets, which effectively shifts the LT to an ST-dominated regime. A second-moment turbulence budget analysis suggests that 1) the near-surface OSBL responds rapidly to the surface forcing, 2) Stokes drift impacts heat and momentum budgets in profoundly different ways, and 3) buoyancy terms are to leading order negligible. Building on these findings and introducing a physics-based mixing length, we develop a simplified SMC model that can be solved for near-surface expressions for key turbulent variables and mixing coefficients in terms of known variables. For ST, these expressions are consistent with the Monin–Obukhov similarity theory. For LT, these expressions reveal a fundamental dependence of turbulent variables on Stokes drift shear.