Large-eddy simulation of Langmuir turbulence in pure wind seas

The scaling of turbulent kinetic energy (TKE) and its vertical component (VKE) in the upper ocean boundary layer, forced by realistic wind stress and surface waves including the effects of Langmuir circulations, is investigated using large-eddy simulations (LESs). The interaction of waves and turbulence is modeled by the Craik-Leibovich vortex force. Horizontally uniform surface stress tau(0) and Stokes drift profiles u(S)(z) are specified from the 10-m wind speed U-10 and the surface wave age C-P/U-10, where C-P is the spectral peak phase speed, using an empirical surface wave spectra and an associated wave age-dependent neutral drag coefficient C-D. Wave-breaking effects are not otherwise included. Mixed layer depths H-ML vary from 30 to 120 m, with 0.6 <= C-P/U-10 <= 1.2 and 8 m s(-1) < U-10 < 70 m s(-1), thereby addressing most possible oceanic conditions where TKE production is dominated by wind and wave forcing. The mixed layer-averaged bulk VKE < w(2)>/u*(2) is equally sensitive to the nondimensional Stokes e-folding depth D*(S)/H-ML and to the turbulent Langmuir number La-t = root u*/U-S, where u* = root vertical bar tau(0)vertical bar/rho(w) in water density rho(w) and U-S = |u(S)|(z=0). Use of a D-S* scale-equivalent monochromatic wave does not accurately reproduce the results using a full-surface wave spectrum with the same e-folding depth. The bulk VKE for both monochromatic and broadband spectra is accurately predicted using a surface layer (SL) Langmuir number La-SL = root u*/< u(S)>(SL), where < u(S)>(SL) is the average Stokes drift in a surface layer 0 > z > -0.2H(ML) relative to that near the bottom of the mixed layer. In the wave-dominated limit La-SL -> 0, turbulent vertical velocity scales as w(rms) similar to u*La-SL(-2/3). . The mean profile w(2)(z) of VKE is characterized by a subsurface peak, the depth of which increases with D-S*/H-ML to a maximum near 0.22H(ML) as its relative magnitude w(2)/< w2 > decreases. Modestly accurate scalings for these variations are presented. The magnitude of the crosswind velocity convergence scales differently from VKE. These results predict that for pure wind seas and HML congruent to 50 m, < w(2)>/u*(2) varies from less than 1 for young waves at U-10 = 10 m s(-1) to about 2 for mature seas at winds greater than U-10 = 30 m s(-1). Preliminary comparisons with Lagrangian float data account for invariance in < w(2)>/u*(2) measurements as resulting from an inverse relationship between U-10 and C-P/U-10 in observed regimes.