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ABSTRACT
The Reynolds stress equation is modified to include the Craik-Leibovich vortex force, arising from the interaction of the phase-averaged surface wave Stokes driftuS with upper-ocean turbulence. An algebraic second-moment closure of the Reynolds stress equation yields an algebraic Reynolds stress model (ARSM) that requires a component of the vertical momentum flux to be directed down the gradient e^sub z^u^sup S^ of the Stokes drift, in addition to the conventional component down the gradient e^sub z^u of the ensembleaveraged Eulerian velocity. For vertical w0 and horizontal u' component fluctuations, the momentum flux must be closed using the form ... where the coefficient K^sup S^^sub M^ is generally distinct from the eddy viscosity K^sub M^ or eddy diffusivity K^sub H^. Rational expressions for the stability functions ... are derived for use in second-moment closure models where the turbulent velocity q and length l scales are dynamically modeled by prognostic equations for q^sup 2^ and q^sup 2^l. The resulting second-moment closure (SMC) includes the significant effects of the vortex force in the stability functions, in addition to source terms contributing to the q^sup 2^ and q^sup 2^l equations. Additional changes are made to the way in which l is limited by proximity to boundaries or by stratification. The new SMC model is tuned to, and compared with, a suite of steady-state large-eddy simulation (LES) solutions representing a wide range of oceanic wind and wave forcing conditions. Comparisons with LES show the modified SMC captures important processes of Langmuir turbulence, but not without notable defects that may limit model generality.
(ProQuest: ... denotes formulae omitted.)
1. Introduction
Upper-ocean mixing models without explicit representations of surface waves may implicitly represent their impact when tuned to oceanic observations because of the natural correlation between wind and wave forcing. However, such models may be inaccurate if dimensional scales of surface waves do not scale simply with the wind, as is the case for variations in sea state or wave age at a given wind speed, or for variations in the relative strength of wave versus wind effects with the upper ocean mixed layer depth.
Mixed layer models have primarily sought to explicitly articulate surface wave effects in two generally distinct ways. One approach, after Craig and Banner (1994), accounts for...