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1. Introduction
The upper region of the ocean is subjected to dramatic ambient forcing, which enhances and controls the turbulent exchanges of momentum, heat, and other quantities across the air-sea interface (Leibovich 1983; Thorpe 2004; Sullivan and Williams 2010). Among these forces are breaking and nonbreaking waves, where the latter interacts with wind stress to produce local recirculating motions called Langmuir circulations (LC), which was first studied by Langmuir (1938). LC can be observed on the sea surface as parallel streaks, coaligned with the prevailing wind direction, with lateral spacing varying between a few meters to hundreds of meters. These streaks are the product of surface convergence, where, by continuity, the water must sink, and the collective result is formation of counterrotating vortical structures. LC is characterized as a turbulent self-organization due to the interaction of surface waves and wind-driven shear instability in the surface mixed layer. Langmuir turbulence can be numerically modeled via solution of the momentum transport equations with an additional vortex forcing term, which modulates turbulent momentum transport in the lateral and vertical direction such that counterrotating LCs emerge; this transport equation term is referred to as the Craik-Leibovich (C-L), first proposed by Craik and Leibovich (1976). An improved second generation (CL-2) is more commonly used to model Langmuir turbulence (Leibovich 1977a,b). The vortex force fL (also called C-L force) is included in the momentum transport equations and is the curl of the Stokes drift [us(z)] and ambient vorticity [Inline formula omitted: See PDF] ([Inline formula omitted: See PDF] denotes a grid-filtered LES quantity), given by [Inline formula omitted: See PDF] (in this article, the streamwise, spanwise, and vertical direction correspond with the first, second, and third component of any vector, where the spatial vector is [Inline formula omitted: See PDF]; vectors are denoted with bold roman, e.g., x, while tensors are denoted by bold sans serif, e.g., [Inline formula omitted: See PDF]). This vortex force represents an inviscid wave-induced instability of the unidirectional current, which monotonically decreases with depth.
LC is a key contributor to vertical mixing and transport of materials in the upper mixed layer of the ocean and significantly contributes to physical and geochemical processes relevant to oil spill turbulent dispersion (Lehr...