Ocean Turbulence. Part II: Vertical Diffusivities of Momentum, Heat, Salt, Mass, and Passive Scalars

Abstract

Abstract A Reynolds stress–based model is used to derive algebraic expressions for the vertical diffusivities Kα(α = m, h, s) for momentum, heat, and salt. The diffusivities are expressed as Kα(Rρ, N, RiT, ϵ)in terms of the density ratio Rρ = αs∂S/∂z(αT∂T/∂z)−1, the Brunt–Vaisala frequency N2 = −gρ−10∂ρ/∂z, the Richardson number RiT = N2/Σ2 (Σ is the shear), and the dissipation rate of kinetic energy ϵ. The model is valid both in the mixed layer (ML) and below it. Here Rρ and N are computed everywhere using the large-scale fields from an ocean general circulation model while RiT is contributed by resolved and unresolved shear. In the ML, the wind-generated large-scale shear dominates and can be computed within an OGCM. Below the ML, the wind is no longer felt and small-scale shear dominates. In this region, the model provides a new relation RiT = cf(Rρ) with c ≈ 1 in lieu of Munk's suggestion RiT ≈ c. Thus, below the ML, the Kα become functions of Rρ, N, and ϵ. The dissipation ϵ representing the physical ...