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

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(R?, N, RiT, ?)in terms of the density ratio R? = αs?S/?z(αT?T/?z)?1, the Brunt?Väisälä frequency N2 = ?g??10??/?z, the Richardson number RiT = N2/Σ2 (Σ is the shear), and the dissipation rate of kinetic energy ?. The model is valid both in the mixed layer (ML) and below it. Here R? 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(R?) with c ≈ 1 in lieu of Munk's suggestion RiT ≈ c. Thus, below the ML, the Kα become functions of R?, N, and ?. The dissipation ? representing the physical processes responsible for the mixing, which are different in different parts of the ocean, must also be expressed in terms of the large-scale fields. In the ML, the main source of stirring is the wind but below the ML there is more than one possible source of stirring. For regions away from topography, one can compute ? using a model for internal waves. On the other hand, near topography, one must employ different expressions for ?. In agreement with the data, the resulting diffusivities are location dependent rather than universal values. Using North Atlantic Tracer Release Experiment (NATRE) data, the authors test the new diffusivities with and without an OGCM. The measured diffusivities are well reproduced. Also, a set of global T and S profiles is computed using this model and the KPP model. The profiles are compared with Levitus data. In the North Atlantic, at 24°N, the meridional overturning is close to the measured values of 17 ± 4 Sv and 16 ± 5 Sv (Sv ≡ 106 m3 s?1). The polar heat transport for the North Atlantic Ocean, the Indo?Pacific Ocean, and the global ocean are generally lowered by double diffusion. The freshwater budget is computed and compared with available data.