V. M. Canuto

Ocean Turbulence. Part I: One-Point Closure Model—Momentum and Heat Vertical Diffusivities

Since the early forties, one-point turbulence closure models have been the canonical tools used to describe turbulent flows in many fields. In geophysics, Mellor and Yamada applied such models using the 1980 state-of-the art. Since then, no improvements were introduced to alleviate two major difficulties: 1) closure of the pressure correlations, which affects the correct determination of the critical Richardson number Ri(sub cr) above which turbulent mixing is no longer possible and 2) the need to express the non-local third-order moments (TOM) in terms of lower order moments rather than via the down-gradient approximation as done thus far, since the latter seriously underestimates the TOMs. Since 1) and 2) are still being dealt with adjustable parameters which weaken the credibility of the models, alternative models, not based on turbulence modeling, have been suggested. The aim of this paper is to show that new information, partly derived from the newest 2-point closure model discussed, can be used to solve these shortcomings. The new one-point closure model, which in its simplest form is algebraic and thus simple to implement, is first shown to reproduce a variety of data. Then, it is used in a Ocean-General Circulation Model (O-GCM) where it reproduces well a large variety of ocean data. While phenomenological models are specifically tuned to ocean turbulence, the present model is not. It is first tested against laboratory data on stably stratified flows and then used in an O-GCM. It is more general, more predictive and more resilient, e.g., it can incorporate phenomena like wave-breaking at the surface, salinity diffusivity, non-locality, etc. One important feature that naturally comes out of the new model is that the predicted Richardson critical value Ri(sub cr) is Ri (sub cr approx. = 1) in agreement with both Large Eddy Simulations (LES) and empirical evidence while all previous models predicted Ri (sub cr approx. = 0.2) which led to a considerable underestimate of the extent of turbulent mixing and thus to an incorrect mixed layer depth. The predicted temperature and salinity profiles (vs. depth) are presented and compared with those of the Kolmogorov-Petruvsky-Piskunuv (KPP) model and Levitus data.

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(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 Munks suggestion RiT ≈ c. Thus, below the ML, the Kα become functions of Rρ, N, and ϵ. The dissipation ϵ representing the physical ...

Parameterization of Mixed Layer and Deep-Ocean Mesoscales including Nonlinearity

AbstractIn 2011, Chelton et al. carried out a comprehensive census of mesoscales using altimetry data and reached the following conclusions: “essentially all of the observed mesoscale features are nonlinear” and “mesoscales do not move with the mean velocity but with their own drift velocity,” which is “the most germane of all the nonlinear metrics.” Accounting for these results in a mesoscale parameterization presents conceptual and practical challenges since linear analysis is no longer usable and one needs a model of nonlinearity. A mesoscale parameterization is presented that has the following features: 1) it is based on the solutions of the nonlinear mesoscale dynamical equations, 2) it describes arbitrary tracers, 3) it includes adiabatic (A) and diabatic (D) regimes, 4) the eddy-induced velocity is the sum of a Gent and McWilliams (GM) term plus a new term representing the difference between drift and mean velocities, 5) the new term lowers the transfer of mean potential energy to mesoscales, 6) th...