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

Abstract

Ocean mixing processes have traditionally been formulated using one-point turbulence closure models, specifically the Mellor and Yamada (MY) models, which were pioneered in geophysics using 1980 state-of-the-art turbulence modeling. These models have been widely applied over the years, but the underlying core physical assumptions have hardly improved since the 1980s; yet, in the meantime, turbulence modeling has made sufficient progress to allow four improvements to be made. 1)?The value of Ricr. MY-type models yield a low value for the critical Richardson number, Ricr = 0.2 (the result of linear stability is Ricr = 1/4). On the other hand, nonlinear stability analysis, laboratory measurements, direct numerical simulation, large eddy simulation, and mixed layer studies indicate that Ricr ? 1. The authors show that by improving the closure for the pressure correlations, the result Ricr ? 1 naturally follows. 2)?Nonlocal, third-order moments (TOMs). The downgradient approximation used in all models thus far seriously underestimates the TOMs. A new expression that includes both stratification and shear is presented here for the first time. It is obtained by solving the dynamic equations for the third-order moments. 3)?Rotation. The MY-type models with rotation assume that the latter does not affect turbulence, specifically, neither the pressure correlations nor the rate of dissipation of turbulent kinetic energy. Recent studies show that both quantities are affected. 4)?Mixing below the mixed layer. Thus far, the momentum and heat diffusivities below the mixed layer have been treated as adjustable parameters. A new model that allows use of the same turbulence model throughout the ocean depth is proposed. A new model is presented that includes 1), 2), and 4). Rotation will be dealt with in a subsequent paper. The new model is fully algebraic and easy to use in an ocean code. The new model is used in an OGCM, and the predicted global temperature and salinity profiles are compared with those of the KPP model and Levitus data.