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

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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... 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...