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Canuto, V.M., M.S. Dubovikov, and Y. Cheng, 2005: Entrainment: Local and non-local turbulence models with double diffusion. Geophys. Res. Lett., 32, L22604, doi:10.1029/2005GL023771.
Taylor's entrainment equation contains the entrainment function E that has traditionally been treated heuristically, as attested by 30 different expressions for E(Ri) available in the literature. Using a model independent procedure, we first derive the new relation: E = 2Pshū-3 which expresses E in terms of Ps, the shear production (of turbulent kinetic energy) averaged across the interface of the gravity current whose thickness and mean velocity are denoted by h and ū. Second, using a turbulence model for the turbulence kinetic energy K and its rate of dissipation ε (K-ε model, integrated across the flow), we compute Ps to express E in terms of the Richardson number Ri and the density ratio Rρ characterizing double-diffusion. Third, we show that in the local (along the flow) case, the model reproduces the Ellison and Turner (1959) data while the non-local case reproduces the data by Princevac et al. (2005) which are up to ten times larger than the ET data.
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