Entrainment: Local and non‐local turbulence models with double diffusion

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 = 2P s h −3 which expresses E in terms of P s , 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 . Second, using a turbulence model for the turbulence kinetic energy K and its rate of dissipation ɛ (K‐ɛ model, integrated across the flow), we compute P s to express E in terms of the Richardson number Ri and the density ratio R ρ 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.