Multilayered depth-averaged formulation for immiscible gravity currents

Abstract

Lock exchange represents the progression of a gravity current caused by the instantaneous release of a heavy fluid into a lighter ambient fluid. The pressure gradient, on account of density difference, imparts motion of the current, leading to flow in the ambient fluid. Full-scale multiphase models (Eulerian/Lagrangian) have been developed to simulate these processes; however, they have substantial computational costs due to the specific nature of the models. On the contrary, the single/two-layered depth-averaged models are restricted by the range of density ratio owing to their simplified nature. In the current work a variable density multilayered shallow water model is developed to simulate the gravity current dynamics. The progression of the density front is delineated by a scalar transport equation, with the multilayered formulation offering a piecewise vertical variation of flow properties (velocity). The model is applied to the theoretical lake-at-rest condition, a set of lock exchange experimental scenarios and spreading of an oil spill over water surface. The model yields substantial agreement in computed and observed profiles of density current. Additionally, the model’s applicability to high-density gradients is explored through a representative case depicting the model’s capability for non-Boussinesq density graded flows.