On the propagation of planar gravity currents into a stratified ambient

Abstract

Gravity currents are of high interest both for their relevance in natural scenarios and because varying horizontal buoyancy presents a canonical problem in fluid mechanics [Huppert, “Gravity currents: A personal perspective,” J. Fluid Mech. 554, 299–322 (2006)]. In this paper, attention is directed to gravity currents with a full-depth lock release propagating into a linearly stratified ambient fluid. For the case of an unstratified ambient, similarity solutions are known to capture the evolving height profile of the gravity current. We will compare this solution class with numerical data from high fidelity simulations. The presence of ambient stratification (quantified by the stratification intensity, S) introduces internal gravity waves that interact with the propagating current head, which will inhibit Kelvin–Helmholtz billows, decelerate current propagation, and smooth the shape of the current head. We perform direct numerical simulations of planar two- and three-dimensional gravity currents released into stratified ambient fluid of varying S and analyze the gravity current kinematics. Our analysis complements existing findings from performed laboratory and numerical experiments [Dai et al., “Gravity currents propagating at the base of a linearly stratified ambient,” Phys. Fluids 33, 066601 (2021)] that show a stratified ambient modifies the current front velocity. Previous literature employed has inconsistent Reynolds numbers and boundary conditions, complicating interpretations. In the present numerical campaign, a closer analysis clarifies influence of the top boundary condition choice on formation and structure of the internal gravity waves. While acknowledging there is no available choice for a high-accuracy simplified numerical representation of a free-surface, a family of profiles for internal wave formation emerges varying with buoyancy Reynolds number and top boundary condition selection. The subsequent results appraise similarity solutions for the distribution of the heavy fluid in the gravity current. Our results show that for unstratified and low stratification ambient fluid, height profiles permit a similarity solution but higher values of S are less amenable; these profiles suggest a continuing time dependency on the traveling internal wave.