Gravity Currents in Confined Channels with Environmental Shear

Abstract

Abstract This study examines properties of gravity currents in confined channels with sheared environmental flow. Under the assumptions of steady and inviscid flow, two-dimensional analytic solutions are obtained for a wide range of shear values. The slope of a gravity current interface just above the surface increases as environmental shear α increases, which is consistent with previous studies, although here it is shown that the interface slope can exceed 80° for nondimensional shear α > 2. Then the inviscid-flow analytic solutions are compared with two- and three-dimensional numerical model simulations, which are turbulent and thus have dissipation. The simulated current depths are systematically lower, compared to a previous study, apparently because of different numerical techniques in this study that allow for a faster transition to turbulence along the gravity current interface. Furthermore, simulated gravity current depths are 10%–40% lower than the inviscid analytic values. To explain the model-produced current depths, a steady analytic theory with energy dissipation is revisited. It is shown that the numerical model current depths are close to values associated with the maximum possible dissipation rate in the simplest form of the analytic model for all values of α examined in this study. A primary conclusion is that dissipation plays an important and nonnegligible role in gravity currents within confined channels, with or without environmental shear.