The Intrusion Depth of Density Currents Flowing into Stratified Water Bodies

Abstract

Theory and laboratory experiments are presented describing the depth at which a density current intrudes into a linearly stratified water column, as a function of the entrainment ratio E, the buoyancy flux in the dense current B, and the magnitude of the stratification N. The main result is that Z ? E?1/3B1/3/N. It is shown that the depth of the intrusion scales as Z ? (3 ± 1)B1/3/N for laboratory experiments, and as for oceanic density currents. The velocity of a large-scale density current is controlled by a geostrophic balance defined as Ugeo = 0.25g?s/f, where s is the slope and f is the Coriolis parameter. The geostrophic buoyancy flux is then defined by Bgeo = g?Ugeoh, with g? the reduced gravity and h the thickness of the current. The scaling herein implies that the depth of an oceanic intrusion is relatively insensitive to changes in source water properties but is very sensitive to changes in the stratification of the water column, consistent with the previous scaling of Price and Baringer. For example, if the buoyancy flux of a dense current were to double while the stratification remained constant, then there would only be a 25% increase in the intrusion depth, whereas doubling the stratification would result in a 50% decrease of the intrusion depth.