Far-Field Flow Forced by the Entrainment of a Convective Plane Plume in a Rotating Stratified Fluid

Abstract

The streamfunction for a two-dimensional (line) mass sink in an unbounded rotating stratified fluid on an f-plane is derived using the linearized equations of motion. The solution is applied to the large scale circulation forced by the entrainment mechanism of a convective turbulent plane plume in a rotating stratified fluid. The linearity of the equations allow the effect of the plume on the ambient fluid to be modeled by an appropriate distribution of sources and sinks. A simple analytic expression for the streamfunction describing the far-field flow is obtained using this method. The streamfunction illustrates the modifying effect that entrainment by a turbulent plume has an the surrounding velocity and density fields. The theory is applied to predict the scale of the circulation in the vicinity of a hydrothermal plume and to successfully predict the surface cyclonic swirl observed in deep open-ocean convection events.