Near‐Field Model for a High‐Momentum Negatively Buoyant Line Source Within a Three‐Dimensional Hydrostatic Lake Model

Abstract

AbstractThis work is motivated by a case study in which cooling water effluent is discharged from a line source diffuser onto the shallow southern shelf of a large lake. The effluent is discharged with high momentum to the north, and the plume influences the surrounding flow for hundreds of meters before becoming a passive tracer. We plan to use a three‐dimensional hydrodynamic model to examine the impact of this effluent on water residence time within the southern shelf, but in order to accomplish this task, we require a method for incorporating the effluent‐driven flow into the hydrodynamic model, which by default does not predict the correct rate of spreading of the plume or the correct rate of lateral entrainment of ambient water. In this paper we develop a method for incorporating the effects of high‐momentum line source discharges into any three‐dimensional or two‐dimensional (depth‐averaged) hydrodynamic model that employs a horizontal eddy viscosity and diffusivity. Our approach is to modify horizontal eddy viscosity and diffusivity to enforce the correct rate of lateral entrainment of the plume. We validate the new method using three test cases relevant to our case study: a neutrally buoyant jet, a cylindrical gravity current, and a negatively buoyant jet.