Solutions for the flow induced by a turbulent line plume in the near-nozzle region

In experimental studies of turbulent dense saline plumes, plumes typically emerge from a nozzle submerged in a visualization tank of freshwater. In a simple case, the exterior of a nozzle used to create a line plume can be characterized as a long rectangular prism of width 2S immersed to a depth D beneath the free surface. A long thin slot centered on the nozzle base provides the plume source. The plume and its induced flow are expected to be influenced by the boundaries near the source: the nozzle base and sides, and the free surface. We studied the effect of this external nozzle geometry on the flow induced by a turbulent line plume due to entrainment. Using a potential flow model and techniques from complex analysis, we solve Laplace's equation to find the stream function of the induced flow for any ratio D/S. The solutions show that the induced flow is sensitive to the nozzle geometry and that the streamline inclination can significantly depart from the expected horizontal inflow. Some implications for experimental design and measurements of plume entrainment are discussed.