Surface Discharge of Heated Water, Part I: Three-Dimensional Jet-Type Surface Plumes in Theory and in the Laboratory

The steady flow of heated water from a channel into a reservoir or lake has been studied analytically and experimentally. A three-dimensional buoyant-jet-type model has been developed to predict the main trajectory, velocity, and temperature distributions in that portion of the plume in which the flow is dominated by the momentum and the buoyancy of the discharge and has free boundaries. The interaction between turbulent mixing, buoyant spreading, and surface cooling, which are crucial for the development of any thermal plume, can be illustrated with the aid of the model. The effects of weak cross currents and weak wind on the development of a surface plume are also incorporated into the model. The model does not apply to heated water discharges which cling to a shoreline due to a particular shoreline configuration or to wind or current conditions. The effects of cold water wedge penetration into an outlet channel can be accommodated by the model. Experimental results on temperature and velocity distributions in free-jet-type three-dimensional thermal plumes have been used to verify some of the assumptions made in the numerical model, particularly those regarding Gaussian velocity and temperature distributions and lateral spread coefficients. In addition, the measurements have been used to illustrate changes in total flow rate, total heat storage, and dimensions of a surface plume. The distribution of temperatures, velocities, and Richardson numbers in an experimental surface plume has been illustrated using different types of contour plots. There is reasonable agreement between the results of the experiments and the proposed analytical prediction method.