Similarity Solutions for Turbulent Jets and Plumes

Problems of the convection and diffusion of momentum and of heat (or salinity) in turbulent jets and buoyant plumes, with or without crosswind, are of importance to modern civil engineering practice. Analytical solutions of these problems are presented. First, by dimensional analysis or, if a crosswind is present, by using the equations of motion and of heat diffusion, it is found that the mean velocity, the mean temperature (or mean salinity), and the eddy viscosity obey power laws (in powers of the distance from the source along the general direction of flow). Then, based on the appropriate form of the eddy viscosity, the analytical solution for each case studied is found. For every problem the solution found is characterized by mathematical and dynamic similarity at all cross sections—a fact of great significance.