Unique Superposition Solution of Multiple Plumes’ Flow via Mean Kinetic Energy Fluxes

This paper simplifies the partial differential equation (PDE) of total mean energy in the plumelike region of turbulent buoyant jets under the well-known distributions in the longitudinal and transverse direction for the mean values of velocities and concentrations, in conjunction with experimental evidence for turbulence contributions. The energy fluxes are found to be self-similar. The PDE is separated into two linear ordinary differential equations (ODEs) designating particular solutions for the axial and transverse direction. The linearity of the ODEs implies uniqueness of the superposition method (SM) for the acquisition of the general solution of the mean flow field arising from the merger of shortly-spaced individual plumes. The SM is validated by the successful predictions of the well-known centerline velocity variation of an actual line, plane, or round plume composed of infinitesimal sources. Moreover, a successful application of SM highlights its ability to take into account the reciprocal displacement of interacting plumes in a simple manner. The SM predictions have errors of less than 10% simulating both zones, i.e. the zone of flow establishment (core region) and the zone of established flow. The SM may be applied to plumes formed by ocean outfall diffusers, cooling towers, chimneys, forest fires, and volcanoes.