Similarity Solutions for Turbulent Jets and Plumes in a Rotating Fluid

T. J. Pedley The Johns Hopkins University, Baltimore, Md.

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Abstract

Similarity solutions are derived for a turbulent jet (constant momentum flux) and a turbulent plume (constant buoyancy flux) directed along the axis of rotation of a body of fluid in solid-body rotation, on the assumption that the Rossby number is small. The jet radius is found to increase with axial coordinate z as z1/5, and the plume radius as z3/7. A detailed discussion of the order of magnitude of the Reynolds stress terms is made necessary by the fact that there is, a priori, more than one velocity scale in the flow. There is sonic evidence that the given solutions do not represent real flows, but this question cannot he answered fully until certain problems in hydrodynamic stability are solved. An experiment is therefore suggested.

Abstract

Similarity solutions are derived for a turbulent jet (constant momentum flux) and a turbulent plume (constant buoyancy flux) directed along the axis of rotation of a body of fluid in solid-body rotation, on the assumption that the Rossby number is small. The jet radius is found to increase with axial coordinate z as z1/5, and the plume radius as z3/7. A detailed discussion of the order of magnitude of the Reynolds stress terms is made necessary by the fact that there is, a priori, more than one velocity scale in the flow. There is sonic evidence that the given solutions do not represent real flows, but this question cannot he answered fully until certain problems in hydrodynamic stability are solved. An experiment is therefore suggested.

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