Turbulence generated by the interaction of entropy fluctuations with non-uniform mean flows

Abstract

This paper is primarily concerned with the turbulence generated by the interaction of random entropy fluctuations with non-uniform mean flows. The results are obtained by using rapid distortion theory in conjunction with a high frequency solution of a previously developed wave equation that governs the small amplitude unsteady vortical and entropic motion on steady potential flows (Goldstein 1978). The analysis is applied to symmetric contractions or expansions (or combinations of the two) and comparisons are made with a corresponding theory of Batchelor & Proudman (1954) for the rapid distortion of upstream turbulence by a contraction of this type. It is shown that the energy of the entropy-generated turbulence increases much more rapidly with contraction ratio than that of the imposed upstream turbulence. Turbulence of the former type can therefore dominate the latter even when the upstream entropy fluctuations are weak relative to the imposed turbulent intensities. Moreover the structure of the entropy-generated turbulence is found to be quite different from that of the contracted upstream turbulence.A secondary purpose of the paper is to discuss some effects of compressibility on rapid distortion theory.