Self-similarity criteria in anisotropic flows with viscosity stratification

Abstract

Variable-viscosity flows exhibit a faster trend towards a fully developed turbulent state since fluctuations are produced at a larger amount. A legitimate expectation is that self-similarity to be tenable earlier than in classical, single-viscosity flows. The question which begs to be answered is: which are the self-similarity criteria for variable-viscosity, density-matched, flows? The similarity assumption, i.e., all scales evolve in a similar fashion in space/time, is applied to the transport equation for one- and two-point statistics of anisotropic, variable-viscosity flows. It is shown that the similarity assumption is valid for regions of the flow where viscosity (mean values and the fluctuations root-mean-square) is uniform. In regions where viscosity gradients are important, such as the sheared region and jet boundaries, similarity is not tenable. Our claims are applicable to any decaying flow, isotropic or anisotropic. Support is provided by experimental data obtained in the near field region of a jet issuing into a more viscous environment. The viscosity ratio is 3.5.