Numerical-based theoretical analysis on the decay of homogeneous turbulence affected by small strain based on constant and linear strain variations

Abstract

This study clarifies the effects of small strain on the decay of homogeneous turbulence by focusing on the temporal profile of the small strain. Small strain is defined in such a way as to not affect the anisotropy of the homogeneous turbulence. We apply the framework of the standard k–ε model to examine the effects of small strain. Constant and linearly varying small strains are studied. The effects of linearly varying small strain are found to be greater than those of constant strain. To discuss the results, we derive an analytical solution that describes the effects of the two types of small strain. Although the form of the analytical solutions is the same for constant and linearly varying strains, the coefficients used in the analytical solutions, for which an equation is also obtained, differ. The difference observed in the effects of the two types of small strain is thus caused by the difference in coefficient.