Simple analytical solutions of one-equation modelling for steady/decaying homogeneous turbulence sensitized to small strain

Abstract

Abstract This study presents a simple mathematical solution describing the turbulent kinetic energy in steady or decaying homogeneous turbulence sensitized to small strain. Small strain is found to have little effect on the anisotropy of decaying homogeneous turbulence, which is consistent with a previous experiment. The effect of small strain on dissipation in the governing equations of turbulent kinetic energy is examined using the standard k-ε model. Two temporal profiles, namely a constant profile and a linear profile, with small strain are used. The steady homogeneous turbulence is maintained by linear forcing, as previously reported. This study mainly focuses on the effects of small strain on the turbulence time scale. When the magnitude of the small strain is small, the effects on the turbulence time scale can be negligibly small, especially for a constant profile. Based on this result, the governing equations for steady or decaying homogeneous turbulence sensitized to small strain can be reduced to simple linear equations. The analytical solution of these equations, a simple exponential function, is the same for the two types of homogeneous turbulence.