Time-dependent isotropic turbulence

Abstract

Homogeneous isotropic turbulence subject to linearly increasing forcing is investigated as a unit problem for statistically unsteady turbulence. The transient spectral dynamics is analysed using a closure theory. A long time asymptotic state is found with k ^−7/3 corrections to the energy spectrum as proposed by Yoshizawa. Although the cancellation of O(Re ^1/2) terms underlying the standard dissipation rate equation is confirmed in this asymptotic state, it is found that this equation cannot predict the transient dynamics accurately. The discrepancies are explained in terms of the basic mechanisms of vortex stretching and enstrophy destruction responsible for the evolution of the dissipation rate.

This paper was chosen from Selected Proceedings of the Third International Symposium on Turbulence and Shear Flow Phenomena (Sendai, Japan, 24–27 June 2003).