Decay of turbulence in a power-law fluid

Abstract

The final stages of decay of isotropic homogeneous turbulence are studied in a generalized Newtonian fluid, with a viscosity that depends on the mean rate of energy dissipation. The analysis is similar to that for Newtonian fluids. For a power-law fluid with power-law index n, the turbulent kinetic energy varies with time t as t−10/(7n−3), agreeing with the classical result t−5/2 when n=1. The decay is exponential when n=3/7, and turbulence vanishes in a finite time if n<3/7.