Retardation of the onset of turbulence by minor viscosity contrasts

Abstract

Motivated by turbulent drag reduction by minute concentrations of polymers we study the effects of minor viscosity contrasts on the stability of hydrodynamic flows. The key player is a localized region where fluctuations are produced by interactions with the mean flow (the "critical layer"). We show that a layer of weakly space-dependent viscosity placed near the critical layer has a very large stabilizing effect on hydrodynamic fluctuations, retarding significantly the onset of turbulence. The effect is not due to a modified dissipation (as is assumed in theories of drag reduction) but is due to reduced energy intake from the mean flow to the fluctuations. Similar physics may act in turbulent drag reduction.