Transition to turbulence through decline of viscosity

TL;DR

This paper proposes a modified Navier-Stokes model incorporating fluid strength to explain subcritical transition to turbulence at lower Reynolds numbers, aligning theoretical predictions with experimental observations.

Contribution

It introduces a novel fluid failure mechanism into the Navier-Stokes equations, enabling analysis of subcritical turbulence transition phenomena.

Findings

Critical Reynolds number is proportional to fluid strength.

Classical Navier-Stokes model cannot predict subcritical transition.

Modified model captures flow destabilization due to fluid failure.

Abstract

Experiments (Mullin and Kreswell, 2005) show that transition to turbulence can start at Reynolds numbers lower than it is predicted by the linear stability analysis - the subcritical transition to turbulence. To explain these observations qualitatively we suggest that the onset of subcritical instability is related to decline of viscosity of the fluid: friction between fluid layers fails with the increase of the velocity gradient. To describe the declinie of friction theoretically we relax the the assumption of the stability of the fluid material and introduce a constant of fluid strength. Particularly, we enhance the Navier-Stokes model with a failure description by introducing the fluid strength in the constitutive equation for the viscous stress. The clasical model is obtained from the enhanced one when strength goes to infinity. We use the modified Navier-Stokes model to analyze the Couette flow between two parallel plates and find that the lateral perturbations can destabilize the flow and the critical Reynolds number is proportional to the fluid strength. The latter means that the classical Navier-Stokes model of a stable material with infinite strength does not capture the subcritical transition to turbulence while the mofified model does.