Linear instability of viscous parallel shear flows: revisiting the perturbation no-slip condition

TL;DR

This paper revisits the boundary conditions in linear stability analysis of viscous flows, proposing alternative models that predict instabilities aligned with turbulence transition, challenging the traditional no-slip assumption.

Contribution

It introduces alternative boundary conditions that produce linear instabilities consistent with turbulence transition, questioning the classical no-slip boundary condition in wall-bounded flows.

Findings

Alternative boundary conditions predict instabilities similar to classical models.

These instabilities could explain turbulence transition.

No-slip condition may oversimplify fluid-solid interface physics.

Abstract

Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities that could be sufficient to explain turbulence transition. In many cases, the near-wall behavior of the discovered instabilities is empirically indistinguishable from the classical no-slip condition. The ability of these alternative boundary conditions to predict linear instabilities that are consistent with turbulence transition suggests that the no-slip condition may be an overly simplified model of fluid-solid interface physics, particularly as a description of the flow perturbations that lead to turbulence transition in wall-bounded flows.