Linear instability of plane Couette and Poiseuille flows

TL;DR

This paper demonstrates that plane Couette flow can become linearly unstable at finite Reynolds numbers, challenging traditional assumptions by considering non-periodic disturbances, aligning theory with experimental observations.

Contribution

It introduces a novel linear stability analysis that abandons the assumption of longitudinal periodicity, revealing instability at finite Reynolds numbers.

Findings

Linear instability occurs at finite Reynolds numbers.

Traditional assumptions of periodic disturbances are not necessary.

Results align with experimental data.

Abstract

It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers which meets with known experimental data. This new result of the linear theory of hydrodynamic stability is obtained only due by abandoning traditional assumption of the longitudinal periodicity of disturbances in the flow direction.