Linear stability of Poiseuille flow over a steady spanwise Stokes layer

TL;DR

This paper investigates how spanwise wall forcing creating a steady Stokes layer influences the linear stability of Poiseuille flow, showing it can delay transition to turbulence and reduce friction.

Contribution

It provides a comprehensive numerical analysis of the stability effects of spanwise forcing on Poiseuille flow at various Reynolds numbers, highlighting potential flow control benefits.

Findings

Spanwise Stokes layer significantly alters flow stability.

Wall forcing more than doubles the negative eigenvalue part.

Transient energy growth is reduced by nearly a factor of four.

Abstract

The temporal linear stability of plane Poiseuille flow modified by spanwise forcing applied at the walls is considered. The forcing consists of a stationary streamwise distribution of spanwise velocity that generates a steady transversal Stokes layer, known to reduce skin-friction drag in a turbulent flow with little energetic cost. A large numerical study is carried out, where the effects of both the physical and the discretization parameters are thoroughly explored, for three representative subcritical values of the Reynolds number Re. Results show that the spanwise Stokes layer significantly affects the linear stability of the system. For example, at Re=2000 the wall forcing is found to more than double the negative real part of the least-stable eigenvalue, and to decrease by nearly a factor of four the maximum transient growth of perturbation energy. These observations are Re-dependent and further improve at higher $Re$. Comments on the physical implications of the obtained results are provided, suggesting that spanwise forcing might be effective to obtain at the same time a delayed transition to turbulence and a reduced turbulent friction.