The relative roles of divergence and velocity slip in the stability of plane channel flow

¹ Department of Chemical Engg., Imperial College, UK
² International Centre for Theoretical Physics, Trieste 34014, Italy
³ Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560 064, India

Corresponding author: asameen@ictp.it

Received: 21 January 2008
Revised: 23 May 2008
Accepted: 6 June 2008
Published online: 6 August 2008

Abstract

Wall slip and wall divergence are known to have large and opposing effects on the stability of flow in a two-dimensional channel. While divergence hugely destabilises, slip dramatically stabilizes the linear mode. In a non-parallel stability analysis, we study a combination of these two effects, since both will coexist in small-scale flows with wall roughness. Our main results are (i) that the stabilising effect of slip is reversed at higher angles of divergence, (ii) transient growth of disturbances is unaffected by either wall-divergence, or by slip at any divergence. Moreover, at the Reynolds numbers relevant here, transient growth is too low to be a significant player in transition to turbulence, which is more likely to be driven by linear instability. The results would have implications for the onset of unsteadiness and mixing in small scale flows.