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

TL;DR

This study investigates how wall divergence and slip influence the stability of plane channel flow, revealing complex interactions where slip can stabilize or destabilize flow depending on divergence angles, with implications for turbulence transition.

Contribution

It provides a combined analysis of wall divergence and slip effects on flow stability, highlighting the reversal of slip stabilization at higher divergence angles and the limited role of transient growth.

Findings

Slip stabilizes flow at low divergence angles.

Higher divergence angles reverse slip's stabilizing effect.

Transient growth is negligible at relevant Reynolds numbers.

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.