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

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

2008-01-30

arxiv.org/abs/0801.4644v2

Physics

Fluid Dynamics

This paper has been withdrawn by the authors. 6 pages, 7 figures, Euro. Phys. J. Appl. Phys., 44(1), 101-107

Scientific paper

10.1051/epjap:2008141

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.

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