Three-dimensional instabilities of laminar flow in a rough channel and the concept of hydraulically smooth wall

Flow in a channel with distributed surface roughness is considered. Results of the linear stability analysis show that the presence of the roughness destabilizes the traveling-wave instability as well as introduces a new instability that manifests itself in the form of streamwise vortices. The critical conditions for the occurrence of both instabilities are given for different, classes of roughness shape. It is shown that these conditions can be predicted with a reasonable accuracy in the case of an arbitrary.(but Fourier transformable) roughness by considering only the leading Fourier mode (wavy-wall model). It is argued that the onset of instabilities provides a decision mechanism that determines whether a particular rough wall can be viewed as being hydraulically smooth in the case of transitional flows. (c) 2006 Elsevier Masson SAS. All rights reserved.