The Lubrication of Unidirectional Striated Roughness: Consequences for Some General Roughness Theories

Relations expressing the effects of unidirectional striated roughness on hydrodynamic quantities, relative to the normal x–y coordinate system are derived. It is shown that the angle between the direction of the grooves and that of motion may be expressed by the Kubo-Peklenik number, γ, for random striations. A comparison between the ensuing results and those claimed by other authors to be valid for area-distributed random roughness, is made. The two sets are identical for γ equal to unity, regardless of autocorrelation functions, but strong arguments indicating this correspondence to hold for all γ’s are presented. It is concluded that the results are, in general, valid for unidirectional striations only.