Universal Roughness Functions for Naturally-Occurring Surfaces

The possibility that simple correlations might exist between certain geometrical parameters describing naturally-occurring surfaces and the corresponding roughness functions is explored. The importance of describing the surface geometry in terms of parameters which have some relevance to the mechanics in the immediate vicinity of the surface excrescences is emphasised. A crude model is proposed which leads to the concept of an ‘effective roughness height’ the purpose of which is to collapse the roughness functions, corresponding to a particular class of surfaces, onto a universal curve. Since the surface description is a function of the bandwidth of wavelengths used in the analysis, it is necessary for this purpose to consider which wavelengths relating to a typical surface profile are responsible for localised eddy-shedding. The above points are discussed and an experiment is described in which some of the ideas are applied to a set of irregularly-rough surfaces corresponding to seven different ship-hull replicas. Although the results are somewhat tentative it is the author’s’ opinion that more research along the lines outlined in this paper may enable the roughness function corresponding to a naturally-occurring surface to be predicted with reasonable accuracy on the basis of a knowledge of the surface geometry.