An Analytical Simulation of Boundary Roughness for Incompressible Viscous Flows

Abstract

The intention of this paper is to investigate the boundary roughness of a mounted obstacle which is inserted into an incompressible, external and viscous flow field of a Newtonian fluid. In particular, the present study focuses on the cross – sectional area of the obstacle, which is assumed to be a non deformable body (rigid object) with a predefined shape of random roughness. For facility reasons and without violating the generality, one may select the cross – section of the body which contains its center of gravity and is perpendicular to the main flow direction. The boundary of this cross – sectional area is mathematically simulated as the polygonal path of the length of a single – valued continuous function. Evidently, this function should be of bounded variation. The novelty of this work is that the formulation of the random roughness of the boundary has been carried out in a deterministic manner.