On the incompressible viscous flow over a rough surface and the Navier slip condition
by
Andro Mikelic
Université Claude Bernard Lyon 1, FRANCE

We consider the laminar viscous incompressible flow over a boundary containing surface irregularities. Such surfaces cause boundary layers for the velocity gradient and the pressure field, and solving numerically the Navier-Stokes equations requires very fine grids. In engineering practice, the grooved boundary effects are reduced to a coefficient in the effective interface law, posed on a smooth surface. These upscaled laws are called the wall laws and are of importance in applications.

In this talk we suppose the periodic irregularities of the same characteristic length and height. Characteristic size of the imperfections is small and we study the asymptotic behavior of the solution for the incompressible Navier-Stokes equation, when it tends to zero. After constructing appropriate boundary layers, we obtain the Navier slip condition as the corresponding wall law. We justify it for moderate Reynolds numbers by estimating the difference between the physical solution and the upscaled solution in appropriate norms. The norm of the difference behaves as a power of the characteristic roughness. The effective coefficient in the Navier's law is determined through an auxiliary boundary layer. Finally, we show that presence of the irregularities (riblets) diminishes the tangential drag force.

Date received: May 5, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-74.