Abstract

The talk will discuss effective boundary conditions, correct to second order in a small parameter epsilon, for a rough wall with periodic micro-indentations. The length scale of the indentations is l, and epsilon = l/L << 1, with L a characteristic length of the macroscopic problem. At leading order the Navier slip condition is recovered; at next order the slip velocity includes a term arising from the streamwise pressure gradient. At second order also a transpiration velocity appears at the fictitious wall where the effective boundary conditions are enforced. For ease of derivation, the microscopic theory, based on a power series expansion of the dependent variables, will be limited to the case of two- dimensional roughness, the three-dimensional extension being trivial. The application to a macroscopic problem is carried out considering the case of the Hiemenz stagnation point flow over a rough wall.