Gortler vortices promoted by wall roughness

Numerical experiments are conducted to investigate spatially developing Gortler vortices and the way in which wall roughness promotes their formation and growth. Several different types of walls are examined and their relative merits as vortex promoters assessed. The only disturbances of the flow are due to the rough wall; hence, at each downstream station the local field feels (1) the upstream flow distribution (produced by the upstream wall conditions) and (2) the local forcing at the wall. Rapid vortex formation and growth, like in the case of ribleted walls, can be qualitatively explained by the positive combination of these two effects; when the two influences on the local flow field compete, e.g. for randomly distributed wall roughness, the equations with the boundary conditions filter the disturbances over some streamwise length, function of the roughness amplitude, to create coherent patches of vorticity out of the random noise. These patches can then be amplified by the instability mechanism. If a thin rough strip is aligned along the span of an otherwise smooth wall to trip the boundary layer, the filtering region is shorter and growth of the vortices starts earlier. Also for the case of an isolated three-dimensional hump a rapid disturbance amplification is produced, but in this case the vortices remain confined and a very slow spanwise spreading of the perturbation occurs. In all naturally developing cases, where no specific wavelengths are explicitly favored, the average spanwise wavelengths computed are very close to those of largest growth from the linear stability theory.