GALCIT Special Seminar

This talk will discuss the effect of surface texture on wall turbulence, with a particular focus on surfaces designed to reduce skin-friction drag like riblets, streamwise-preferential permeability, and superhydrophobic surfaces. The drag-reduction effect typically arises from an offset between the apparent origin for the mean velocity profile, the height at which it appears to vanish, and that for the turbulence dynamics. This effect is intrinsically the same as the often-cited more effective impedance of the cross flow than the streamwise flow, and can be traced back to the protrusion-height theory of Paolo Luchini in the 1990s. This origin-offset effect can be captured when substituting the texture by an equivalent set of boundary conditions.

Homogenisation is the typical technique used to derive these, but its usefulness is limited in turbulence, where the lengthscales of the texture and the smallest eddies in the flow soon become comparable, and where the assumption that the flow in the immediate vicinity of the surface is governed by Stokes' equations breaks down. We propose instead a multiscale approach that accounts for inertia and does not require scale separation, and which shows good agreement with DNS data. Once the texture size is sufficiently large, other competing mechanisms set in, degrading drag and limiting the surface performance. One of these is the non-linear coupling of the texture-coherent flow and the overlying, texture-incoherent turbulence, which acts on the latter as a forcing term on the momentum equations. We will show that this can be re-introduced into texture-less simulations, and that the results are in good agreement with fully resolved ones.