A triple-deck analysis of the steady flow over a rotating disk with surface roughness

The flow over a rotating disk in still fluid is a canonical flow case that has attracted much attention with several studies focused on its stability properties.  For a smooth disk, the steady laminar flow is described by the self-similar solution provided by Von Kármán.

The aim of this work is to assess the effect of surface roughness on von Kármán’s solution . Besides the interest in itself, the evaluation of the resulting baseflow is the first step to estimate the effect of roughness on the flow stability

From a numerical point of view, modelling roughness elements that are much smaller than the boundary layer requires high local refinement and therefore a rapid increment of the computational cost. Conversely, by exploiting triple-deck decomposition, we proposed a model which requires only the surface geometry and provides an analytic solution in the Fourier space, and for this reason it is computationally cheap. The proposed theory is validated against the results of numerical simulations for different geometries that are representative of real rough surface. The analysis is further extended to the  case in which the roughness geometry is described only in statistical terms.