Unsteady Separation for High Reynolds Numbers Navier-Stokes Solutions

In this paper we compute the numerical solutions of Navier-Stokes equations in the case of the two dimensional disk impulsively started in a uniform back- ground flow. We shall solve the Navier-Stokes equations (for different Reynolds numbers ranging from 1.5 · 10^3 up to 10^5 ) with a fully spectral numerical scheme. We shall give a description of unsteady separation process in terms of large and small scale interactions acting over the flow. The beginning of these interactions will be linked to the topological change of the streamwise pressure gradient on the disk. Moreover we shall see how these stages of separation are related to the complex singularities of the solution. Infact the analysis of the spectrum of the angular velocity component is carried out by using the sin- gularity tracking method, and in particular we shall see how the behavior of the rate of exponential decay in time is influenced by the presence of large and small scale interactions.