Experimental study of rotating disk flow instability. II. Forced flow

Abstract

The destabilization of the rotating disk flow subject to a forcing is experimentally investigated. An isolated roughness element of size of order δ (the constant boundary layer thickness) is placed under the linear threshold of the cross-flow instability in order to create a hydrodynamic pattern of finite amplitude and localized in space. The experimental neutral stability curve is first established. The resulting double parabolic curve exhibits two minima: one of which is due to the amplification of fundamental modes, the other one is linked to the emergence of superharmonic modes. Dispersion curves determined by means of two-point measurements appear to be shifted away from those measured in the natural case (without forcing). We show that this discrepancy is due to the presence of weak nonlinear effects which can be described by a Ginzburg–Landau amplitude equation. Lastly, we present an original method that enables to determine both components of the group velocity vector using the measured dispersion relations and wave packet propagation angle.