Transition mechanisms in a boundary layer controlled by rotating wall-normal cylindrical roughness elements

Abstract

The transition to turbulence induced by counter-rotating wall-normal rotating cylindrical roughness pairs immersed within a laminar boundary layer on a flat plate is investigated with direct numerical simulations, dynamic mode decomposition (DMD) and perturbation kinetic energy (PKE) analysis. As long as the cylinder stub is rotating, the wake contains a steady dominating inner vortex (DIV) surrounded by a secondary inner vortex. Its circumferential velocity accelerates the fluid on one side of the cylinder and decelerates it on the other side. With low rotation speed, the perturbation is initiated by a combination of elliptical and centrifugal instabilities in the near wake. At medium rotation speeds, Taylor–Couette-like streamwise vortices are generated on the decelerated side, resulting in a protruding reverse-flow zone. Results from DMD analysis and corresponding PKE analysis reveal the unstable nature of the deceleration region and the wake. At the largest rotation speed investigated, the onset of perturbations is directly located on the decelerated side of the cylinder stubs, where a deceleration mechanism feeds the instability. In the near wake, the mechanism gradually changes to a pure centrifugal instability when the rotation speed increases. In the far wake, both elliptical and centrifugal instabilities fade away, and the streaky flow featuring a vigorous DIV is then only subject to inviscid inflectional instability.