Vortex wave interaction theory to understand self sustaining processes in transitional flows

Abstract

In this work the self-sustaining processes are investigated within a Couette flow de- veloping a method able to apply directly the stress jumps predicted by the vortex wave interaction theory. The challenge of the approach is to implement a technique able to directly implement the stress jumps and to implement a procedure able to deform the mesh to the flow variations. The derivation of the vortex wave interaction theory is also discussed and the numerical formulations of the governing equations are discretized through a spectral/hp element method. The method turns out to agree with the other approaches already utilised in literature and the results repro- duce a constraint of the mathematically inviscid flow suggesting that the flow is weakly dependent on the viscosity. The characteristics of the obtained flow are then discussed. These Navier-Stokes solutions are then perturbed by a sinusoidal wall forcing to study the robustness of the self-sustained mechanism by varying the amplitude of the forcing. The results show the possibility to control the behaviour of the flow and the effectiveness of the considered forcing to induce a drag reduction. Overcoming a certain amplitude threshold, a breakdown of the flow occurs in which the vortex core splits into multiple cores. Also after the breakdown the vortex wave interaction theory has been able to generate a self-sustained multiple core flow.