Final Report Summary - COT (Control of Turbulence)
The work carried out by the fellow in the course of the ERG grant was of numerical type. The fellow used a spectral collocation technique to identify new nonlinear solutions of the Navier-Stokes equations for boundary layer flows, solutions believed to hold a significant role in the transition to turbulence. The approach which eventually proved successful in identifying such new solutions relied on a flow-structure-regeneration-process known as the SSP (self-sustaining process). These flow states form the backbone around which turbulence is organised and maintained near a wall. They also provide clues on the origins of turbulence, i.e. on the transition process. Clearly, a turbulent flow is more dissipative than a corresponding laminar flow at the same speed; this results in more energy being spent to move any vehicle within a fluid which behaves chaotically. It is thus of importance to find means to mitigate turbulence or delay its onset, in order to reduce fuel consumption and emissions. The second part of the fellow's work thus focussed on a flow control approach, wall suction, which is being widely studied, for example in the aeronautics community, for its capacity to delay the onset of transition. The effect of suction onto the birth of nonlinear travelling wave solutions was studied by the fellow with a technique similar to that used previously. Dr. Wedin was able to demonstrate that nonlinear solutions could find their onset only at much larger values of the Reynolds number (thus at much larger fluid speeds) as compared to the conventional boundary layer flow without suction. This proves indirectly the capacity of this flow control technique to address successfully the goal of transition delay.
The study pursued paves the way for many further studies, of both theoretical and more applied nature.