Stability/receptivity of high-speed external flows

The goal of this project is to provide detailed theoretical modelling of high-speed fluid flow over a surface with a (small scale) roughness pattern. Such surface roughness plays a significant part in the transition from laminar to turbulent flow and it is an important question to address how the properties of the resulting flow near to the surface are related to the detailed geometry of the roughness.

The approach to be taken is a combination of modern asymptotic methods that allow for simplification of the problem (from a theoretical perspective) under an assumption that the flow speed is sufficiently fast, combined with bespoke numerical schemes for the resulting simplified equations. Such descriptions typically lead to different systems of partial-differential equations applying to different regions of the flow, all of which must be solved and related to each other before a complete overview of the flow response can be provided.

The novelty in this project arises from the length scales assumed for the distributed surface roughness. When the roughness is sufficiently elongated in the flow direction, one must apply a more complex and new asymptotic description in the high-speed limit than the established technique. This results in a novel nonlinear problem for the flow near to the surface, crucially allowing for disturbances to grow downstream, thereby allowing for secondary effects to transition the flow to turbulence.

EPSRC areas: continuum mechanics; fluid dynamics & aerodynamics.