Oblique Laminar Turbulent Interfaces in Couette Flow and Self-Sustaining Process in Boundary Layer Flows
In this talk we will consider two canonical flow cases, Couette and ASBL (asymptotic suction boundary layer) flow, and study two aspects related to transition to turbulence. In Couette flow (and other shear flows such as Poiseuille flow), the onset of transition to turbulence in subcritical wall-bounded flows is characterised by large-scale localized structures such as turbulent spots or turbulent stripes.
Interestingly, the laminar-turbulent interfaces associated with these structures always display obliqueness with respect to the mean direction of the flow. We will attempt to explain this phenomenon using an assumption of scale separation between large and small scales, and we can show analytically why the corresponding laminar-turbulent interfaces are always oblique with respect to the mean direction of the flow inthe case of plane Couette flow.
In the second part, we study edge states, i.e. the flow that is confined to the separatrix between laminar and turbulent states, in the ASBL, a flow that is a physically correct prototype for a parallel boundary layer flow. Using a bisection algorithm, these states are obtained in span-wise extended domains, which leads to spatial localisation. Interestingly, these states are not steady states or travelling waves, but show interesting internal dynamics very similar to the self-sustaining process of wall turbulence. Several aspects of these edge states are shown, e.g. their dependency on domain size.