Transition in the asymptotic suction boundary layer over a heated plate

Abstract

The asymptotic suction boundary layer (ASBL) is a parallel shear flow that becomes turbulent in a bypass transition in parameter regions where the laminar profile is stable. We here add a temperature gradient perpendicular to the plate and explore the interaction between convection and shear in determining the transition. We find that the laminar state becomes unstable in a subcritical bifurcation and that the critical Rayleigh number and wavenumber depend strongly on the Prandtl number. We also track several secondary bifurcations and identify states that are localized in two directions, showing different symmetries. In the subcritical regime, transient turbulent states which are connected to exact coherent states and follow the same transition scenario as found in linearly stable shear flows are identified and analyzed. The study extends the bypass transition scenario from shear flows to thermal boundary layers and highlights the intricate interactions between thermal and shear forces.

Transition to turbulence when the Tollmien–Schlichting and bypass routes coexist

“…The methods presented here can also be used to explore the relation between bypass transition and TS waves in boundary layers (Duguet et al 2012;Kreilos et al 2016). More generally, they can be applied to any kind of transition where two different paths compete: examples include shear-driven or convection-driven instabilities in thermal convection (Clever & Busse 1992;Zammert, Fischer & Eckhardt 2016), the interaction between transitions driven by different symmetries (Faisst & Eckhardt 2003;Wedin & Kerswell 2004;, or the interaction between the established subcritical scenario and the recently discovered linear instability in Taylor-Couette flow with a rotating outer cylinder (Deguchi 2017).…”

Origin of localized snakes-and-ladders solutions of plane Couette flow

“…More recently, invariant states with localized support have been computed for spatially extended domains. Examples include localized equilibria and traveling waves in plane Couette flow [1][2][3][4][5][6][7][8][9], traveling waves and periodic orbits of plane Poiseuille flow [6,[10][11][12], traveling waves in a parallel boundary layer [13,14] and periodic orbits of pipe flow [15][16][17]. Such localized solutions intrinsically feature turbulent-laminar coexistence and are thus key to extending the dynamical systems approach to turbulence to the spatiotemporal dynamics of transitional shear flows in extended domains.…”

Laboratory realization of an asymptotic wall flow

“…2013; Khapko et al. 2014; Zammert, Fischer & Eckhardt 2016). In particular, these are -invariant wall flows (statistically homogeneous in the TASBL case) that also have a constant velocity and irrotational free stream.…”

“…The momentum equation for the laminar ASBL and the mean momentum equation for the TASBL have simplifying analytical features that make them attractive for theoretical studies of transition, edge states and exact coherent structures (Kreilos et al 2013;Khapko et al 2014;Zammert, Fischer & Eckhardt 2016). In particular, these are x-invariant wall flows (statistically homogeneous in the TASBL case) that also have a constant velocity and irrotational free stream.…”