Mode interaction and the bypass route to transition. (English) Zbl 1070.76024

Zaki, Tamer A.; Durbin, Paul A.

J. Fluid Mech. 531, 85-111 (2005).

Summary: We examine the manner by which external vortical disturbances penetrate the laminar boundary layer and induce transition. Linear theory suggests that the well-known Klebanoff mode precursor to transition can be understood as a superposition of Squire continuous modes. Shear sheltering influences the ability of free-stream disturbances to generate a packet of Squire modes. A coupling coefficient between continuous spectrum Orr-Sommerfeld and Squire modes is used to characterize the interaction. Full numerical simulations with prescribed modes at the inlet substantiate this approach. With two weakly coupled modes at the inlet, the boundary layer is little perturbed; with two strongly coupled modes, Klebanoff modes are produced; with one strongly coupled and one weakly coupled high-frequency mode, the complete transition process is simulated.

MSC:

76E05	Parallel shear flows in hydrodynamic stability
76D10	Boundary-layer theory, separation and reattachment, higher-order effects
76F06	Transition to turbulence

Keywords:

Squire modes; Orr-Sommerfeld modes; Klebanoff modes