Continuous mode transition and the effects of pressure gradient. (English) Zbl 1177.76136

Zaki, Tamer A.; Durbin, Paul A.

J. Fluid Mech. 563, 357-388 (2006).

Summary: Continuous mode transition is an instance of the bypass route to boundary-layer turbulence. The stages that precede breakdown are explained in terms of continuous Orr–Sommerfeld and Squire spectra. In that context, the role of pressure gradient is less evident than it is in natural transition. Its role is investigated using linear theory and numerical simulations. Both approaches demonstrate that adverse pressure gradients enhance the coupling of low-frequency vortical disturbances to the boundary-layer shear. The result is stronger boundary-layer perturbation jets – or Klebanoff distortions. The correlation between the intensity of the perturbation jets and transition location is tested by direct numerical simulations of pairwise continuous mode interactions; such interactions can reproduce the entire transition process. The results confirm that stronger perturbation jets are more unstable, and hence provoke early transition in adverse pressure gradient. This is also consistent with the experimental observation that transition becomes independent of pressure gradient at high turbulent intensities. Under such conditions, boundary-layer streaks are highly unstable and transition is achieved swiftly, independent of the mean gradient in pressure.

MSC:

76F06	Transition to turbulence
76D10	Boundary-layer theory, separation and reattachment, higher-order effects