The Development of Packets of Hairpin Vortices in Laminar Channel Flows in Response to Localized Disturbances
We report the responses of laminar channel flows to localized disturbances at different Reynolds numbers and initial perturbation amplitudes by using direct numerical simulations (DNS). It is found that, when the Reynolds number and the local perturbation are above some critical values, the local disturbance generates a strong and long low speed streak among many weaker ones together with a pair of streamwise vortices next to the strong low speed streak. The spatiotemporal development of the flow structures shows that the first hairpin vortex appears above and at the middle of the strong low speed streak and several secondary hairpin vortices then appear behind and ahead of the primary hairpin vortex, and thus forming a packet of hairpin vortices. It is found that the hairpin vortices seem to be generated by the Kevin–Helmhotz type instability, and some of the hairpin vortices are formed from pairing two adjacent smaller hairpin vortices generated from the roll up of shear layer near the streamwise vortex pair. It is also found that the variance of the vertical velocity is a better indicator for showing the start of nonlinear effect.
The author has benefited greatly from the discussions on instability and transition with Prof. C.B. Lee of Peking University, China.
- 1.M.V. Morkovin, The many faces of transition, in Viscous Drag Reduction, ed. by C. Wells (Plenum, Berlin, 1969)Google Scholar