Transition in Plane Channel Flow with Spatially Periodic Perturbations.
Abstract
We studied experimentally the primary and secondary instabilities in a plane channel flow perturbed by a streamwise periodic array of cylinders. Wallbounded shear flow in plane channels typically undergoes a direct transition from simple laminar behavior to turbulence with complex spatial and temporal intermittency; such behavior is characteristic of open flows, where fluid can advect through the system. However, the spatially perturbed channel flow displays bifurcations to wellordered stable states, similar to transition exhibited by closed flows (flows confined in a box). The primary transition is a supercritical Hopf bifurcation arising from convective rather than absolute instability. The critical value of Reynolds number R _1 = 130 for the transition is more than an order of magnitude less than that for the unperturbed flow (R_1 = 5772 from linear stability theory). The stable secondary flow, a twodimensional travellingwave, resembles TollmeinSchlichting waves, the linear modes of plane Poiseuille flow. As in the spatially unperturbed case, intentionally imposed, controlled disturbances are required to reveal transition since the bifurcation arises from convective instability. Numerical simulations are in quantitative agreement with the experimental observations. The secondary flow loses stability at R _2~ 160 to a threedimensional state with a preferred spanwise periodicity. This tertiary flow demonstrates standingwave behavior as it evolves along the streamwise direction; equivalent behavior results from differing initial disturbances. The flow structure and the strictly periodic spectra resemble the beginning stages of turbulent breakdown typically displayed by unperturbed plane channel flow; however, we observed no evidence in our experiment that the threedimensional states continue to evolve toward turbulence. For R _sp {~}{>} 200, power spectra from our experiment have broad subharmonics that are also observed in other wallbounded shear flows. Our work demonstrates experimentally that spatially periodic perturbations in plane channel flow isolates and stabilizes structures that are only fleetingly observed in the unperturbed flow.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.......279S
 Keywords:

 Physics: Fluid and Plasma