Onset of self-oscillations upon the loss of stability of spatially periodic two-dimensional viscous fluid flows relative to long-wave perturbations
Andrew P. Melekhov, S. V. Revina · Fluid Dynamics · 2008
The long-wave asymptotics of the secondary flow that arises after a steady, spatially periodic flow loses stability are studied when one of the periods tends to infinity and the rate of base flow along the longer period is equal to zero. It is shown that if certain non-degeneracy conditions are satisfied, then from the base solution a self-oscillatory regime branches off and both hard and soft stability loss is possible. For the leading terms of the asymptotics explicit formulas are obtained. Examples of self-oscillations calculated for specific flows are presented and the behavior of the fluid particle trajectories in the self-oscillatory regime branching off from the base flow is investigated.