2-dimensional streamwise periodical solutions of Navier–Stokes equations for plane channel

Results of computer simulations are given for nonstationary viscous incompressible fluid flows in an infinite plane channel. Two-dimensional streamwise periodic solutions of the Navier–Stokes equations are investigated. It is shown that if the wave number $\alpha_0$ tends to zero the integral characteristics of the flows are no longer dependent on $\alpha_0$ and determined by the Reynolds number only. Nonuniqueness of secondary longwave flows is established. Regions of existence for the secondary flows with different $\alpha_0$ are studied.