The structure of the streamwise periodical solutions of Navier–Stokes equations for low wave numbers

Direct numerical simulations of nonstationary viscous incompressible flows in an infinite plane channel are performed. Two dimensional streamwise periodical solutions of the Navier–Stokes equations are investigated. It is shown that if wave number $\alpha_0$ tends to zero, then integral characteristics of the flows weakly depend on $\alpha_0$ and depend only on Reynolds number. Nonuniqueness of secondary long wave flows is established. Regions of the existence of the secondary flows for different $\alpha_0$ are investigated.