Stabilization and evolution of parameters of a symmetric laminar flow in a plane channel with sudden expansion

A problem is formulated for computing the fields of parameters of a stationary laminar symmetric flow. A two-dimensional flow in a channel with a sudden change in the cross-sectional area is computed. The evolution of a three-dimensional perturbation inserted into the channel at the initial stage of computations is analyzed. It is demonstrated that the parameters of a two-dimensional flow in the channel at a Reynolds number $\mathrm{Re}=50$ become stabilized at a dimensionless time $t>20$, whereas the steady state is reached under the same conditions at $t\approx100$. At a distance of approximately $10h$ ($h$ is the channel width at the entrance), the flow becomes one-dimensional, but the streamwise component of the velocity vector remains a function of the streamwise coordinate owing to flow compressibility.