A study of bifurcation of Kolmogorov flows with an emphasis on the singular limit
We consider a family of stationary Navier-Stokes flows on two-dimensional flat tori. The flow is driven by an external force which is of the form (\(\sin y\), \(0\)). Varying the Reynolds number and the aspect ratio of the torus, we numerically compute bifurcating solutions by a path-continuation method. Folds and cusps are obtained in the range where the Reynolds number is \(<100\). Some solutions are computed up until the Reynolds number becomes 10,000. Asymptotic properties as the Reynolds number tends to infinity are discussed. Also given is an analysis as the aspect ratio of the torus tends to zero.
scientific article; zbMATH DE number 1184389