Flows between orthogonally stretching parallel plates

Navier–Stokes equilibrium solutions of a viscous fluid confined between two infinite parallel plates that can independently stretch or shrink in orthogonal directions are studied. It is assumed the admissible satisfy spatial self-similarity stretching shrinking perpendicular coordinates. The nonlinear steady boundary-value problem discretized using spectral Legendre method, and found tracked two-dimensional parameter space by means pseudo-arclength continuation Newton–Krylov schemes. Different families have been identified, some which correspond to classical Wang Wu self-similar flows arising plane channel with one stretching–shrinking wall [Wang, C.-A. Wu, T.-C., “Similarity accelerating walls,” Comput. Math. Appl. 30, 1–16 (1995)]. However, large variety three-dimensional also found, even for low rates. When slightly increasing those rates, these disappear at saddle-node bifurcations. By contrast, when both simultaneously higher wide new equilibria created annihilated neighborhood cuspidal codimension-2 bifurcation points. This behavior has similarities observed other planar cylindrical flows.