Computation of anomalous modes in the Taylor experiment
Multigrid continuation methods are used to solve the steady, axisymmetric incompressible Navier-Stokes equations for Taylor-Couette flows between cylinders of finite or infinite length. Using Schaeffer's homotopy, we compute (for finite cylinders) anomalous modes (those seeming to have an odd number of vortices, or seeming to have the ''wrong'' direction of rotation at an endplate). The results show that these modes possess extra vortices not observed in the experiments. Our computations verify conjectures of Schaeffer, and of Benjamin and Mullin on the unfolding of the bifurcation diagram as periodic (infinite cylinder) flows are continuously transformed to flows with rigid ends. We obtain five distinct solutions with the same Reynolds number, aspect ratio, and radius ratio, and give a systematic procedure for obtaining them. The numerical results show qualitative agreement with the experiments of Benjamin and Mullin. They also show quantitative agreement with the more recent experiments.
steady, axisymmetric incompressible Navier-Stokes equations
scientific article; zbMATH DE number 3982834
scientific article