Computation of anomalous modes in the Taylor experiment
type: Item
instance of: scholarly article
title: Computation of anomalous modes in the Taylor experiment
zbMATH Open document ID: 0607.76110
DOI: 10.1016/0021-9991(87)90164-1
author: J. H. Bolstad
author: Herbert B. Keller
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3982834
zbMATH Keywords: Multigrid continuation methods
zbMATH Keywords: steady, axisymmetric incompressible Navier-Stokes equations
zbMATH Keywords: Taylor-Couette flows
zbMATH Keywords: homotopy
zbMATH Keywords: vortices
zbMATH Keywords: bifurcation diagram
describes a project that uses: LINPACK
MaRDI profile type: Publication
full work available at URL: 0021-9991(87)90164-1
OpenAlex ID: W1986489477
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description: scientific article; zbMATH DE number 3982834