Computing Problems in Nonlinear Hydrodynamic Stability

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Abstract
Questions arising in nonlinear hydrodynamic stability such as the calculation of an equilibrium flow field when the basic flow is unstable, wavenumber selection, and successive instabilities are considered for the classical problem of flow between concentric rotating cylinders. Recent numerical and analytical work dealing with calculation of the Taylor vortex of a given axial wavelength, the selection of the axial wavelength, the subsequent breakdown of the Taylor‐vortex flow to wavy‐vortex flow, and the calculation of the wavy‐vortex flow is reviewed. Some of the open questions, possible methods of solving them, and the order of magnitude of the required calculations are discussed.