Temporal Development of the Taylor Vortices in a Rotating Fluid. III
TLDR
In this paper, a model system of equations governing the Taylor Couette flow between two concentric cylinders is presented, which is an extension of the system given by the author in I and contains both axisymmetric and non-axisymetric Taylor vortex modes.Abstract:
With fhe aid of the Galerkin method. a model system of equations governing the Taylor Couette flow between two concentric cylinders is presented. which is an extension of the system given by the author in I and contains both axisymmetric and non-axisymmetric Taylor vortex modes. Direct numerical time integration of the present system shows that. with the increase of the angular velocity of the inner cylinder. the motion changes its character one after another as follows: periodic motion ~ quasi-periodic motion with two fundamental frequencies ~ periodic motion accompanied by noise ~ chaotic (noisy) motion.read more
Citations
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Book ChapterDOI
Instabilities and transition in flow between concentric rotating cylinders
R. C. Di Prima,Harry L. Swinney +1 more
Journal ArticleDOI
Simulation of Taylor-Couette flow. Part 1. Numerical methods and comparison with experiment
TL;DR: In this article, the Navicr-Stokes equation with boundary conditions for the viscous flow between two concentrically rotating cylinders is solved as an initial value problem using a pseudospectral code.
Journal ArticleDOI
Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave
TL;DR: In this paper, the authors used a numerical method that was described in Part 1 (Marcus 1984 a ) to solve the time-dependent Navier-Stokes equation and boundary conditions that govern Taylor-Couette flow.
Journal ArticleDOI
Spatial and temporal characteristics of modulated waves in the Circular Couette system
M. Gorman,Harry L. Swinney +1 more
TL;DR: In this article, the authors used flow-visualization and spectral techniques to study the spatial and temporal properties of the flow that precedes the onset of weak turbulence in a fluid contained between concentric cylinders with the inner cylinder rotating.
Journal ArticleDOI
Nonlinear Taylor vortices and their stability
TL;DR: In this paper, the Navier-Stokes equations for flow between rotating cylinders are obtained and the stability of these solutions to non-axisymmetric perturbations is considered and the results of these calculations are compared with recent experiments.
References
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Journal ArticleDOI
Transition in circular couette flow
TL;DR: In this article, two distinct kinds of transition have been identified in Couette flow between rotating cylinders: the Taylor motion (periodic in the axial direction) and a pattern of travelling waves in the circumferential direction.
Journal ArticleDOI
A mathematical example displaying features of turbulence
TL;DR: In this paper, the authors consider an incompressible and homogeneous viscous fluid within given material boundaries under given exterior forces and assume that the boundary conditions and the outside forces are stationary, i.e. independent of time.
Journal ArticleDOI
Stochastic instability of non-linear oscillations
G M Zaslavskiĭ,B V Chirikov +1 more
TL;DR: In this paper, a one-dimensional non-linear Oscillator Acted on by a Periodic Perturbation (PP) is described, and the condition of overlapping resonance is investigated.
Journal ArticleDOI
On the application of infinite systems of ordinary differential equations to perturbations of plane Poiseuille flow
C. L. Dolph,D. C. Lewis +1 more
TL;DR: In this paper, the Navier-Stokes equations are replaced by a set of functions of the space variables which have divergence zero and which vanish outside sets of compact support, and the existence of a solution of this system is then established by a process of successive approximations involving a square truncation of the system.