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Book Description
The Taylor-Couette system is one of the most studied examples of fluid flow exhibiting the spontaneous formation of dynamical structures. In this book the variety of time independent solutions with periodic spatial structure is numerically investigated by solution of the Navier-Stokes equations. Topics and questions addressed are: Mathematical modeling. Numerical modeling. What kinds of flow patterns do the equations allow in the nonlinear regime? How many solutions exist for given values of the control parameters? Are they stable? How do spatial patterns and the number of solutions vary with the parameters? For some parameter values many more solutions were found than previously expected (up to 21), in other parameter regimes not even those solutions could be found whose ecistence had been taken for granted. These "experimental" numerical results led to conjectures on the global strcuture of secondary bifurcations in the Taylor system and thus to possible explanations for existence and non-existence of solutions. These conjectures were verified and generalized for the mathematically closely related equations of Rayleigh-Bénard convection, and they were numerically confirmed for the Taylor system. .
Book Info
Discusses the Taylor problem in great detail and concentrates on those aspects of the Rayleigh-Benard problem that are of importance for understanding the Taylor problem.
Pattern Formation in Viscous Flows: The Taylor-Couette Problem and Rayleigh-Benard Convection (International Series of Numerical Mathematics),Rita Meyer-Spasche,Birkhauser,376436047X,Advanced,Analytic Mechanics (Mathematical Aspects),Fluid Mechanics,General,Hydraulics,Mathematics,Mechanics - General,Science/Mathematics,Technology & Industrial Arts,Applications of Computing,Mathematical modelling,Mathematics / General,Sound, vibration & waves (acoustics),dynamical systems,fluid dynamics,scientific computing
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