Variational and Stability Properties of Swirling Flows PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Variational and Stability Properties of Swirling Flows PDF full book. Access full book title Variational and Stability Properties of Swirling Flows by Lindsay MacKinnon Hamilton Douglas. Download full books in PDF and EPUB format.
Author: Lindsay MacKinnon Hamilton Douglas
Publisher:
ISBN:
Category : Fluid mechanics
Languages : en
Pages : 78
Get Book Here
Book Description
Author: Lindsay MacKinnon Hamilton Douglas
Publisher:
ISBN:
Category : Fluid mechanics
Languages : en
Pages : 78
Get Book Here
Book Description
Author: Amrish Kumar Garg
Publisher:
ISBN:
Category :
Languages : en
Pages : 406
Get Book Here
Book Description
Author: Zhigang Yang
Publisher:
ISBN:
Category :
Languages : en
Pages : 344
Get Book Here
Book Description
Author: Andrew John Szeri
Publisher:
ISBN:
Category : Eddies
Languages : en
Pages : 396
Get Book Here
Book Description
Author: Paolo Luzzatto Fegiz
Publisher:
ISBN:
Category :
Languages : en
Pages : 231
Get Book Here
Book Description
This dissertation focuses on the development of theoretical and numerical methodologies to study equilibrium and stability in conservative fluid flows. These techniques include: a bifurcation-diagram approach to obtain the stability properties of families of steady flows; a theory of Hamiltonian resonance for vortex arrays; an efficient numerical method for computing vortices with arbitrary symmetry; and a variational principle for compressible, barotropic or baroclinic flows. We employ these theoretical and numerical approaches to obtain new results regarding the structure and stability of several fundamental vortex and wave flows. The applications that we examine involve simple representations of fundamental fluid problems, which may be regarded as prototypical of flows associated with transport and mixing in the ocean and in the atmosphere, with aquatic animal propulsion, and with the dynamics of vortices in quantum condensates. We address two issues affecting the use of a variational argument to determine stability of families of steady flows. By building on ideas from bifurcation theory, we link turning points in a velocity-impulse diagram to gains or losses of stability. We introduce concepts from imperfection theory into these problems, enabling us to reveal hidden solution branches. The resulting methodology detects exchanges of stability through an "imperfect velocity-impulse" (IVI) diagram. We apply the IVI diagram approach to wide variety of vortex and wave flows. These examples include elliptical vortices, translating and ro- tating vortex pairs, single and double vortex rows, distributed vortices, as well as steep gravity waves. For a few of the flows considered, our work yields the first available stability boundaries. In addition, the IVI diagram methodology leads us to the discovery of several new families of steady flows, which exhibit lower symmetry. We next examine conditions for the development of an oscillatory instability in two-dimensional vortex arrays. By building on the theory of Krein signatures for Hamiltonian systems, we show that a resonant instability cannot occur for one or two vortices. To predict the onset of resonance for three or more vortices, we develop a simple approximate technique, which compares favorably with full analyses. In addition, we propose a simple technique to immediately check the accuracy of a detailed linear stability analysis. All of the uniform-vorticity equilibria analyzed in this dissertation were computed using a newly developed numerical approach. This methodology, which is based on Newton iteration, employs a new discretization to radically increases the efficiency of the calculation. In addition, we introduce a procedure to remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry, in an unbounded flow. Finally, we re-examine the variational principle that underpins the IVI diagram stability approach. We show that this principle may be obtained, in a conceptually straightforward manner, by first considering the classical principle of virtual work. This link enables us to readily formulate generalizations to compressible, barotropic and baroclinic flows.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 804
Get Book Here
Book Description
Author: Jillian Ann Kate Stott
Publisher:
ISBN:
Category :
Languages : en
Pages : 208
Get Book Here
Book Description
Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 9780521525411
Category : Mathematics
Languages : en
Pages : 630
Get Book Here
Book Description
Hydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. Drazin and Reid emphasise throughout the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, relate the theory to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems not only provide exercises for students but also provide many additional results in a concise form. This new edition of this celebrated introduction differs principally by the inclusion of detailed solutions for those exercises, and by the addition of a Foreword by Professor J. W. Miles.
Author: Lester Hsin-Pei Lee
Publisher:
ISBN:
Category : Hydrodynamics
Languages : en
Pages : 228
Get Book Here
Book Description
Author: Ashwani K. Gupta
Publisher: Routledge
ISBN:
Category : Science
Languages : en
Pages : 496
Get Book Here
Book Description
