Download or read book The N Vortex Problem written by Paul K. Newton and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to current research on the N- vortex problem of fluid mechanics. It describes the Hamiltonian aspects of vortex dynamics as an entry point into the rather large literature on the topic, with exercises at the end of each chapter.
Download or read book Chaotic Motion of the N vortex Problem on a Sphere written by and published by . This book was released on 2007 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Equivariant Degree and Periodic Solutions of the N vortex Problem written by Björn Gebhard and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book IUTAM Symposium on Hamiltonian Dynamics Vortex Structures Turbulence written by Alexey V. Borisov and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.
Download or read book Periodic Solutions of the N Point vortex Problem in Planar Domains written by Qianhui Dai and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Chaotic Motion of the N vortex Problem on a Sphere I Saddle centers in Two degree of freedom written by Takashi Sakajo and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book N vortex problem on a rotating sphere written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Unrestricted.
Download or read book The N Vortex Problem written by Paul K. Newton and published by Springer. This book was released on 2001-05-25 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to current research on the N- vortex problem of fluid mechanics. It describes the Hamiltonian aspects of vortex dynamics as an entry point into the rather large literature on the topic, with exercises at the end of each chapter.
Download or read book Invariant Dynamical Systems Embedded in the N vortex Problem on a Sphere with Pole Vortices written by and published by . This book was released on 2005 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Viscous N Vortex Problem written by David T. Uminsky and published by . This book was released on 2009 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In this work a new model is proposed to describe the motion of N localized vortex structures in two dimensional incompressible viscous flow. We will use the velocity-vorticity representation, commonly known as the vorticity equation, of incompressible flow which has the particular advantage in two dimensions of reducing to a scalar equation. An early model of two-dimensional inviscid flow in terms of moving point vortices was developed by Kirchhoff and Helmholtz. While the Helmholtz-Kirchhoff point vortex model captures many of the basic physical phenomena observed in 2D rotational flows, experiments with even simple vortex configurations exhibit complications far beyond the point vortex predictions. This new model replaces the Dirac point vortex with a Hermite expansion to represent each vortex. This is a natural choice of representation as the leading order term in the expansion is a Gaussian which is both a common regularization of a delta function and, even more importantly, is an exact solution of the 2D vorticity equation. Furthermore these Hermite functions have recently been shown by Gallay and Wayne to be related to invariant manifolds in the phase space of the vorticity equation which govern its long time asymptotics. With mild restrictions on the initial data we prove that the expansions are convergent for all time. The model reduces the 2D vorticity equation to a system of quadratic ordinary differential equations (ODEs) that track the centers of each vortex along with the evolution of each Hermite moment. As a first application of this approach a single Hermite expansion is used to model a co-rotating pair of vortices to greatly improve the accuracy of the far field acoustic pressure. Additionally, leading-order corrections to the frequency of rotation due to viscosity and finite core size are derived in the case of two well separated like-signed vortices. Finally, combinatorial formulas for the coefficients of the resulting ODEs are derived to improve the numerical implementation of the model. With these combinatorial formulae classic numerical experiments such as vortex merger are computed with our new model and results are discussed.
Download or read book Nonlinear Problems Present and Future written by A. Bishop and published by Elsevier. This book was released on 1982-01-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Problems: Present and Future
Download or read book Vortex Dynamics and Vortex Methods written by Christopher Radcliff Anderson and published by American Mathematical Soc.. This book was released on 1991-12-23 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding vortex dynamics is the key to understanding much of fluid dynamics. For this reason, many researchers, using a great variety of different approaches--analytical, computational, and experimental--have studied the dynamics of vorticity. The AMS-SIAM Summer Seminar on Vortex Dynamics and Vortex Methods, held in June 1990 at the University of Washington in Seattle, brought together experts with a broad range of viewpoints and areas of specialization. This volume contains the proceedings from that seminar. The focus here is on the numerical computation of high Reynolds number incompressible flows. Also included is a smaller selection of important experimental results and analytic treatments. Many of the articles contain valuable introductory and survey material as well as open problems. Readers will appreciate this volume for its coverage of a wide variety of numerical, analytical, and experimental tools and for its treatment of interesting important discoveries made with these tools.
Download or read book The N vortex Problem on a Rotating Shere written by Paul K. Newton and published by . This book was released on 2006 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Station re L sungen Des N Wirbel Problems Der Fluiddynamik written by Christian Kuhl and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vortex Methods written by Georges-Henri Cottet and published by Cambridge University Press. This book was released on 2008-04-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
Download or read book Dynamics of Vortex Structures in a Stratified Rotating Fluid written by Mikhail A. Sokolovskiy and published by Springer Science & Business Media. This book was released on 2013-08-28 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an extensive analysis of the dynamics of discrete and distributed baroclinic vortices in a multi-layer fluid that characterizes the main features of the large and mesoscales dynamics of the atmosphere and the ocean. It widely covers the case of hetonic situations as well as the case of intrathermocline vortices that are familiar in oceanographic and of recognized importance for heat and mass transfers. Extensive typology of such baroclinic eddies is made and analysed with the help of theoretical development and numerical computations. As a whole it gives an overview and synthesis of all the many situations that can be encountered based on the long history of the theory of vortex motion and on many new situations. It gives a renewed insight on the extraordinary richness of vortex dynamics and open the way for new theoretical, observational and experimental advances. This volume is of interest to experts in physical oceanography, meteorology, hydrodynamics, dynamic systems, involved in theoretical, experimental and applied research and lecturers, post-graduate students, and students in these fields.
Download or read book Vortex Dominated Flows A Volume Celebrating Lu Ting s 80th Birthday written by Denis Blackmore and published by World Scientific. This book was released on 2005-08-08 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Honoring the contributions of one of the field's leading experts, Lu Ting, this indispensable volume contains important new results at the cutting edge of research. A wide variety of significant new analytical and numerical results in critical areas are presented, including point vortex dynamics, superconductor vortices, cavity flows, vortex breakdown, shock/vortex interaction, wake flows, magneto-hydrodynamics, rotary wake flows, and hypersonic vortex phenomena.The book will be invaluable for those interested in the state of the art of vortex dominated flows, both from a theoretical and applied perspective.Professor Lu Ting and Joe Keller have worked together for over 40 years. In their first joint work entitled “Periodic vibrations of systems governed by nonlinear partial differential equations”, perturbation analysis and bifurcation theory were used to determine the frequencies and modes of vibration of various physical systems. The novelty was the application to partial differential equations of methods which, previously, had been used almost exclusively on ordinary differential equations. Professsor Lu Ting is an expert in both fluid dynamics and the use of matched asymptotic expansions. His physical insight into fluid flows has led the way to finding the appropriate mathematical simplications used in the solutions to many difficult flow problems.
