Download or read book Equilibrium and Stability in Vortex and Wave Flows written by Paolo Luzzatto Fegiz and published by . This book was released on 2011 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stability of a Vortex Sheet in Non equilibrium Flows written by K. C. Wang and published by . This book was released on 1960 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report the stability of a plane vortex sheet between two uniform streams with respect to small disturbances is examined when the two media are dissociating diatomic gases such as oxygen and nitrogen. For the equilibrium and frozen cases, it is found that the eigenvalue equation is formally identical with that of the conventional case, and the stability is decreased due to the dissociation. For the non-equilibrium case, the eigenvalue equation is a complex one and depends on the wave number of the disturbances, the vortex sheet is shown to be always unstable. Included also is a discussion of the stability of a vortex sheet between two equal but opposite steady streams from the consideration of pressure distribution.

Download or read book Calculations of the Stability of Some Axisymmetric Flows Proposed as a Model of Vortex Breakdown written by Nessan Mac Giolla Mhuiris and published by . This book was released on 1986 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Small amplitude steady water waves with vorticity written by Evgeniy Lokharu and published by Linköping University Electronic Press. This book was released on 2017-01-30 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of describing two-dimensional traveling water waves is considered. The water region is of finite depth and the interface between the region and the air is given by the graph of a function. We assume the flow to be incompressible and neglect the effects of surface tension. However we assume the flow to be rotational so that the vorticity distribution is a given function depending on the values of the stream function of the flow. The presence of vorticity increases the complexity of the problem and also leads to a wider class of solutions. First we study unidirectional waves with vorticity and verify the Benjamin-Lighthill conjecture for flows whose Bernoulli constant is close to the critical one. For this purpose it is shown that every wave, whose slope is bounded by a fixed constant, is either a Stokes or a solitary wave. It is proved that the whole set of these waves is uniquely parametrised (up to translation) by the flow force which varies between its values for the supercritical and subcritical shear flows of constant depth. We also study large-amplitude unidirectional waves for which we prove bounds for the free-surface profile and for Bernoulli’s constant. Second, we consider small-amplitude waves over flows with counter currents. Such flows admit layers, where the fluid flows in different directions. In this case we prove that the initial nonlinear free-boundary problem can be reduced to a finite-dimensional Hamiltonian system with a stable equilibrium point corresponding to a uniform stream. As an application of this result, we prove the existence of non-symmetric wave profiles. Furthermore, using a different method, we prove the existence of periodic waves with an arbitrary number of crests per period.

Download or read book Stability of Parallel Flows written by R. Betchov and published by Elsevier. This book was released on 2012-12-02 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability of Parallel Flows provides information pertinent to hydrodynamical stability. This book explores the stability problems that occur in various fields, including electronics, mechanics, oceanography, administration, economics, as well as naval and aeronautical engineering. Organized into two parts encompassing 10 chapters, this book starts with an overview of the general equations of a two-dimensional incompressible flow. This text then explores the stability of a laminar boundary layer and presents the equation of the inviscid approximation. Other chapters present the general equations governing an incompressible three-dimensional flow, which requires the massive use of a computer. This book discusses as well the experimental studies on the oscillations of the boundary layer wherein the mean flow is affected by the presence of oscillations. The final chapter describes the concept of the stability of turbulent flows found in boundary layers, wakes, and jets. This book is a valuable resource for physicists, mathematicians, engineers, scientists, and researchers.

Download or read book Stability of Two fluid Wheel Flows with an Imposed Uniform Axial Magnetic Field written by Carl F. Monnin and published by . This book was released on 1969 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydrodynamic stability and vortex containment of two fluid wheel flow to helical disturbances contained by axial magnetic field.

Download or read book Numerical Calculations of the Stability of Some Axisymmetric Flows Proposed as a Model for Vortex Breakdown written by Nessan Mac Giolla Mhuiris and published by . This book was released on 1986 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mechanics Of Fluid Deformations Rigid Body Rotations And Plane Channel Flow Stability written by Oleg V Troshkin and published by World Scientific. This book was released on 2021-03-22 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a new approach to analyzing hydrodynamic stability.With the use of standard remedies of functional analysis, theory of boundary value problems and infinitesimal Lie algebras, it is shown in the book that large vortex mushrooms of an ideal incompressible fluid in a vertical strip behind a water hammer proves to be 2D (plane-parallel) nonlinear (for arbitrary disturbances of initial velocities) and long wave stable. It is one of the many examples provided in the book discussing hydrodynamic stability.

Download or read book Stability of a Plane Vortex Sheet Between Gases Exchanging Heat by Radiation written by Burton E. Eno and published by . This book was released on 1971 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Two Cases of Symmetry Breaking of Free Surface Flows written by Hamid Ait Abderrahmane and published by . This book was released on 2008 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hydrodynamic Stability of Fluid Flows written by John Trevor Stuart and published by . This book was released on 1968 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1971 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability and Transition in Shear Flows written by Peter J. Schmid and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.

Download or read book Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and published by . This book was released on 1961-04 with total page 1746 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fluid Vortices written by Sheldon Green and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 905 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid Vortices is a comprehensive, up-to-date, research-level overview covering all salient flows in which fluid vortices play a significant role. The various chapters have been written by specialists from North America, Europe and Asia, making for unsurpassed depth and breadth of coverage. Topics addressed include fundamental vortex flows (mixing layer vortices, vortex rings, wake vortices, vortex stability, etc.), industrial and environmental vortex flows (aero-propulsion system vortices, vortex-structure interaction, atmospheric vortices, computational methods with vortices, etc.), and multiphase vortex flows (free-surface effects, vortex cavitation, and bubble and particle interactions with vortices). The book can also be recommended as an advanced graduate-level supplementary textbook. The first nine chapters of the book are suitable for a one-term course; chapters 10--19 form the basis for a second one-term course.

Download or read book A Weakly Nonlinear Theory for Wave vortex Interactions in Curved Channel Flow written by Bart A. Singer and published by . This book was released on 1992 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Wave and Stability in Fluids written by Din-Yu Hsieh and published by World Scientific. This book was released on 1994 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level textbook covers the topics of sound waves, water waves and stability problems in fluids. It also touches upon the subject of chaos which is related to stability problems. It aims to lead students in an accessible and efficient way to this important subject area in fluid mechanics and applied mathematics. The emphasis is on gaining an understanding of the essential features of the subject matter, thus often ignoring complicating details which may confuse non-experts. The topics chosen also reflect the personal bias and research activity of the authors.