Modeling Two-dimensional Fluid Flows with Chaos Theory
Author | : J. C. Sommerer |
Publisher | : |
Total Pages | : |
Release | : 1997 |
Genre | : Fluid dynamics |
ISBN | : |
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Author | : J. C. Sommerer |
Publisher | : |
Total Pages | : |
Release | : 1997 |
Genre | : Fluid dynamics |
ISBN | : |
Author | : Martín López de Bertodano |
Publisher | : Springer |
Total Pages | : 367 |
Release | : 2016-11-09 |
Genre | : Technology & Engineering |
ISBN | : 3319449680 |
This book addresses the linear and nonlinear two-phase stability of the one-dimensional Two-Fluid Model (TFM) material waves and the numerical methods used to solve it. The TFM fluid dynamic stability is a problem that remains open since its inception more than forty years ago. The difficulty is formidable because it involves the combined challenges of two-phase topological structure and turbulence, both nonlinear phenomena. The one dimensional approach permits the separation of the former from the latter.The authors first analyze the kinematic and Kelvin-Helmholtz instabilities with the simplified one-dimensional Fixed-Flux Model (FFM). They then analyze the density wave instability with the well-known Drift-Flux Model. They demonstrate that the Fixed-Flux and Drift-Flux assumptions are two complementary TFM simplifications that address two-phase local and global linear instabilities separately. Furthermore, they demonstrate with a well-posed FFM and a DFM two cases of nonlinear two-phase behavior that are chaotic and Lyapunov stable. On the practical side, they also assess the regularization of an ill-posed one-dimensional TFM industrial code. Furthermore, the one-dimensional stability analyses are applied to obtain well-posed CFD TFMs that are either stable (RANS) or Lyapunov stable (URANS), with the focus on numerical convergence.
Author | : Paul Manneville |
Publisher | : World Scientific |
Total Pages | : 456 |
Release | : 2010 |
Genre | : Science |
ISBN | : 1848163924 |
This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.
Author | : Christos H Skiadas |
Publisher | : World Scientific |
Total Pages | : 467 |
Release | : 2011-05-31 |
Genre | : Science |
ISBN | : 9814460478 |
The work done in chaotic modeling and simulation during the last decades has changed our views of the world around us and has introduced new scientific tools, methods and techniques. Advanced topics of these achievements are included in this volume on Chaos Theory which focuses on Chaotic Modeling, Simulation and Applications of the nonlinear phenomena. This volume includes the best papers presented in the 3rd International Conference on CHAOS. This interdisciplinary conference attracted people from many scientific fields dealing with chaos, nonlinear dynamics, fractals and the works presented and the papers included here are of particular interest that could provide a broad understanding of chaos in its various forms.The chapters relate to many fields of chaos including Dynamical and Nonlinear Systems, Attractors and Fractals, Hydro-Fluid Dynamics and Mechanics, Chaos in Meteorology and Cosmology, Chaos in Biology and Genetics, Chaotic Control, Chaos in Economy and Markets, and Computer Composition and Chaotic Simulations, including related applications.
Author | : Hassan Aref |
Publisher | : Pergamon |
Total Pages | : 396 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : |
This volume contains a collection of papers selected by Professor H. Aref, who pioneered chaotic advection and established it as an important discipline in nonlinear dynamics. These papers represent not only the latest developments in this subject: in addition some of the longer articles serve as an excellent introduction to the subject, suitable for beginners, with only a basic knowledge of nonlinear dynamics. With numerous illustrations and extensive references throughout, this volume provides an inspirational collection of examples for researchers concerned with a wide variety of problems that involve fluid mixing and related processes.
Author | : Julien Clinton Sprott |
Publisher | : World Scientific |
Total Pages | : 302 |
Release | : 2010-03-22 |
Genre | : Mathematics |
ISBN | : 9814468673 |
This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.
Author | : Raymond A. Humble |
Publisher | : Eburon Uitgeverij B.V. |
Total Pages | : 338 |
Release | : 2008 |
Genre | : Organizational change |
ISBN | : 9059722957 |
Author | : Marcel Lesieur |
Publisher | : Springer Science & Business Media |
Total Pages | : 435 |
Release | : 2012-12-06 |
Genre | : Technology & Engineering |
ISBN | : 9400905335 |
Turbulence is a dangerous topic which is often at the origin of serious fights in the scientific meetings devoted to it since it represents extremely different points of view, all of which have in common their complexity, as well as an inability to solve the problem. It is even difficult to agree on what exactly is the problem to be solved. Extremely schematically, two opposing points of view have been advocated during these last ten years: the first one is "statistical", and tries to model the evolution of averaged quantities of the flow. This com has followed the glorious trail of Taylor and Kolmogorov, munity, which believes in the phenomenology of cascades, and strongly disputes the possibility of any coherence or order associated to turbulence. On the other bank of the river stands the "coherence among chaos" community, which considers turbulence from a purely deterministic po int of view, by studying either the behaviour of dynamical systems, or the stability of flows in various situations. To this community are also associated the experimentalists who seek to identify coherent structures in shear flows.
Author | : Radford Mitchell |
Publisher | : |
Total Pages | : |
Release | : 2013 |
Genre | : Fluid dynamics |
ISBN | : |
The research in this thesis was motivated by a desire to understand the mixing properties of quasi-two-dimensional flows whose time-dependence arises naturally as a result of fluid-dynamic instabilities. Additionally, we wished to study how flows such as these transition from the laminar into the turbulent regime. This thesis presents a numerical and theoretical investigation of a particular fluid dynamical system introduced by Kolmogorov. It consists of a thin layer of electrolytic fluid that is driven by the interaction of a steady current with a magnetic field produced by an array of bar magnets. First, we derive a theoretical model for the system by depth-averaging the Navier-Stokes equation, reducing it to a two-dimensional scalar evolution equation for the vertical component of vorticity. A code was then developed in order to both numerically simulate the fluid flow as well as to compute invariant solutions. As the strength of the driving force is increased, we find a number of steady, time-periodic, quasiperiodic, and chaotic flows as the fluid transitions into the turbulent regime. Through long-time advection of a large number of passive tracers, the mixing properties of the various flows that we found were studied. Specifically, the mixing was quantified by computing the relative size of the mixed region as well as the mixing rate. We found the mixing efficiency of the flow to be a non-monotonic function of the driving current and that significant changes in the flow did not always lead to comparable changes in its transport properties. However, some very subtle changes in the flow dramatically altered the degree of mixing. Using the theory of chaos as it applies to Hamiltonian systems, we were able to explain many of our results.
Author | : Oleg G. Bakunin |
Publisher | : Springer Science & Business Media |
Total Pages | : 349 |
Release | : 2011-08-29 |
Genre | : Science |
ISBN | : 3642203507 |
The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.