Download or read book Statistical Equilibria and Coherent Structures in Two dimensional Magnetohydrodynamic Turbulence written by Richard K. Jordan and published by . This book was released on 1994 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Statistical Equilibrium Model of Coherent Structures in Magnetohydrodynamics written by Richard Jordan and published by . This book was released on 1994 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A statistical equilibrium theory is developed which characterizes the large-scale coherent structures that emerge during the course of the evolution of an ideal two-dimensional magnetofluid. Macrostates are defined to be local joint probability distributions, or Young measures, on the values of the fluctuating magnetic field and velocity field at each point in the spatial domain. The most probable macrostate is found by maximizing a Kullback-Liebler entropy functional subject to constraints dictated by the conserved integrals of the ideal dynamics. This maximum entropy macrostate is, for each point in the spatial domain, a Gaussian probability distribution, whose local mean is an exact stationary solution of the evolution equations of the magnetohydrodynamic system. The predictions of the statistical equilibrium model are found to be in excellent qualitative and quantitative agreement with recent high resolution numerical simulations of turbulence in slightly dissipative two-dimensional magnetofluids."
Download or read book Ideal Magnetofluid Turbulence in Two Dimensions written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1996 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A continuum model of coherent structures in two-dimensional magnetohydrodynamic turbulence is developed. These structures are macroscopic states which persist amongst the turbulent microscopic fluctuations, typically as magnetic islands with flow. They are modeled as statistical equilibrium states for the ideal (nondissipative) dynamics, which conserves energy and families of cross-helicity and flux integrals. The model predicts that an ideal magnetofluid will evolve into a turbulent relaxed state having steady mean magnetic and velocity fields, and Gaussian local fluctuations in these fields. Excellent qualitative and quantitative agreement is found with the results of direct numerical simulations. A rigorous justification of the theory is also provided, in the sense that the continuum model is derived from a lattice model in a fixed-volume, small-spacing limit. This construction uses the discrete Fourier transform to link the discretization of x-space with the truncation of k-space. The lattice model is defined by the most probable distribution on the discretized phase space that respects the approximated dynamical constraints. A concentration property shows that this distribution is equivalent to the microcanonical distribution in the continuum limit."
Download or read book Parametrized Measures and Variational Principles written by Pablo Pedregal and published by Birkhäuser. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets. Nonetheless, weak conver gence does not behave as one would desire with respect to nonlinear functionals and operations. This difficulty is what makes nonlinear analysis much harder than would normally be expected. Parametrized measures is a device to under stand weak convergence and its behavior with respect to nonlinear functionals. Under suitable hypotheses, it yields a way of representing through integrals weak limits of compositions with nonlinear functions. It is particularly helpful in comprehending oscillatory phenomena and in keeping track of how oscilla tions change when a nonlinear functional is applied. Weak convergence also plays a fundamental role in the modern treatment of the calculus of variations, again because uniform bounds in norm for se quences allow to have weak convergent subsequences. In order to achieve the existence of minimizers for a particular functional, the property of weak lower semicontinuity should be established first. This is the crucial and most delicate step in the so-called direct method of the calculus of variations. A fairly large amount of work has been devoted to determine under what assumptions we can have this lower semicontinuity with respect to weak topologies for nonlin ear functionals in the form of integrals. The conclusion of all this work is that some type of convexity, understood in a broader sense, is usually involved.
Download or read book Maximum Entropy and Bayesian Methods written by Kenneth M. Hanson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Fifteenth International Workshop on Maximum Entropy and Bayesian Methods, Santa Fe, New Mexico, USA, 1995
Download or read book Advances in Geometric Analysis and Continuum Mechanics written by Paul Concus and published by International Press of Boston. This book was released on 1994-12-31 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume documents a conference celebrating Robert Finn's 70th birthday. The introduction discusses Finn's career, and highlights his contributions to the field of mathematics and its applications. The following papers cover advances in geometric analysis and continuum mechanics.
Download or read book Fundamental Problematic Issues in Turbulence written by Albert Gyr and published by Birkhäuser. This book was released on 2012-12-06 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of contributions on a variety of mathematical, physical and engineering subjects related to turbulence. Topics include mathematical issues, control and related problems, observational aspects, two- and quasi-two-dimensional flows, basic aspects of turbulence modeling, statistical issues and passive scalars.
Download or read book Progress in Turbulence Research written by Yeshajahu Unger and published by AIAA. This book was released on 1994 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Mechanics of Organized Structures in Two dimensional Magnetofluid Turbulence written by Richard Jordan and published by . This book was released on 1997 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2002 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics of Two Dimensional Turbulence written by Sergei Kuksin and published by Cambridge University Press. This book was released on 2012-09-20 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier-Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) - proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.
Download or read book Statistical Analysis of a Numerical Simulation of Two dimensional Turbulence written by Boris Vasiliev and published by . This book was released on 2000 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An important feature of the time evolution of the vorticity fields in two-dimensional turbulence is the emergence of isolated and coherent structures or vortices. A vortex is a region enclosed by a closed contour, or equivalently a disjoint component, of a sufficiently high value of the vorticity field." --
Download or read book Dynamics and Coherent Structures in Two dimensional Turbulence written by Yang Liao and published by . This book was released on 2015 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Constructive Modeling of Structural Turbulence and Hydrodynamic Instabilities written by Oleg Mikha?lovich Belot?serkovski? and published by World Scientific. This book was released on 2009 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an original approach in the research of structural analysis of free developed shear compressible turbulence at high Reynolds number on the base of direct numerical simulation (DNS) and instability evolution for ideal medium (integral conservation laws) with approximate mechanism of dissipation (FLUX dissipative monotone ?upwind? difference schemes) and does not use any explicit sub-grid approximation and semi-empirical models of turbulence. Convective mixing is considered as a principal part of conservation law.Appropriate hydrodynamic instabilities (free developed shear turbulence) are investigated from unique point of view. It is based on the concept of large ordered structures with stochastic core of small scale developed turbulence (?turbulent spot?). Decay of ?turbulent spot? are simulated by Monte Carlo method. Proposed approach is based on two hypotheses: statistical independence of the characteristic of large ordered structures (LOS) and small-scale turbulence (ST) ?and? weak influence of molecular viscosity (or more generally, dissipative mechanism) on properties of large ordered structures.Two versions of instabilities, due to Rayleigh-Taylor and Richtmyer-Meshkov are studied detail by the three-dimensional calculations, extended to the large temporal intervals, up to turbulent stage and investigation turbulent mixing zone (TMZ).The book covers both the fundamental and practical aspects of turbulence and instability and summarizes the result of numerical experiments conducted over 30 years period with direct participation of the author.In the book are cited the opinions of the leading scientists in this area of research: Acad. A S Monin (Russia), Prof. Y Nakamura (Japan, Nagoya University) and Prof. F Harlow (USA, Los-Alamos).
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1994 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Approaches and Concepts in Turbulence written by Themistocles A. Dracos and published by Birkhauser. This book was released on 1993 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hydrodynamic and Magnetohydrodynamic Turbulent Flows written by A. Yoshizawa and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: TUrbulence modeling encounters mixed evaluation concerning its impor tance. In engineering flow, the Reynolds number is often very high, and the direct numerical simulation (DNS) based on the resolution of all spatial scales in a flow is beyond the capability of a computer available at present and in the foreseeable near future. The spatial scale of energetic parts of a turbulent flow is much larger than the energy dissipative counterpart, and they have large influence on the transport processes of momentum, heat, matters, etc. The primary subject of turbulence modeling is the proper es timate of these transport processes on the basis of a bold approximation to the energy-dissipation one. In the engineering community, the turbulence modeling is highly evaluated as a mathematical tool indispensable for the analysis of real-world turbulent flow. In the physics community, attention is paid to the study of small-scale components of turbulent flow linked with the energy-dissipation process, and much less interest is shown in the foregoing transport processes in real-world flow. This research tendency is closely related to the general belief that universal properties of turbulence can be found in small-scale phenomena. Such a study has really contributed much to the construction of statistical theoretical approaches to turbulence. The estrangement between the physics community and the turbulence modeling is further enhanced by the fact that the latter is founded on a weak theoretical basis, compared with the study of small-scale turbulence.
