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Journal ArticleDOI

On the Dynamics of Revolving Fluids

TL;DR: So much of meteorology depends ultimately upon the dynamics of revolving fluid that it is desirable to formulate as clearly as possible such simple conclusions as are within the authors' reach, in the hope that they may assist their judgment when an exact analysis seems impracticable.
Abstract: So much of meteorology depends ultimately upon the dynamics of revolving fluid that it is desirable to formulate as clearly as possible such simple conclusions as are within our reach, in the hope that they may assist our judgment when an exact analysis seems impracticable. An important contribution to this subject is that recently published by Dr. Aitken. It formed the starting point of part of the investigation which follows, but I ought perhaps to add that I do not share Dr. Aitken’s views in all respects. His paper should be studied by all interested in these questions. As regards the present contribution to the theory it may be well to premise that the limitation to symmetry round an axis is imposed throughout.
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TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Abstract: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

6,145 citations

Journal ArticleDOI
TL;DR: The authors reviewed the studies undertaken on vortex breakdown over the past 45 years and provided a "guide" to the literature and where necessary directed the reader to more indepth reviews in specific areas.

722 citations

Journal ArticleDOI
TL;DR: In this article, the authors analyse theorique et experimentale des conditions de stabilite and d'eclatement de tourbillons isoles incompressible for des valeurs elevees du nombre de Reynolds.
Abstract: Analyse theorique et experimentale des conditions de stabilite et d'eclatement de tourbillons isoles incompressibles pour des valeurs elevees du nombre de Reynolds. On rappelle des methodes d'experimentation en laboratoire qui ont ete utilisees. On decrit les deux types principaux d'eclatements de tourbillons. On discute de l'importance de la symetrie par rapport a l'axe. On donne un bref apercu de la theorie de l'onde transcritique

575 citations

Journal ArticleDOI
TL;DR: A review of vortex breakdown research can be found in this paper, where the authors give an overview of the current level of understanding and assess, in the light of the available experimental evidence, the various theoretical proposals which have been made over the years.

517 citations