Journal ArticleDOI
Integrable and chaotic motions of four vortices II. Collision dynamics of vortex pairs
Bruno Eckhardt,Hassan Aref +1 more
TLDR
In this article, the interaction of two vortex pairs is investigated analytically and by numerical experiments from the vantage point of dynamical-systems theory, and a formal reduction to two degrees of freedom by canonical transformations and an identification and discussion of integrable cases of which one is apparently new are given.Abstract:
The interaction of two vortex pairs is investigated analytically and by numerical experiments from the vantage point of dynamical-systems theory. Vortex pairs can escape to infinity, so the phase space of this system is unbounded in contrast to that of four identical vortices investigated previously. Chaotic motion is nevertheless possible both for ‘bound states’ of the system and for ‘scattering states’. For the bound states standard Poincare section techniques suffice. For scattering states chaos appears as complex structure in the numerically generated plot of scattering angle against impact parameter. Interpretations of physical space mechanisms leading to chaos are given. Analytical characterizations of the system include a formal reduction to two degrees of freedom by canonical transformations and an identification and discussion of integrable cases of which one is apparently new.read more
Citations
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Journal ArticleDOI
Turbulence transition in pipe flow
TL;DR: Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile as discussed by the authors, which can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space.
Journal ArticleDOI
Chemical and biological activity in open flows: A dynamical system approach
TL;DR: In this paper, the authors review recent progress in this field, which became possible due to the application of methods taken from dynamical system theory, and place special emphasis on the derivation of effective rate equations which contain singular terms expressing the fact that the reaction takes place on a moving fractal catalyst, on the unstable foliation of the reaction free advection dynamics.
Book ChapterDOI
The Introductory Chapter
TL;DR: In this paper, the authors give a mathematical introduction to Geophysical Fluid Dynamics and give the description of main vortex structures that have become objects of the present book: (a) Heton, a two-layer vortex with opposite rotations in different layers, and (b) Intrathermocline lens, which is studied in this work as a vortex patch in the intermediate layer of a three-layer ocean model.
Journal ArticleDOI
Chaotic advection of fluid particles
TL;DR: In this paper, the concept of chaotic advection is introduced and a number of applications are discussed. And some emerging directions of investigation for this application of chaos to fluid mechanics are indicated.
Journal ArticleDOI
Bifurcation to chaotic scattering
TL;DR: In this article, the authors investigate a novel type of bifurcation to chaos which occurs in the context of chaotic scattering, where the deflection angle versus impact parameter is singular on a set of impact parameters which is fractal.
References
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Journal ArticleDOI
Fine structure in the dependence of final conditions on initial conditions in classical collinear H2+H dynamics
TL;DR: In this paper, the dependence of final vibrational energy, final phase, and trajectory time on the initial phase of the H2 reagent was examined on a novel potential energy surface for the collinear H3 system.