Propagation in Systems Far from Equilibrium: Proceedings of the Workshop, Les Houches, France, March 10–18, 1987

430 Pages·1988·15.354 MB·English

by  P. Manneville, H. R. Brand, J. E. Wesfreid (auth.), Dr. José E. Wesfreid, Dr. Helmut R. Brand, Dr. Paul Manneville, Dr. Gilbert Albinet, Professor Nino Boccara (eds.)

Springer Series in Synergetics
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A.l. Mandell P. Manneville, G. Albinet, N. Boccara
Propagation in
Systems Far from
Equilibrium
Proceedings of the Workshop,
Les Houches, France, March 10-18, 1987
Editors: J. E. Wesfreid, H. R. Brand,
P. Manneville, G. Albinet, and N. Boccara
With 225 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo
Dr. Jose E. Wesfreid
Laboratoire d'Hydrodynamique et Mecanique Physique, E.S.P.C.I. Paris,
10, rue Vauquelin, F-7S231 Paris Cedex OS, France
Dr. Helmut R. Brand
Fachbereich 7 (Physik), Universitat Essen, D-4300 Essen 1, Fed. Rep. of Germany
Dr. Paul Manneville
IRF-DPh-G/PSRM, CEN-Saclay, F-91191 Gif-sur-Yvette, France
Dr. Gilbert Albinet
Lab. de Recherches en Combustion, Universite de Provence,
Centre St. Jerome, F-13397 Marseille Cedex 13, France
Professor Nino Boccara
Centre de Physique Theorique, F-7431O Les Houches, France
Series Editor:
Professor Dr. Dr. h. c. Hermann Haken
Institut rur Theoretische Physik der Universitat Stuttgart, Pfaffenwaldring S7/IV,
D-7000 Stuttgart 80, Fed. Rep. of Germany and
Center for Complex Systems, Florida Atlantic University,
Boca Raton, FL 33431, USA
ISBN-13:978-3-642-73863-0 e-ISBN-13:978-3-642-73861-6
DOl: 10.1007/978-3-642-73861-6
Library of Congress Cataloging-in-Publication Data. Propagation in systems far from equilibrium: proceedings
of the workshop, Les Houches, France, March 10-18, 1987 I editors, J. E. Wesfreid ... let al.l. (Springer series
in synergetics ; v. 41) Includes index. 1. Hydrodynamics-Congresses. 2. Crystals-Growth-Congresses. I. Wes
freid, J.E. II. Series. QC150.P76 1988 532'.5-dc19 88-20146
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2154/3150-543210
Preface
Macroscopic physics provides us with a broad variety of pattern-forming sys
tems displaying propagation phenomena, from reactive fronts in combustion
to wavy structures in convection or shear flow instabilities in hydrodynamics.
Recent progress recorded in this rapidly expanding field calls for a compari
son and possibly a unification of the different approaches followed. This was
the aim of the international workshop on "Propagation in Nonequilibrium
Systems" held at the Centre de Physique Theorique des Houches (France),
March 10-18, 1987.
This workshop brought together physicists working on pattern formation
in systems far from equilibrium, applied mathematicians working on nonlin
ear dynamics involving spatial degrees of freedom,and specialists from fluid
dynamics working on open flow systems.
The lectures and contributions that were presented were organized around
three themes:
1) The problems of velocity selection and front morphology of propagating in
terfaces in multiphase media, with emphasis on recent theoretical (mathemat
ical) and experimental results on dendritic crystal growth, Saffman-Taylor
fingering, directional solidification and chemical waves.
2) The "unfolding" of large-scale, low-frequency behavior in weakly confined
homogeneous systems driven far from equilibrium, and more specifically, the
approach using envelopes for the mathematical description of textures in
different cases: steady cells, propagating waves, structural defects, phase in
stabilities; with a discussion of its concrete implementation and relevance to
laboratory experiments.
3) The implications of the presence of global downstream transport in open
flows for the nature, convective or absolute, of shear flow instabilities, with
application to real boundary layer flows or shear layers, as reported in contri
butions covering experimental situations of fundamental and/or engineering
interest.
We would like to thank all the lecturers and participants, as well as the
other members of the Organizing Committee and the staff of the Centre de
Physique Theorique, who contributed to the success of this workshop.
Financial support from the CNRS, the Universite de Provence, and the
DRET is gratefully acknowledged.
Paris, Essen J.E. Wesfreid, H.R. Brand
Gif-sur-Yvette, Marseille P. Manneville, G. Albinet
Les Houches, April 1988 N. Boccara
v
Contents
Part I Introduction
Propagation in Systems Far from Equilibrium: Introduction and
Overview
By P. Manneville, H.R. Brand, and J .E. Wesfreid .............. 2
Part II Interfaces and Fronts
Dendritic Crystal Growth: Recent Progress and Current Issues
By D.A. Kessler and H. Levine (With 4 Figures) .............. 14
Velocity Selection for Needle Crystals in the 2-D One-Sided Model
By C. Misbah ........................................ 28
The Problem of Directional Solidification Revisited
By M. Ben Amar, T. Dombre, and V. Hakim (With 3 Figures) 35
Cellular Instabilities in Directional Solidification
By S. de Cheveigne and C. Guthmann (With 7 Figures) ......... 44
Cellular and Dendritic Fronts in Directional Solidification:
Experiments by the Light of Pattern Selection
By B. Billia, H. Jamgotchian, and L.Capella (With 6 Figures) 50
On the Analogy of Anomalous Viscous Fingers with Crystalline
Dendrites
By Y. Couder (With 7 Figures) ........................... 63
Diffuse Interfaces
By P. Clavin (With 5 Figures) ............................ 78
Part III Chemical Waves
Chemical Waves and Periodic Precipitation Processes
By J. Ross (With 5 Figures) ............................. 90
Wave Propagation in Chemical Nonequilibrium Systems: New
Experimental Results
By Z. Nagy-Ungvarai and S.C. Miiller (With 13 Figures) ........ 100
VII
Spatio-Temporal Phase Patterns Near a Hopf Bifurcation in 2D
Systems
By D. Walgraef (With 4 Figures) .......................... 112
Part IV Envelope Equations and Localized Excitations
The Dynamics of Patterns: A Survey
By A.C. Newell (With 11 Figures) ......................... 122
Phase Turbulence and Mean Flow Effects in Rayleigh-Benard
Convection
By A. Pocheau (With 7 Figures) .......................... 156
Defects in Waves
By L. Gil and J. Lega (With 11 Figures) .................... 164
Propagative Structures and Localization in the Convection of a Liquid
Crystal
By A. Joets and R. Ribotta (With 6 Figures) ................. 176
Dynamics of Codimension-One Defects
By P. Coullet, C. Elphick, and D. Repaux (With 3 Figures) 185
Localized Instabilites and Nucleation of Dislocations in Convective
Rolls
By X.D. Yang, A. Joets, and R. Ribotta (With 6 Figures) ...... .. 194
Part V Phase Dynamics and Pattern Selection
Phase Dynamics - A Review and a Perspective
By H.R. Brand ....................................... 206
Phase Diffusion in a Ramped Convection Channel
By I. Rehberg and F.H. Busse (With 13 Figures) .............. 225
Pattern Selection in the Benard-Marangoni Instability
By C. Perez-Garcia, P. Cerisier, and R. Occelli (With 7 Figures) ... 232
Pattern Selection in Convective Instabilities with Axial Anisotropy
By L. Kramer, W. Zimmermann, E. Bodenschatz, and W. Pesch
(With 3 Figures) ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 240
Pattern Selection in Salt Fingers
By C. Normand (With 1 Figure) .......................... 250
Model Systems for Long-Scale Convection
By P. Metzener and S.H. Davis (With 2 Figures) .............. 258
The Kuramoto-Sivashinsky Equation: A Progress Report
By P. Manneville (With 7 Figures) ........................ 265
VIII
Part VI Propagation in Confined Systems
Two-frequency States at the Onset of Convection in Binary Fluid
Mixtures
By P. Kolodner, C.M. Surko, H.L. Williams, and A. Passner
(With 7 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 282
A Galerkin Approximation for Convection in Binary Mixtures with
Realistic Concentration Boundary Conditions
By S.J. Linz and M. Lucke (With 7 Figures) ................. 292
Convection in Binary Mixtures
By G. Ahlers, D.S. Cannell, R. Heinrichs, and T.S. Sullivan 305
Convection in Viscoelastic Fluids
By B.J.A. Zielinska (With 1 Figure) 307
An Overview of the Flow Regimes in a Circular Couette System
By C.D. Andereck and G.W. Baxter (With 7 Figures) .......... 315
New Bifurcations in a Partially Filled, Horizontal, Rotating Cylinder
By A. Aitta (With 5 Figures) ............................ 325
New Patterns in the Flow Between Two Horizontal Coaxial Rotating
Cylinders with Partially Filled Gap
By 1. Mutabazi, H. Peerhossaini, and J.E. Wesfreid (With 3 Figures) 331
Strong Resonance in Forced Oscillatory Convection
By S. Fauve ......................................... 338
Part VII Open Flow Systems
On the Absolute/Convective Nature of Primary and Secondary
Instabilities
By P. Huerre (With 13 Figures) .......................... 340
The Benard-Von Karman Instability in Laminar Regimes
By M. Provansal (With 5 Figures) ......................... 354
Nonlinear Limit-Cycle Solutions - A Rational Method for Transition
Prediction in Shear Flows?
By W. Koch (With 7 Figures) ............................ 360
Questions About an Experiment on the Wake of a Sphere in a
Stratified Fluid
By O. Thual (With 3 Figures) ............................ 369
Experimental and Theoretical Studies of the Three-Dimensional
Boundary-Layer Transition
By U. Dallmann et al. (With 14 Figures) .................... 378
IX
On the Instability of Laminar Boundary Layers Along Concave Walls
Towards Gortler Vortices
By V. Kottke (With 8 Figures) ........................... 390
Experimental Study of the Taylor-Gortler Instability
By H. Peerhossaini and J .E. Wesfreid (With 11 Figures) 399
Lattice Gas Hydrodynamics
By D. d'Humieres and P. Lallemand (With 3 Figures) 413
Index of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . .. 425
x
Part I
Introd uction