Springer Series in Synergetics Editor: Hermann Haken Synergetics, an interdisciplinary field of research, is concerned with the cooper ation of individual parts of a system that produces macroscopic spatial, temporal or functional structures. It deals with deterministic as well as stochastic processes. 1 Synergetics An Introduction 3rd Edition 24 Chaos and Statistical Methods By H. Haken Editor: Y. Kuramoto 2 Synergetics A Workshop 25 Dynamics of Hierarchical Systems Editor: H. Haken An Evolutionary Approach By 1.S. Nicolis 3 Synergetics Far from Equilibrium Editors: A. Pacault. e. Vidal 26 Self-Organization and Management of Social Systems 4 Structnral Stability in Physics Editors: H. Ulrich, G.l.B. Probst Editors: W. Giittinger, H. Eikemeier 5 Pattern Formation by Dynamic Systems and 27 Non-Eqnilibrium Dynamics in Chemical Pattern Recognition Editor: H. Haken Systems Editors: e. Vidal, A. Pacault 6 Dynamics of Synergetic Systems 28 Self-Organization Autowaves and Structures Editor: H. Haken Far from Equilibrium Editor: V. I. Krinsky 7 Problems of Biological Physics By L. A. Blumenfeld . 29 Temporal Order 8 Stochastic Nonlinear Systems Editors: L. Rensing, N. I. Iaeger in Physics. Chemistry. and Biology 30 Dynamical Problems in Soliton Systems Editors: L. Arnold. R. Lefever Editor: S. Takeno 9 Nnmerical Methods in the Stndy of Critical 31 Complex Systems - Operational Approaches Phenomena Editors: J. Della Dora. in Neurobiology, Physics, and Computers 1. Demongeot. B. Lacolle Editor: H. Haken 10 The Kinetic Theory of Electromagnetic Processes By Yu. L. Klimontovich 32 Dimensions and Entropies in Chaotic Systems 11 Chaos and Order in Nature Quantification of Complex Behavior Editor: H. Haken Editor: G. Mayer-Kress 12 Nonlinear Phenomena in Chemical Dynamics 33 Selforganization by Nonlinear Irreversible Editors: C. Vidal, A. Pacault Processes Editors: W. Ebeling, H. Ulbricht 13 Handbook of Stochastic Methods 34 Instabilities and Chaos in Quantum Optics for Physics. Chemistry. and the Natural Sciences Editors: F. T. Arecchi, R. G. Harrison 2nd Edition By e. W. Gardiner 14 Concepts and Models of a Quantitative 35 Noneqnilibrium Phase Thansitions in Sociology The Dynamics of Interacting Semiconductors Self-Organization Induced by Populations By W. Weidlich. G. Haag Generation and Recombination Processes 15 Noise-Induced Transitions Theory and By E. Scholl Applications in Physics, Chemistry, and Biology 36 Temporal Disorder in Human By W. Horsthemke, R. Lefever Oscillatory Systems 16 Physics of Bioenergetic Processes Editors: L. Rensing, U. an der Heiden, By L. A. Blumenfeld M.e. Mackey 17 Evolntion of Order and Chaos in Physics. Chemistry. and Biology Editor H. Haken 37 The Physics of Structure Formation Theory and Simulation 18 The Fokker-Planck Equation Editors: W. Giittinger and G. Dangelmayr By H. Risken 19 Chemical Oscillations, Waves, and Turbulence 38 Computational Systems - Natural and By Y. Kuramoto Artificial Editor: H. Haken 20 Advanced Synergetics 2nd Edition 39 From Chemical to Biological Organization By H. Haken Editors: M. Markus, S. e. Miiller, G. Nicolis 21 Stochastic Phenomena and Chaotic Behavionr in Complex Systems Editor: P. Schuster 40 Information and Self-Organization A Macroscopic Approach to Complex Systems 22 Synergetics - From Microscopic to Macroscopic ByH. Haken Order Editor: E. Frehland 23 Synergetics of the Brain 41 Propagation in Systems Far from Eqnilibrium Editors: E. Ba~ar. H. Flohr. H. Haken. Editors: J.E. Wesfreid, H.R. Brand, 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 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1988 Softcover reprint of the hardcover 1s t edition 1988 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 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