Recent Developments in Rayleigh-Bénard Convection

▪ Abstract This review summarizes results for Rayleigh-Benard convection that have been obtained over the past decade or so. It concentrates on convection in compressed gases and gas mixtures with Prandtl numbers near one and smaller. In addition to the classical problem of a horizontal stationary fluid layer heated from below, it also briefly covers convection in such a layer with rotation about a vertical axis, with inclination, and with modulation of the vertical acceleration.

[1]  Spatio-temporal structures in phase-turbulent convection , 1992 .

[2]  M. Cross,et al.  Forcing of convection due to time-dependent heating near threshold , 1983, Journal of Fluid Mechanics.

[3]  Steinberg,et al.  Time dependence of flow patterns near the convective threshold in a cylindrical container. , 1985, Physical review letters.

[4]  J. Swift,et al.  Hydrodynamic fluctuations at the convective instability , 1977 .

[5]  Ronnie Mainieri,et al.  Excitation of Spirals and Chiral Symmetry Breaking in Rayleigh-B�nard Convection , 1995, Science.

[6]  P. Hohenberg,et al.  Externally modulated Rayleigh-Bénard convection: experiment and theory , 1984 .

[7]  Arne J. Pearlstein,et al.  Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots , 1989, Journal of Fluid Mechanics.

[8]  Lorenz Kramer,et al.  Convection instabilities in nematic liquid crystals , 1995 .

[9]  Vincent Croquette,et al.  Nonlinear waves of the oscillatory instability on finite convective rolls , 1989 .

[10]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[11]  Friedrich,et al.  Defect Motion in Rotating Fluids. , 1995, Physical review letters.

[12]  Wave-number selection and traveling vortex waves in spatially ramped Taylor-Couette flow. , 1990, Physical review letters.

[13]  Eberhard Bodenschatz,et al.  Importance of Local Pattern Properties in Spiral Defect Chaos , 1998 .

[14]  Michael E. Fisher,et al.  Renormalization of Critical Exponents by Hidden Variables , 1968 .

[15]  H. Beijeren,et al.  The effects of thermal noise in a Rayleigh-Benard cell near its first convective instability , 1988 .

[16]  R. M. Clever,et al.  Transition to time-dependent convection , 1974, Journal of Fluid Mechanics.

[17]  Y. Pomeau,et al.  Axisymmetric cellular structures revisited , 1985 .

[18]  Ahlers,et al.  Transitions between patterns in thermal convection. , 1991, Physical review letters.

[19]  E. Koschmieder,et al.  Heat transfer through a shallow, horizontal convecting fluid layer , 1974 .

[20]  M. Cross,et al.  The amplitude equation near the convective threshold: application to time-dependent heating experiments , 1981, Journal of Fluid Mechanics.

[21]  Spirals and chaos , 1994, Nature.

[22]  J. Buell,et al.  Wavenumber selection in large‐amplitude axisymmetric convection , 1986 .

[23]  J. Whitehead,et al.  Instabilities of convection rolls in a high Prandtl number fluid , 1971, Journal of Fluid Mechanics.

[24]  Brand,et al.  Thermally induced hydrodynamic fluctuations below the onset of electroconvection. , 1991, Physical review letters.

[25]  A. Zippelius,et al.  Pattern Selection in Rayleigh-Bénard Convection near Threshold , 1981 .

[26]  F. Reif,et al.  Enhancement of Hydrodynamic Stability by Modulation , 1962 .

[27]  G. Ahlers,et al.  Pattern Formation and Wave-Number Selection by Rayleigh–Bénard Convection in a Cylindrical Container , 1985 .

[28]  C. Bowman,et al.  Patterns, defects and integrability , 1998 .

[29]  F. Daviaud,et al.  SENSITIVITY OF CONVECTIVE STRUCTURES TO MEAN FLOW BOUNDARY CONDITIONS : A CORRELATION BETWEEN SYMMETRY AND DYNAMICS , 1997 .

[30]  Interaction and dynamics of defects in anisotropic pattern-forming systems. , 1990, Physical review letters.

[31]  K. Stewartson,et al.  On finite amplitude Bénard convection in a cylindrical container , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[32]  H. Oertel,et al.  Three-dimensional thermal cellular convection in rectangular boxes , 1988, Journal of Fluid Mechanics.

[33]  W. Pesch,et al.  Complex spatiotemporal convection patterns. , 1996, Chaos.

[34]  Schmitz,et al.  Spatially periodic modulated Rayleigh-Bénard convection. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  R. Kelly,et al.  Mixed mode convection in an inclined slot , 1993, Journal of Fluid Mechanics.

[36]  Paul Manneville,et al.  Stability and fluctuations of a spatially periodic convective flow , 1979 .

[37]  Ahlers,et al.  Thermal convection under external modulation of the driving force. I. The Lorenz model. , 1985, Physical review. A, General physics.

[38]  Ciliberto,et al.  Defects in roll-hexagon competition. , 1990, Physical review letters.

[39]  Direct transition to turbulence in rotating Bénard convection. , 1986, Physical review letters.

[40]  M. Cross,et al.  Chaotic domains: A numerical investigation. , 1994, Chaos.

[41]  P. Manneville,et al.  Zigzag instability and axisymmetric rolls in Rayleigh-Bénard convection: The effects of curvature , 1983 .

[42]  W. M. Coughran,et al.  Nonlinear pattern formation near the onset of Rayleigh-Bénard convection , 1982 .

[43]  Experimental studies of defect dynamics and interaction in electrohydrodynamic convection. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[44]  Friedrich H. Busse,et al.  Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis , 1979, Journal of Fluid Mechanics.

[45]  Department of Physics,et al.  Extensive scaling and nonuniformity of the Karhunen-Loève decomposition for the spiral-defect chaos state , 1998, chao-dyn/9808006.

[46]  Morris,et al.  Spiral defect chaos in large aspect ratio Rayleigh-Bénard convection. , 1993, Physical review letters.

[47]  D. Cannell,et al.  Noise amplification in open Taylor-Couette flow. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[48]  F. Busse,et al.  Three-dimensional convection in an inclined layer heated from below , 1992 .

[49]  R. E. Kelly,et al.  The Onset and Development of Thermal Convection in Fully Developed Shear Flows , 1994 .

[50]  G. Küppers.  The stability of steady finite amplitude convection in a rotating fluid layer , 1970 .

[51]  R. M. Clever,et al.  Finite Amplitude Longitudal Convection Rolls in an Inclined Layer , 1973 .

[52]  Hexagonal and roll flow patterns in temporally modulated Rayleigh-Bénard convection. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[53]  Alan C. Newell,et al.  ORDER PARAMETER EQUATIONS FOR PATTERNS , 1993 .

[54]  P. Manneville.  A two-dimensional model for three-dimensional convective patterns in wide containers , 1983 .

[55]  J. Hart.  Transition to a wavy vortex régime in convective flow between inclined plates , 1971, Journal of Fluid Mechanics.

[56]  J. P. Gollub.  Experiments on Spatiotemporal Chaos , 1995 .

[57]  Gunton,et al.  Spiral defect chaos in a model of Rayleigh-Bénard convection. , 1993, Physical review letters.

[58]  Lee A. Segel,et al.  Distant side-walls cause slow amplitude modulation of cellular convection , 1969, Journal of Fluid Mechanics.

[59]  Alan C. Newell,et al.  Defects are weak and self-dual solutions of the Cross-Newell phase diffusion equation for natural patterns , 1996 .

[60]  Weber,et al.  Spiral defect chaos in Rayleigh-Bénard convection. , 1994, Physical Review Letters.

[61]  M. Prange,et al.  Period Doubling Cascade to Chaotic Phase Dynamics in Taylor Vortex Flow , 1997 .

[62]  G. Kueppers,et al.  Transition from laminar convection to thermal turbulence in a rotating fluid layer , 1969, Journal of Fluid Mechanics.

[63]  G. Ahlers,et al.  Convection under rotation for Prandtl numbers near 1: Linear stability, wave-number selection, and pattern dynamics , 1997 .

[64]  Hu,et al.  Time and length scales in rotating Rayleigh-Bénard convection. , 1995, Physical review letters.

[65]  S. Ciliberto,et al.  The role of defects in the transition between different symmetries in convective patterns , 1991 .

[66]  Wu,et al.  Thermally Induced Fluctuations below the Onset of Rayleigh-Bénard Convection. , 1995, Physical review letters.

[67]  Hu,et al.  Convection near threshold for Prandtl numbers near 1. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[68]  R. Ecke,et al.  Spiral defect chaos in Rayleigh-Be´nard convection: defect population statistics , 1997 .

[69]  V. Croquette,et al.  Spatial Features of the Transition to Chaos in an Extended System , 1986 .

[70]  F. Busse,et al.  Three-dimensional convection driven by centrifugal buoyancy , 1995, Journal of Fluid Mechanics.

[71]  Steinberg,et al.  Observation of coexisting upflow and downflow hexagons in Boussinesq Rayleigh-Bénard convection. , 1996, Physical review letters.

[72]  Cross,et al.  Climbing of dislocations in nonequilibrium patterns. , 1986, Physical review. A, General physics.

[73]  Alan C. Newell,et al.  The Geometry of the Phase Diffusion Equation , 2000, J. Nonlinear Sci..

[74]  H. Haken,et al.  Pattern formation in rotating Be´nard convection , 1992 .

[75]  V. Croquette,et al.  Large-Scale Flow Characterization in a Rayleigh-Bénard Convective Pattern , 1986 .

[76]  Stephen H. Davis,et al.  Convection in a box: linear theory , 1967, Journal of Fluid Mechanics.

[77]  Transition from Spatiotemporal Chaos to Ideal Straight Rolls in Rayleigh-Benard Convection , 1997, patt-sol/9702003.

[78]  G. Ahlers,et al.  Rayleigh-Benard convection in binary-gas mixtures: Thermophysical properties and the onset of convection , 1997 .

[79]  The spatio-temporal structure of spiral-defect chaos , 1996, chao-dyn/9604013.

[80]  F. Busse,et al.  Experiments on thermal convection in rotating systems motivated by planetary problems , 1998 .

[81]  K. Hollands,et al.  On the secondary instability in inclined air layers , 1980 .

[82]  L. Tsimring.  Dynamics of penta-hepta defects in hexagonal patterns , 1996 .

[83]  John Whitehead,et al.  Finite bandwidth, finite amplitude convection , 1969, Journal of Fluid Mechanics.

[84]  P. Ashwin.  Chaotic Intermittency of Patterns in Symmetric Systems , 1999 .

[85]  F. Busse,et al.  Non-linear properties of thermal convection , 1978 .

[86]  R. Kelly,et al.  Interaction between longitudinal convection rolls and transverse waves in unstably stratified plane Poiseuille flow , 1995 .

[87]  G. Ahlers,et al.  COMPETITION BETWEEN SPIRAL-DEFECT CHAOS AND ROLLS IN RAYLEIGH-BENARD CONVECTION , 1997, patt-sol/9702004.

[88]  Eberhard Bodenschatz,et al.  Core dynamics of multi-armed spirals in Rayleigh-Bénard convection , 1996, patt-sol/9602003.

[89]  P. Hohenberg,et al.  Effects of additive noise at the onset of Rayleigh-Bénard convection. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[90]  V. Croquette.  Convective pattern dynamics at low Prandtl number: Part I , 1989 .

[91]  Alan C. Newell,et al.  Natural patterns and wavelets , 1998 .

[92]  Steinberg,et al.  Rayleigh-Bénard convection near the gas-liquid critical point. , 1993, Physical review letters.

[93]  R. J. Goldstein,et al.  Visualization of longitudinal convection roll instabilities in an inclined enclosure heated from below , 1990, Journal of Fluid Mechanics.

[94]  Structure of dislocations in the hexagonal pattern , 1993 .

[95]  G. Ahlers.  Experiments on spatio-temporal chaos , 1998 .

[96]  Tsimring,et al.  Dynamics of dislocations in hexagonal patterns. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[97]  Kristina Lerman,et al.  Experiments on three systems with non-variational aspects , 1992 .

[98]  Ciliberto,et al.  Competition between different symmetries in convective patterns. , 1988, Physical review letters.

[99]  Dynamical properties of multiarmed global spirals in Rayleigh-Bénard convection. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[100]  V. Croquette,et al.  Rayleigh-Bénard convective structures in a cylindrical container , 1983 .

[101]  L. Tsimring,et al.  Large-Scale Flow and Spiral Core Instability in Rayleigh-Benard Convection , 1996, patt-sol/9608003.

[102]  Riecke,et al.  Perfect wave-number selection and drifting patterns in ramped Taylor vortex flow. , 1987, Physical review letters.

[103]  Knobloch,et al.  Pattern selection in rotating convection with experimental boundary conditions. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[104]  F. Busse.  The oscillatory instability of convection rolls in a low Prandtl number fluid , 1972, Journal of Fluid Mechanics.

[105]  Rehberg,et al.  Direct measurement of hydrodynamic fluctuations in a binary mixture. , 1995, Physical review letters.

[106]  D. Ruth.  On the transition to transverse rolls in inclined infinite fluid layers — steady solutions , 1980 .

[107]  Rotating Rayleigh-Be´nard convection: Ku¨ppers-Lortz transition , 1991 .

[108]  A. Newell,et al.  The phase diffusion and mean drift equations for convection at finite Rayleigh numbers in large containers , 1990, Journal of Fluid Mechanics.

[109]  I. Rehberg,et al.  The influence of thermal noise on the onset of travelling-wave convection in binary fluid mixtures: an experimental investigation , 1994, Journal of Fluid Mechanics.

[110]  S. Ciliberto,et al.  Transition from hexagons to rolls in convection in fluids under non-Boussinesq conditions , 1992, Journal of Fluid Mechanics.

[111]  U. Kurzweg.  Stability of Natural Convection Within an Inclined Channel , 1970 .

[112]  A. Getling.  Formation of spatial structures in Rayleigh–Bénard convection , 1991 .

[113]  Hermann Haken,et al.  Order parameter equation and model equation for high Prandtl number. Rayleigh-Bénard convection in a rotating large aspect ratio system , 1993 .

[114]  Chaotic domain structure in rotating convection. , 1992, Physical review letters.

[115]  J. Hart.  Stability of the flow in a differentially heated inclined box , 1971, Journal of Fluid Mechanics.

[116]  G. Z. Gershuni,et al.  Stability of plane-parallel convective motion with respect to spatial perturbations: PMM vol. 33, n≗5, 1969, pp. 855–860 , 1969 .

[117]  L. Kramer,et al.  General Mathematical Description of Pattern-Forming Instabilities , 1996 .

[118]  Lev S.Tsimring.  Penta-hepta defect motion in hexagonal patterns. , 1995, Physical review letters.

[119]  Inhibition of phase turbulence close to onset of convection by permeable lateral boundary condition for the mean flow , 1989 .

[120]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[121]  Busse,et al.  Hexagonal convection cells under conditions of vertical symmetry. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[122]  Paul Manneville,et al.  Dissipative Structures and Weak Turbulence , 1995 .

[123]  Victor Steinberg,et al.  Transition between spiral and target states in Rayleigh–Bénard convection , 1994, Nature.

[124]  A. Graham.  Shear Patterns in an Unstable Layer of Air , 1934 .

[125]  H. Reed.  Gallery of Fluid Motion , 1985 .

[126]  Wave-vector field of convective flow patterns. , 1987, Physical review. A, General physics.

[127]  Swift,et al.  Pattern competition in temporally modulated Rayleigh-Bénard convection. , 1988, Physical review letters.

[128]  J. Buell,et al.  Wavenumber selection in ramped Rayleigh–Bénard convection , 1986, Journal of Fluid Mechanics.

[129]  Daniels,et al.  Pattern formation in inclined layer convection , 1999, Physical review letters.

[130]  M. Cross.  Theoretical modelling of spiral chaos in Rayleigh-Benard convection , 1996 .

[131]  F. Busse,et al.  Instabilities of longitudinal convection rolls in an inclined layer , 1977, Journal of Fluid Mechanics.

[132]  G. Ahlers,et al.  Apparatus for the study of Rayleigh–Bénard convection in gases under pressure , 1996 .

[133]  J. Gollub,et al.  Convection patterns: Time evolution of the wave-vector field. , 1985, Physical review letters.

[134]  R. Ecke,et al.  Pattern dynamics and heat transport in rotating Rayleigh-Benard convection. , 1992, Chaos.

[135]  G. Ahlers,et al.  Square Patterns in Rayleigh-Benard Convection with Rotation about a Vertical Axis , 1997, patt-sol/9802002.

[136]  M. Berry,et al.  Caustics, multiply reconstructed by Talbot interference , 1999 .

[137]  Stochastic Landau equation with time-dependent drift. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[138]  Phase dynamics of convective rolls , 1983 .

[139]  V. Croquette,et al.  Wavenumber selection in Rayleigh-Benard convective structure , 1984 .

[140]  Cross,et al.  Defect dynamics for spiral chaos in Rayleigh-Bénard convection. , 1995, Physical review letters.

[141]  M. Cross.  Ingredients of a theory of convective textures close to onset , 1982 .

[142]  A. Zippelius,et al.  Dynamics of defects in Rayleigh-Bénard convection , 1981 .

[143]  Williams,et al.  Nonlinear competition between waves on convective rolls. , 1989, Physical review. A, General physics.

[144]  F. Busse,et al.  On the stability of steady finite amplitude convection , 1965, Journal of Fluid Mechanics.

[145]  Friedrich H. Busse,et al.  The stability of finite amplitude cellular convection and its relation to an extremum principle , 1967, Journal of Fluid Mechanics.

[146]  Newell,et al.  Instabilities of dislocations in fluid patterns. , 1992, Physical review letters.