Complex spatiotemporal convection patterns.

This paper reviews recent efforts to describe complex patterns in isotropic fluids (Rayleigh-Benard convection) as well as in anisotropic liquid crystals (electro-hydrodynamic convection) when driven away from equilibrium. A numerical scheme for solving the full hydrodynamic equations is presented that allows surprisingly well for a detailed comparison with experiments. The approach can also be useful for a systematic construction of models (order parameter equations). (c) 1996 American Institute of Physics.

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

[2]  Hu,et al.  Spatial and temporal averages in chaotic patterns. , 1993, Physical review letters.

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

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

[5]  Mean flows and the onset of chaos in large-cell convection. , 1988, Physical review letters.

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

[7]  W. Peltier.  Mantle convection : plate tectonics and global dynamics , 1989 .

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

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

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

[11]  M. Cross.  Derivation of the amplitude equation at the Rayleigh–Bènard instability , 1980 .

[12]  L. Kramer,et al.  The electrohydrodynamic instability in homeotropic nematic layers , 1992 .

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

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

[15]  James A. Krumhansl,et al.  Nonlinear science: toward the next frontiers , 1993 .

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

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

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

[19]  K. Heikes,et al.  Convection in a Rotating Layer: A Simple Case of Turbulence , 1980, Science.

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

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

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

[23]  D. Gottlieb,et al.  Numerical analysis of spectral methods , 1977 .

[24]  L. Kramer,et al.  On the theory of Rayleigh-Bénard convection in homeotropic nematic liquid crystals , 1992 .

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

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

[27]  Steinberg,et al.  Traveling waves and defect-initiated turbulence in electroconvecting nematics. , 1989, Physical review letters.

[28]  L. Gil,et al.  Defect-mediated turbulence. , 1989 .

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

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

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

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

[33]  J. W. Eastwood,et al.  Springer series in computational physics Editors: H. Cabannes, M. Holt, H.B. Keller, J. Killeen and S.A. Orszag , 1984 .

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

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

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

[37]  Haken,et al.  Traveling waves and pulses in a two-dimensional large-aspect-ratio system. , 1990, Physical review. A, Atomic, molecular, and optical physics.

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

[39]  Weakly nonlinear theory of pattern-forming systems with spontaneously broken isotropy. , 1996, Physical review letters.