Sensitivity of binary liquid thermal convection to confinement

The stable axisymmetric convective states of a binary liquid enclosed in a vertical cylinder heated from below are exhaustively and accurately identified by pseudo-spectral numerical integration. In order to gain some insight on the influence that nearby boundaries can exert on flow dynamics, three aspect ratios (1/2, 1, and 2), as well as two types of lateral kinematic boundary conditions (either no-slip or free-slip) are investigated. The ranges over which stable quiescent, oscillatory and steady convective states extend and coexist are given. The bifurcations leading to transitions from one branch of solutions to another, as well as those that occur along the oscillatory branch, are analyzed. The most significant effect of varying boundary conditions and aspect ratio involves the route from oscillatory to steady convection. For a given configuration, that route consists of a period doubling cascade followed by chaos, or a subcritical generalized Hopf (or Neimark–Sacker) bifurcation, or a homoclinic bif...

[1]  H. Huppert,et al.  Nonlinear double-diffusive convection , 1976, Journal of Fluid Mechanics.

[2]  G. Labrosse,et al.  A FIRST INCURSION INTO THE 3D STRUCTURE OF NATURAL CONVECTION OF AIR IN A DIFFERENTIALLY HEATED CUBIC CAVITY, FROM ACCURATE NUMERICAL SOLUTIONS , 2000 .

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

[4]  H. B. Hadid,et al.  On the onset of convective instabilities in cylindrical cavities heated from below. I. Pure thermal case , 1999 .

[5]  Kolodner.  Repeated transients of weakly nonlinear traveling-wave convection. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Nadine Aubry,et al.  Characterization of dispersive chaos and related states of binary-fluid convection , 1995 .

[7]  Emmanuel Leriche,et al.  High-Order Direct Stokes Solvers with or Without Temporal Splitting: Numerical Investigations of Their Comparative Properties , 2000, SIAM J. Sci. Comput..

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

[9]  Robert P. Behringer,et al.  Rayleigh-Benard convection and turbulence in liquid helium , 1985 .

[10]  Convection in cylindrical containers at supercritical Rayleigh numbers , 1996 .

[11]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[12]  NUMERICAL STUDY OF RAYLEIGH-BE´NARD CONVECTION IN A CYLINDER , 2002 .

[13]  E. Knobloch,et al.  Onset of oscillatory binary fluid convection in finite containers. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  D. Moore,et al.  Asymmetric oscillations in thermosolutal convection , 1991, Journal of Fluid Mechanics.

[15]  Oscillatory binary fluid convection in large aspect-ratio containers. , 2001, Physical review letters.

[16]  A. Batoul,et al.  Une méthode de résolution directe (pseudo-spectrale) du problème de Stokes 2D/3D instationnaire. Application à la cavité entraînée carrée , 1994 .

[17]  E. Knobloch,et al.  Transitions to chaos in two-dimensional double-diffusive convection , 1986, Journal of Fluid Mechanics.

[18]  G. Labrosse,et al.  A DIRECT( PSEUDO-SPECTRAL) SOLVER OF THE 2D/3D STOKES PROBLEM: TRANSITION TO UNSTEADINESS OF NATURAL-CONVECTION FLOW IN A DIFFERENTIALLY HEATED CUBICAL CAVITY , 1997 .

[19]  Minimal model of binary fluid convection. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[20]  P. Lucas,et al.  Onset of Rayleigh-Bénard convection in binary liquid mixtures of 3He in 4He , 1983, Journal of Fluid Mechanics.

[21]  R. Sani,et al.  Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. I - General theory and stationary stability results , 1990 .

[22]  S. Hollinger,et al.  Pattern Formation in Binary Fluid Convection and in Systems with Throughflow , 1998 .

[23]  Schmitz,et al.  Convection in binary fluid mixtures. I. Extended traveling-wave and stationary states. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Knobloch,et al.  Oscillatory convection in binary mixtures. , 1986, Physical review. A, General physics.

[25]  Kurt Wiesenfeld,et al.  Suppression of period doubling in symmetric systems , 1984 .

[26]  J. K. Platten,et al.  Convection in Liquids , 1983 .

[27]  Hans J. Rath,et al.  Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below , 1996, Journal of Fluid Mechanics.

[28]  T. Mullin,et al.  Flow state multiplicity in convection , 1999 .