Double-diffusive Marangoni convection in a rectangular cavity: Transition to chaos

Abstract Transition to chaos in double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the special case when the resultant thermal and solutal Marangoni effects are equal and opposing. Direct numerical simulation is used and some techniques from nonlinear dynamics are adopted to identify the different dynamic regimes. It is found that the supercritical solution branch takes a quasi-periodicity and phase locking route to chaos while the subcritical branch follows the Ruelle–Takens–Newhouse scenario. Transient intermittency in the supercritical branch is observed and physical instability mechanisms of the subcritical branch are identified.

[1]  P. Grassberger,et al.  Estimation of the Kolmogorov entropy from a chaotic signal , 1983 .

[2]  J. Eckmann.  Roads to turbulence in dissipative dynamical systems , 1981 .

[3]  Edoardo Bucchignani,et al.  Horizontal thermal convection in a shallow cavity: oscillatory regimes and transition to chaos , 2000 .

[4]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[5]  Pierre Bergé,et al.  Order within chaos : towards a deterministic approach to turbulence , 1984 .

[6]  Celso Grebogi,et al.  Are three-frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems , 1983 .

[7]  J. D. Farmer,et al.  Chaotic attractors of an infinite-dimensional dynamical system , 1982 .

[8]  T. Jue.  Numerical analysis of thermosolutal Marangoni and natural convection flows , 1998 .

[9]  J. Gollub,et al.  Many routes to turbulent convection , 1980, Journal of Fluid Mechanics.

[10]  Kwang-Tzu Yang,et al.  Thermal convection in small enclosures: an atypical bifurcation sequence , 1995 .

[11]  K. Arafune,et al.  Interactive thermal and solutal Marangoni convection during compound semiconductor growth in a rectangular open boat , 2001 .

[12]  K. Arafune,et al.  Interactive Solutal and Thermal Marangoni Convection in a Rectangular Open Boat , 1998 .

[13]  Y. Li,et al.  Double-diffusive Marangoni convection in a rectangular cavity: Onset of convection , 2010 .

[14]  P. Kolodner,et al.  Nonchaotic Rayleigh-Bénard Convection with Four and Five Incommensurate Frequencies , 1984 .

[15]  P. Cerisier,et al.  Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection , 2007 .

[16]  K. Ghorayeb,et al.  Double diffusive convection in a vertical rectangular cavity , 1997 .

[17]  Kwang-Tzu Yang,et al.  Rayleigh-Bénard Convection in a Small Aspect Ratio Enclosure: Part I—Bifurcation to Oscillatory Convection , 1993 .

[18]  Kwang-Tzu Yang,et al.  Rayleigh-Bénard Convection in a Small Aspect Ratio Enclosure: Part II—Bifurcation to Chaos , 1993 .

[19]  Rachid Bennacer,et al.  Double diffusion in a vertical fluid layer: Onset of the convective regime , 1994 .

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

[21]  Bifurcation analysis of double-diffusive convection with opposing horizontal thermal and solutal gradients , 1998 .

[22]  T. Bergman.  Numerical simulation of double‐diffusive Marangoni convection , 1986 .

[23]  K. Ghorayeb,et al.  Onset of oscillatory flows in double-diffusive convection , 1999 .

[24]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .