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Modulated rotating convection: radially travelling concentric rolls

Published online by Cambridge University Press:  11 July 2008

A. RUBIO ,
J. M. LOPEZ  and
F. MARQUES
A. RUBIO
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
J. M. LOPEZ
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
F. MARQUES
Affiliation:
Departament de Física Aplicada, Univ. Politècnica de Catalunya, Barcelona 08034, Spain
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Abstract

Recent experiments in rotating convection have shown that the spatio-temporal bulk convective state with Küppers–Lortz dynamics can be suppressed by small-amplitude modulations of the rotation rate. The resultant axisymmetric pulsed target patterns were observed to develop into axisymmetric travelling target patterns as the modulation amplitude and Rayleigh number were increased. Using the Navier–Stokes–Boussinesq equations with physical boundary conditions, we are able to numerically reproduce the experimental results and gain physical insight into the responsible mechanism, relating the onset of the travelling target patterns to a symmetry-restoring saddle-node on an invariant circle bifurcation. Movies are available with the online version of the paper.

JFM classification

Nonlinear Dynamical Systems: Pattern formation Nonlinear Dynamical Systems: Chaos
Type
Papers
Information
Journal of Fluid Mechanics , Volume 608 , 10 August 2008 , pp. 357 - 378
Copyright
Copyright © Cambridge University Press 2008

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References

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Rubio et al. supplementary movie

Movie 1. Numerical simulation of Küpper--Lortz spatio-temporal chaos in Rayleigh--Bénard convection with constant rotation, showing contours of the temperature perturbation field, Θ, at mid-height (z=0) for Rayleigh number Ra=2868.8, mean angular velocity Ω0=23.6 and aspect ratio γ=11.8 over 450 viscous times at 108 viscous times per second, repeated 10 times. This movie corresponds to figure 1 in the paper.

Download Rubio et al. supplementary movie(Video)
Video 4.9 MB

Rubio et al. supplementary movie

Movie 2. Numerical simulation of a pulsed target pattern in Rayleigh--Bénard convection with modulated rotation. At each forcing period, Stokes layers form at the top and bottom boundaries before being deflected into the sidewall to create a strong radial jet that displaces the target pattern over the course of the forcing period. Shown are contours of the temperature field for Ra=2700, Ω0=Ωm=23.6 (where Ωm is the modulation frequency),  relative modulation amplitude A=0.05 and γ=11.8. Ten forcing periods are shown at a rate of 0.266 viscous times per second. This movie corresponds to figure 7(b) in the paper.

Download Rubio et al. supplementary movie(Video)
Video 2.9 MB

Rubio et al. supplementary movie

Movie 3. Numerical simulation of a travelling target state in Rayleigh--Bénard convection with modulated rotation. By raising the Rayleigh number from Ra=2700 to Ra=2705 the target pattern loses stability to a travelling target pattern in which the axisymmetric plumes slowly recede into the centre. Shown are contours of the temperature field for Ra=2705, Ω0=Ωm=23.6, A=0.05 and γ=11.8 over 2500 viscous times at a rate of 102 viscous times per second. This movie corresponds to the space-time diagram shown in figure 12(a) in the paper.

Download Rubio et al. supplementary movie(Video)
Video 489.5 KB

Rubio et al. supplementary movie

Movie 4. Numerical simulation of a travelling target state. Beyond the onset of the travelling target patterns, the solution behaves more like a harmonic oscillator, although the slow-fast nature of the solution is still evident. Shown are contours of the temperature field at Ra=2844, Ω0=Ωm=23.6, A=0.18 and γ=11.8 over 2500 viscous times at a rate of 102 viscous times per second. This movie corresponds to the space--time diagram shown in figure 12(b) in the paper.

Download Rubio et al. supplementary movie(Video)
Video 1.7 MB

Rubio et al. supplementary movie

Movie 5. Numerical simulation of a travelling target state. Far beyond the onset of the travelling target patterns, the solution behaves like a harmonic oscillator. Shown are contours of the temperature field at Ra=2840, Ω0=Ωm=23.6, A=0.06 and γ=11.8 over 2500 viscous times at a rate of 102 viscous times per second. This movie corresponds to the space--time diagram shown in figure 12(c) in the paper.

Download Rubio et al. supplementary movie(Video)
Video 5.2 MB