scholarly journals Nonlinear Bifurcations to Time-dependent Rayleigh?Benard Convection

1988 ◽  
Vol 41 (1) ◽  
pp. 63
Author(s):  
JM Lopez ◽  
JO Murphy
Keyword(s):  
Vertical Component ◽  
Single Mode ◽  
Time Dependent ◽  
Convection Cell ◽  
Initial Growth ◽  
Periodic Behaviour ◽  
Parameter Ranges ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Dependent Behaviour

The single-mode equations of Boussinesq thermal convection have been extended to include a toroidal component of velocity and hence the associated vertical component of vorticity. This formulation allows, under certain determined conditions, the purely poloidal solutions to become unstable to toroidal perturbations via symmetry breaking bifurcations. The bifurcation sequences are governed by a three parameter family: the aspect ratio of the convection cell, the Prandtl number of the fluid and the Rayleigh number of the flow. The initial growth of the vertical vorticity has been found always to be steady. However, in certain parameter ranges there are transitions leading to time-dependent behaviour via a Hopf bifurcation which may be in the form of symmetrical oscillations, asymmetrical oscillations, doubly-periodic behaviour or, possibly, chaos, depending on the form of the transient poloidal phase of the evolution.

The Role of Kinetic Boundary Conditions in Generating Type II Solutions for Rayleigh-Benard Convection

1985 ◽  
Vol 6 (2) ◽  
pp. 216-219 ◽  
Author(s):  
J. O. Murphy ◽  
N. Yannios
Keyword(s):  
Vertical Component ◽  
Single Mode ◽  
Convection Cell ◽  
Type I ◽  
Type Ii ◽  
Vertical Vorticity ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

A new family of solutions for stationary convection (Murphy and Lopez 1984) has been established which exists within the astrophysical range of parameter values — large Rayleigh number and low Prandtl number. These single mode Type II solutions, which have a non-zero component of vertical vorticity, apparently do not exist at higher Prandtl numbers and are characterized by a lower vertical velocity and heat flux, when compared to the equivalent single mode Type I solutions for Rayleigh — Benard convection with zero vertical vorticity. In turn the vertical component of vorticity associated with Type II solutions is responsible for modifying the horizontal components of the velocity field to establish cyclonic or swirling type solutions within the hexagonal convection cell.

Interpretation of shadowgraph patterns in Rayleigh-Bénard convection

1988 ◽  
Vol 190 ◽  
pp. 451-469 ◽  
Author(s):  
D. R. Jenkins
Keyword(s):  
Rayleigh Number ◽  
Linear Theory ◽  
Vertical Component ◽  
Fluid Flows ◽  
Bénard Convection ◽  
Benard Convection ◽  
Higher Order Terms ◽  
The Relationship ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The relationship between observations of cellular Rayleigh-Bénard convection using shadowgraphs and theoretical expressions for convection planforms is considered. We determine the shadowgraphs that ought to be observed if the convection is as given by theoretical expressions for roll, square or hexagonal planforms and compare them with actual experiments. Expressions for the planforms derived from linear theory, valid for low supercritical Rayleigh number, produce unambiguous shadowgraphs consisting of cells bounded by bright lines, which correspond to surfaces through which no fluid flows and on which the vertical component of velocity is directed downwards. Dark spots at the centre of cells, indicating regions of hot, rising fluid, are not accounted for by linear theory, but can be produced by adding higher-order terms, predominantly due to the temperature dependence of a material property of the fluid, such as its viscosity.

scholarly journals Experimental investigation of longitudinal space–time correlations of the velocity field in turbulent Rayleigh–Bénard convection

2011 ◽  
Vol 683 ◽  
pp. 94-111 ◽  
Author(s):  
Quan Zhou ◽  
Chun-Mei Li ◽  
Zhi-Ming Lu ◽  
Yu-Lu Liu
Keyword(s):  
Experimental Investigation ◽  
Velocity Field ◽  
Space Time ◽  
Turbulent Shear ◽  
Convection Cell ◽  
Mean Velocity ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractWe report an experimental investigation of the longitudinal space–time cross-correlation function of the velocity field, $C(r, \tau )$, in a cylindrical turbulent Rayleigh–Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while Taylor’s frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows (He & Zhang, Phys. Rev. E, vol. 73, 055303) is valid for the present velocity field for all over the cell, i.e. the isocorrelation contours of the measured $C(r, \tau )$ have an elliptical curve shape and hence $C(r, \tau )$ can be related to $C({r}_{E} , 0)$ via ${ r}_{E}^{2} = (r\ensuremath{-} U\tau )^{2} + {V}^{2} {\tau }^{2} $ with $U$ and $V$ being two characteristic velocities. We further show that the fitted $U$ is proportional to the mean velocity of the flow, but the values of $V$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell’s central region. It is found that $U$ and $V$ are approximately the same near the sidewall, while $U\simeq 0$ at the cell centre.

The effect of boundary properties on controlled Rayleigh–Bénard convection

2000 ◽  
Vol 411 ◽  
pp. 39-58 ◽  
Author(s):  
LAURENS E. HOWLE
Keyword(s):  
Heat Flux ◽  
Control Method ◽  
Lower Boundary ◽  
Bénard Convection ◽  
Benard Convection ◽  
Boundary Properties ◽  
Parameter Ranges ◽  
Differential Control ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We investigate the effect of the finite horizontal boundary properties on the critical Rayleigh and wave numbers for controlled Rayleigh–Bénard convection in an infinite horizontal domain. Specifically, we examine boundary thickness, thermal diffusivity and thermal conductivity. Our control method is through perturbation of the lower-boundary heat flux. A linear proportional-differential control method uses the local amplitude of a shadowgraph to actively redistribute the lower-boundary heat flux. Realistic boundary conditions for laboratory experiments are selected. Through linear stability analysis we examine, in turn, the important boundary properties and make predictions of the properties necessary for successful control experiments. A surprising finding of this work is that for certain realistic parameter ranges, one may find an isola to time-dependent convection as the primary bifurcation.

Sign in / Sign up

Export Citation Format

Share Document