scholarly journals Bifurcations in two-dimensional Rayleigh-Bénard convection

1998 ◽  
Vol 57 (1) ◽  
pp. 428-435 ◽  
Author(s):  
E. Zienicke ◽  
N. Seehafer ◽  
F. Feudel
Keyword(s):  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The -dependence of the critical roughness height in two-dimensional turbulent Rayleigh–Bénard convection

2021 ◽  
Vol 911 ◽  
Author(s):  
Jian-Lin Yang ◽  
Yi-Zhao Zhang ◽  
Tian-cheng Jin ◽  
Yu-Hong Dong ◽  
Bo-Fu Wang ◽  
...  
Keyword(s):  
Roughness Height ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract

APPROXIMATION OF THE STATIONARY STATISTICAL PROPERTIES OF THE DYNAMICAL SYSTEM GENERATED BY THE TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION PROBLEM

2011 ◽  
Vol 09 (04) ◽  
pp. 421-446 ◽  
Author(s):  
FLORENTINA TONE ◽  
XIAOMING WANG
Keyword(s):  
Dynamical System ◽  
Global Attractors ◽  
Statistical Properties ◽  
Two Dimensional ◽  
Time Step ◽  
Bénard Convection ◽  
Benard Convection ◽  
Convection Problem ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this article, we consider a temporal linear semi-implicit approximation of the two-dimensional Rayleigh–Bénard convection problem. We prove that the stationary statistical properties as well as the global attractors of this linear semi-implicit scheme converge to those of the 2D Rayleigh–Bénard problem as the time step approaches zero.

The effect of distant side-walls on the evolution and stability of finite-amplitude Rayleigh-Bénard convection

1981 ◽  
Vol 378 (1775) ◽  
pp. 539-566 ◽  
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Side Walls ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

A recent study by Cross et al . (1980) has described a class of finite-amplitude phase-winding solutions of the problem of two-dimensional Rayleigh-Bénard convection in a shallow fluid layer of aspect ratio 2 L (≫ 1) confined laterally by rigid side-walls. These solutions arise at Rayleigh numbers R = R 0 + O ( L -1 ) where R 0 is the critical Rayleigh number for the corresponding infinite layer. Nonlinear solutions of constant phase exist for Rayleigh numbers R = R 0 + O ( L -2 ) but of these only the two that bifurcate at the lowest value of R are stable to two-dimensional linearized disturbances in this range (Daniels 1978). In the present paper one set of the class of phase-winding solutions is found to be stable to two-dimensional disturbances. For certain values of the Prandtl number of the fluid and for stress-free horizontal boundaries the results predict that to preserve stability there must be a continual readjustment of the roll pattern as the Rayleigh number is raised, with a corresponding increase in wavelength proportional to R - R 0 . These solutions also exhibit hysteresis as the Rayleigh number is raised and lowered. For other values of the Prandtl number the number of rolls remains unchanged as the Rayleigh number is raised, and the wavelength remains close to its critical value. It is proposed that the complete evolution of the flow pattern from a static state must take place on a number of different time scales of which t = O(( R - R 0 ) -1 ) and t = O(( R - R 0 ) -2 ) are the most significant. When t = O(( R - R 0 ) -1 ) the amplitude of convection rises from zero to its steady-state value, but the final lateral positioning of the rolls is only completed on the much longer time scale t = O(( R - R 0 ) -2 ).

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