scholarly journals A weak attractor and properties of solutions for the three-dimensional Bénard problem

2007 ◽  
Vol 18 (2/3, June) ◽  
pp. 449-481 ◽  
Author(s):  
José Valero ◽  
V. Melnik ◽  
O. Kapustyan
Keyword(s):  
Three Dimensional ◽  
Bénard Problem ◽  
Benard Problem ◽  
Weak Attractor

On the two-component Benard problem a numerical solution

1975 ◽  
Vol 80 (1) ◽  
pp. 76-88 ◽  
Author(s):  
J.C. Legros ◽  
D. Longree ◽  
G. Chavepeyer ◽  
J.K. Platten
Keyword(s):  
Numerical Solution ◽  
Two Component ◽  
Bénard Problem ◽  
Benard Problem

Stabilization of the no-motion state in the Rayleigh–Bénard problem

1994 ◽  
Vol 447 (1931) ◽  
pp. 587-607 ◽  
Keyword(s):  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Control Flow ◽  
Feedback Controller ◽  
Linear Stability Theory ◽  
Motion State ◽  
Conduction State ◽  
Bénard Problem ◽  
Benard Problem ◽  
Rayleigh Benard

Using linear stability theory and numerical simulations, we demonstrate that the critical Rayleigh number for bifurcation from the no-motion (conduction) state to the motion state in the Rayleigh–Bénard problem of an infinite fluid layer heated from below and cooled from above can be significantly increased through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid’s temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such a way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary’s temperature or velocity are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behaviour at relatively low Rayleigh numbers.

scholarly journals Micropolar meets Newtonian in 3D. The Rayleigh–Bénard problem for large Prandtl numbers

Nonlinearity ◽  
2020 ◽  
Vol 33 (11) ◽  
pp. 5686-5732
Author(s):  
Piotr Kalita ◽  
Grzegorz Łukaszewicz
Keyword(s):  
Bénard Problem ◽  
Benard Problem ◽  
Prandtl Numbers ◽  
Rayleigh Benard
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