Global well-posedness of incompressible Bénard problem with zero dissipation or zero thermal diffusivity

2018 ◽  
Vol 321 ◽  
pp. 442-449
Author(s):  
Rong Zhang ◽  
Mingshu Fan ◽  
Shan Li
Keyword(s):  
Thermal Diffusivity ◽  
Well Posedness ◽  
Bénard Problem ◽  
Benard Problem

On the solution of the Bénard problem with boundaries of finite conductivity

1967 ◽  
Vol 296 (1447) ◽  
pp. 469-475 ◽  
Keyword(s):  
Thermal Diffusivity ◽  
Rayleigh Number ◽  
Hydrodynamic Stability ◽  
Critical Rayleigh Number ◽  
Finite Conductivity ◽  
Stationary Convection ◽  
Bénard Problem ◽  
Benard Problem ◽  
The Media

The Bénard problem in hydrodynamic stability is formulated under conditions where the media bounding the fluid have finite thermal diffusivity. It is shown that the principle of the exchange of stabilities remains valid in this case so that instability in the fluid first sets in as stationary convection. Solutions are obtained for various values of the ratio of the thermal diffusivity of the fluid to that of the bounding media; the critical Rayleigh number at which the instability occurs is markedly reduced when this ratio is large.

scholarly journals Global Well-Posedness for the d -Dimensional Magnetic Bénard Problem without Thermal Diffusion

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yinhong Cao
Keyword(s):  
Global Existence ◽  
Thermal Diffusion ◽  
Energy Method ◽  
Global Regularity ◽  
Strong Solutions ◽  
Minimal Amount ◽  
Well Posedness ◽  
Bénard Problem ◽  
Benard Problem

This paper focuses on the global existence of strong solutions to the magnetic Bénard problem with fractional dissipation and without thermal diffusion in ℝ d with d ≥ 3 . By using the energy method and the regularization of generalized heat operators, we obtain the global regularity for this model under minimal amount dissipation.

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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