ON THE NONLINEAR STABILITY OF MARANGONI–BÉNARD PROBLEM WITH FREE SURFACE IN THE BOUSSINESQ APPROXIMATION

2005 ◽  
Vol 15 (01) ◽  
pp. 1-22 ◽  
Author(s):  
GIOVANNA GUIDOBONI ◽  
BUM JA JIN
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Exponential Stability ◽  
Nonlinear Stability ◽  
Sufficient Conditions ◽  
Marangoni Effect ◽  
Boussinesq Approximation ◽  
Energy Functional ◽  
Bénard Problem ◽  
Benard Problem

We study the Bénard problem in the Boussinesq approximation with upper free surface in the presence of surface tension. Both buoyancy and Marangoni effect are taken into account. Defining a suitable energy functional, we obtain sufficient conditions for nonlinear exponential stability of the rest state.

A nonlinear analysis of the stabilizing effect of rotation in the Bénard problem

1985 ◽  
Vol 402 (1823) ◽  
pp. 257-283 ◽  
Keyword(s):  
Prandtl Number ◽  
Nonlinear Analysis ◽  
Nonlinear Stability ◽  
Close Agreement ◽  
Stability Boundary ◽  
Stabilizing Effect ◽  
Bénard Problem ◽  
Benard Problem

This paper uses a novel ‘generalized energy’ to study the stabilizing effect of rotation in the Bénard problem. The nonlinear stability boundary we find is in very close agreement with the experiments of Rossby (Rossby, H. T. J . Fluid Mech . 36, 309–335 (1969)), who predicts sub-critical instabilities for high Taylor numbers for fluids with Prandtl number greater than or equal to 1, such as water.

Nonlinear stability of the viscoelastic Bénard problem

Nonlinearity ◽  
2020 ◽  
Vol 33 (4) ◽  
pp. 1677-1704
Author(s):  
Fei Jiang ◽  
Mengmeng Liu
Keyword(s):  
Nonlinear Stability ◽  
Bénard Problem ◽  
Benard Problem
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