For details on the benchmark problem look for:
"Numerical simulation of oscillatory convection in low-Pr fluids:
A GAMM Workshop" (eq. B.Roux), Notes on Numerical Fluid Mechanics, 1990, vol.27.

Governing parameters:   

Grashof number:  

Prandtl number:  

Aspect ratio: 

The stability problems yields:

• critical Grashof number
• critical frequence  
• the most dangerous perturbation

Case with no-slip lower and stress-free upper surface (Ra-Fa case)

Get dependence of the critical Grashof number on the aspect ratio:

• Critical Grashof number versus aspect ratio Pr=0 and 0.015, 1<A<3
• Critical Grashof number versus aspect ratio Pr=0 and 0.015, 3<A<10

Get dependence of the critical frequency number on the aspect ratio:

• Critical frequency versus aspect ratio Pr=0 and 0.015, 1<A<3
• Critical frequency versus aspect ratio Pr=0 and 0.015, 3<A<10

Get patterns of steady flows and their perturbations at critical Grashof numbers (patterns of the flow - left frames - at the most dangerous perturbarions - right frames - at critical parameters):

• Cavity with A=1
• Cavity with A=4
• Cavity with A=10
  

Get patterns of oscillatory flows (snapshots of streamlines plotted for equal time intervals 0.1T covering the complete period):

• Cavity with A=1
• Cavity with A=4
• Cavity with A=10
  

Case with no-slip upper and lower boundaries (Ra-Ra case)

Get example of multiple steady states

Look how knowledge about multplicity helps to fit experimental results

See comparison between results obtained by Galerkin and finite volume methods:

• Case A=1.4
• Case A=4.7

Get dependence of the critical Grashof number on the aspect ratio:

• Critical Grashof number versus aspect ratio Pr=0, 1<A<4
• Critical Grashof number versus aspect ratio Pr=0.015, 1<A<4
• Critical Grashof number versus aspect ratio Pr=0, 2<A<10
• Critical Grashof number versus aspect ratio Pr=0.015, 4<A<11
• Critical Grashof number versus Prandtl number A=4
  Comparison with experimental results of Braunsfurth & Mullin, 1996
• Critical Grashof number versus Prandtl number A=4
  Comparison with experimental results
• Critical Grashof number versus Prandtl number A=1, 0<Pr<0.03
• Critical Grashof number versus Prandtl number A=1, 0.03<Pr<1

Get dependence of the critical frequency number on the aspect ratio:

• Critical frequency versus aspect ratio Pr=0, 2<A<10
• Critical frequency versus aspect ratio for one and two-cell flows Pr=0.015, 4<A<11
• Critical frequency versus aspect ratio for three- and four-cell flows Pr=0.015, 4<A<11
• Critical frequency versus Prandtl number A=4
• Critical frequency versus Prandtl number A=1. 0<A<0.03
• Critical frequency versus Prandtl number A=1. 0.03<A<1

Get patterns of steady flows and their perturbations at critical Grashof numbers (patterns of the flow - left frames - at the most dangerous perturbarions - right frames - at critical parameters):

• A=1
• A=4, single-cell flow
• A=4, Pr=0
• A=9, 4-cell flow
• A=9.6, 4-cell flow
• A=10, 3-cell flow
• A=10, 4-cell flow
  

Get animated oscillatory flows:

• A=1.4, single-cell flow
• A=2, Pr=0
• A=2, Pr=0.015
• A=3, single-cell flow
• A=3, two-cell flow
• A=3.1, single-cell flow
• A=4, two-cell flow
• A=4, three-cell flow
• A=6, three-cell flow
• A=8, four-cell flow
• A=9, four-cell flow
• A=9.6, four-cell flow
• A=10, three-cell flow
• A=10, four-cell flow