Hydrodynamic Stability
Lecture 15
Rayleigh Benard Convection Continued…
Ruby Krishnamurti (FSU).
1968, JFM, 33, 445.
1970, JFM, 42, 295.
Looked at allowing the heat flux to slowly increase, causing the lower temperature to slowly
increase as well.
The temperature profile becomes slightly nonlinear.
Very slow – obtained rolls.
Unsteady case – obtained hexagon pattern.
No effects of fluid properties, surface tension, viscosity, conductivity.
Made careful measurements of heat flux and visualizations, how flow developed.
Water 20
Pr ~ 7
0
C
Air
20
0
Pr ~ 1
C
Mercury
Pr ~ 0.025
The effect of shear reference.
Reference: Jim Deardorff 1965, Physics of Fluids, 8, 1027. Also Jefferies, (1928)
1
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Replace.
()
2
2
with
v
t
Uz
v
tx
∂
−∇
∂
∂∂
+−
∇
Concluded – if rolls are aligned with flow (
x
 direction)
0
x
∂
=
∂
No effect on linear instability, but if they are not aligned he solved the equations numerically.
Strong effect of shear.
He found that shear tends to be stabilizing (rolls perpendicular to flow).
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 Fall '08
 Staff
 Fluid Dynamics, Kinetic Energy, JFM, ui ui, Mercury Pr

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