scholarly journals Linear theory of particulate Rayleigh-Bénard instability

2021 ◽  
Vol 6 (8) ◽  
Author(s):  
Suryansh Prakhar ◽  
Andrea Prosperetti
Keyword(s):  
Linear Theory ◽  
Rayleigh Benard

Interpretation of shadowgraph patterns in Rayleigh-Bénard convection

1988 ◽  
Vol 190 ◽  
pp. 451-469 ◽  
Author(s):  
D. R. Jenkins
Keyword(s):  
Rayleigh Number ◽  
Linear Theory ◽  
Vertical Component ◽  
Fluid Flows ◽  
Bénard Convection ◽  
Benard Convection ◽  
Higher Order Terms ◽  
The Relationship ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The relationship between observations of cellular Rayleigh-Bénard convection using shadowgraphs and theoretical expressions for convection planforms is considered. We determine the shadowgraphs that ought to be observed if the convection is as given by theoretical expressions for roll, square or hexagonal planforms and compare them with actual experiments. Expressions for the planforms derived from linear theory, valid for low supercritical Rayleigh number, produce unambiguous shadowgraphs consisting of cells bounded by bright lines, which correspond to surfaces through which no fluid flows and on which the vertical component of velocity is directed downwards. Dark spots at the centre of cells, indicating regions of hot, rising fluid, are not accounted for by linear theory, but can be produced by adding higher-order terms, predominantly due to the temperature dependence of a material property of the fluid, such as its viscosity.

On the linear theory of waves in media with periodic structures

1991 ◽  
Vol 161 (9) ◽  
pp. 201-209 ◽  
Author(s):  
Polina S. Landa ◽  
V.F. Marchenko
Keyword(s):  
Linear Theory ◽  
Periodic Structures
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