Derivation of Rayleigh Number for Nonpenetrative Thermal Convection

1997 ◽  
Vol 119 (1) ◽  
pp. 180-183 ◽  
Author(s):  
A. K. Prasad
Keyword(s):  
Rayleigh Number ◽  
Thermal Convection

Linear stability of rotating convection in an imposed shear flow

1997 ◽  
Vol 350 ◽  
pp. 271-293 ◽  
Author(s):  
PAUL MATTHEWS ◽  
STEPHEN COX
Keyword(s):  
Rayleigh Number ◽  
Shear Flow ◽  
Eigenvalue Problem ◽  
Linear Stability ◽  
Thermal Convection ◽  
Critical Rayleigh Number ◽  
Rotation Vector ◽  
Linear Stability Theory ◽  
Fixed Temperature ◽  
Differential Motion

In many geophysical and astrophysical contexts, thermal convection is influenced by both rotation and an underlying shear flow. The linear theory for thermal convection is presented, with attention restricted to a layer of fluid rotating about a horizontal axis, and plane Couette flow driven by differential motion of the horizontal boundaries.The eigenvalue problem to determine the critical Rayleigh number is solved numerically assuming rigid, fixed-temperature boundaries. The preferred orientation of the convection rolls is found, for different orientations of the rotation vector with respect to the shear flow. For moderate rates of shear and rotation, the preferred roll orientation depends only on their ratio, the Rossby number.It is well known that rotation alone acts to favour rolls aligned with the rotation vector, and to suppress rolls of other orientations. Similarly, in a shear flow, rolls parallel to the shear flow are preferred. However, it is found that when the rotation vector and shear flow are parallel, the two effects lead counter-intuitively (as in other, analogous convection problems) to a preference for oblique rolls, and a critical Rayleigh number below that for Rayleigh–Bénard convection.When the boundaries are poorly conducting, the eigenvalue problem is solved analytically by means of an asymptotic expansion in the aspect ratio of the rolls. The behaviour of the stability problem is found to be qualitatively similar to that for fixed-temperature boundaries.Fully nonlinear numerical simulations of the convection are also carried out. These are generally consistent with the linear stability theory, showing convection in the form of rolls near the onset of motion, with the appropriate orientation. More complicated states are found further from critical.

Experiments on the inhibition of thermal convection by a magnetic field

1957 ◽  
Vol 240 (1220) ◽  
pp. 108-113 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Rayleigh Number ◽  
Magnetic Fields ◽  
Thermal Convection ◽  
Kinematic Viscosity ◽  
Critical Rayleigh Number ◽  
Theoretical Relation ◽  
Horizontal Layers

Experiments on the magnetic inhibition of thermal convection in horizontal layers of mercury heated from below are described. A large 36½ in. cyclotron magnet reconditioned for hydromagnetic studies was used in these experiments. By using layers of mercury of depth 3 to 6 cm and magnetic fields of strength 500 to 8000 gauss, it has been possible to determine the dependence of the critical Rayleigh number for the onset of instability on the parameter Q 1 ( = σH 2 d 2 / π 2 ρν , where H denotes the strength of the field, σ the electrical conductivity, ν the coefficient of kinematic viscosity, ρ the density and d the depth of the layer) for Q 1 varying between 40 and 1·6 × 10 6 . The experiments fully confirm the theoretical relation derived by Chandrasekhar.

Large eddy simulations of thermal convection at high Rayleigh number

2000 ◽  
Vol 140 (1) ◽  
pp. 163-174 ◽  
Author(s):  
Noä Cantin ◽  
Alain P. Vincent ◽  
David A. Yuen
Keyword(s):  
Rayleigh Number ◽  
Thermal Convection ◽  
Large Eddy Simulations ◽  
Large Eddy

The Effect of Rotation on Thermal Convection

1972 ◽  
Vol 2 (2) ◽  
pp. 92-93 ◽  
Author(s):  
J. O. Murphy ◽  
R. Van Der Borght
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Cell Size ◽  
Thermal Convection ◽  
Convection Zone ◽  
Total Heat ◽  
The Sun ◽  
Maximum Heat ◽  
Solar Convection Zone ◽  
Solar Convection

An investigation into the influence of rotation on thermal convection has some applicability in the study of the solar convection zone. Of particular interest is the effect of rotation on the total heat transport and the cell size for maximum heat transport at high Rayleigh number, which is estimated to be as high as 1020 for the Sun.

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