The Onset of Thermohaline Convection in a Linearly-Stratified Horizontal Layer

1976 ◽  
Vol 98 (4) ◽  
pp. 558-563 ◽  
Author(s):  
J. H. Wright ◽  
R. I. Loehrke
Keyword(s):  
Porous Metal ◽  
Horizontal Layer ◽  
Free Boundaries ◽  
Constant Concentration ◽  
Concentration Difference ◽  
Thermohaline Convection ◽  
Metal Plates ◽  
Convective Motions ◽  
Fixed Constant ◽  
Rayleigh Numbers

The convective stability of a horizontal layer of water with salt and heat addition from below was studied experimentally. The layer was bounded above and below by porous metal plates through which heat and salt could diffuse. A well-mixed region of warm, salty water below the lower plate and another of cooler, fresher water above the upper plate set the temperature and concentration difference for the intervening quiescent layer. With a fixed, constant concentration gradient established between the plates the temperature difference was slowly increased until convective motions were observed. The instability boundary for this system lies within the unstable region predicted by linear theory for a horizontal layer with constant gradients and stress-free boundaries and approaches the linear boundary at high Rayleigh numbers.

Bounds for growth rate of a perturbation in thermohaline convection

1981 ◽  
Vol 378 (1773) ◽  
pp. 301-304 ◽  
Keyword(s):  
Growth Rate ◽  
Prandtl Number ◽  
Taylor Number ◽  
Governing Equations ◽  
Thermohaline Convection ◽  
Rayleigh Numbers ◽  
Complex Growth Rate

A new scheme of combining the governing equations of thermohaline convection is shown to lead to the following bounds for the complex growth rate p of an arbitrary oscillatory perturbation: | p | 2 < R s σ (Veronis thermohaline configuration), | p | 2 < – R σ (Stern thermohaline configuration), where R and R s are the thermal and the concentration Rayleigh numbers, and σ is the Prandtl number. The analysis is applicable to rotatory thermal and rotatory thermohaline convections for which the corresponding bounds are | p | 2 < T σ 2 (rotatory simple Bénard configuration), | p | 2 < max ( T σ 2 , R s σ) (rotatory Vernois thermohaline configuration), | p | 2 < max ( T σ 2 , – R σ) (rotatory Stern thermohaline configuration), where T is the Taylor number. The above results are valid for all combination of dynamically free and rigid boundaries.

The instability of a layer of fluid heated below and subject to Coriolis forces

1953 ◽  
Vol 217 (1130) ◽  
pp. 306-327 ◽  
Keyword(s):  
Coriolis Force ◽  
Thermal Instability ◽  
Horizontal Layer ◽  
Onset Of Convection ◽  
Dimensional Parameter ◽  
Coriolis Forces ◽  
Effective Gravity ◽  
The Stability ◽  
Bounding Surfaces ◽  
Rayleigh Numbers

This paper is devoted to examining the stability of a horizontal layer of fluid heated below, subject to an effective gravity ( g ) acting (approximately) in the direction of the vertical and the Coriolis force resulting from a rotation of angular velocity Ω about a direction making an angle ϑ with the vertical. It is shown that the effect of the Coriolis force is to inhibit the onset of convection, the extent of the inhibition depending on the value of the non-dimensional parameter T = 4 d 4 Ω 2 cos 2 ϑ/ v 2 , where d denotes the depth of the layer and v is the kinematic viscosity. Tables of the critical Rayleigh numbers ( R c ) for the onset of convection are provided for the three cases ( a ) both bounding surfaces free, ( b ) both bounding surfaces rigid and ( c ) one bounding surface free and the other rigid. In all three cases R c →constant x T 2/3 as T →∞ ; the corresponding dependence of the critical temperature gradient (— β c ) for the onset of convection, on v and d , is gαβ c = constant x ĸ (Ω 4 cos 4 ϑ/ d 4 v ) 1/2 ( ĸ is the coefficient of thermometric conductivity and α is the coefficient of volume expansion). The question whether thermal instability can set in as oscillations of increasing amplitude (i.e. as 'overstability’) is examined for case ( a ), and it is shown that if ĸ/v <1.478, this possibility does not arise; but if ĸ/v >1.478, over-stability is the first type of instability to arise for all T greater than a certain determinate value. It further appears that these latter possibilities should be considered in meteorological and astrophysical applications of the theory.

Thermal Convection in Porous Media at High Rayleigh Numbers

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Daniel J. Keene ◽  
R. J. Goldstein
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Thermal Convection ◽  
Thermal Boundary Layer ◽  
Packed Bed ◽  
Horizontal Layer ◽  
Homogeneous Fluid ◽  
Fluid Systems ◽  
Dimensionless Groups ◽  
Rayleigh Numbers

An experimental study of thermal convection in a porous medium investigates the heat transfer across a horizontal layer heated from below at high Rayleigh number. Using a packed bed of polypropylene spheres in a cubic enclosure saturated with compressed argon, the pressure was varied between 5.6 bar and 77 bar to obtain fluid Rayleigh numbers between 1.68 × 109 and 3.86 × 1011, corresponding to Rayleigh–Darcy numbers between 7.47 × 103 and 2.03 × 106. From the present and earlier studies of Rayleigh–Benard convection in both porous media and homogeneous fluid systems, the existence and importance of a thin thermal boundary layer are clearly demonstrated. In addition to identifying the governing role of the thermal boundary layer at high Rayleigh numbers, the successful correlation of data using homogeneous fluid dimensionless groups when the thermal boundary layer thickness becomes smaller than the length scale associated with the pore features is shown.

On the occurrence of cellular motion in Bénard convection

1967 ◽  
Vol 30 (4) ◽  
pp. 651-661 ◽  
Author(s):  
E. Palm ◽  
T. Ellingsen ◽  
B. Gjevik
Keyword(s):  
Kinematic Viscosity ◽  
Silicone Oil ◽  
Fluid Layer ◽  
Critical Value ◽  
Free Boundaries ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Numbers ◽  
Effect Of Surface ◽  
Cellular Motion

The interval of Rayleigh numbers in Bénard convection corresponding to cellular motion is determined in the case of free-free boundaries, rigid-free boundaries and rigid-rigid boundaries, taking into account the variation of the kinematic viscosity with temperature. Neglecting the effect of surface tension, it is shown that this interval is largest for the rigid-rigid case. The most important feature from the obtained formula (6.1) is, however, that the interval is extremely dependent on the depth of the fluid layer. To obtain a cellular pattern it is therefore necessary to have very small fluid depths. For example, with Silicone oil and a fluid depth of 7 mm, cellular motion will, according to the theory, be observed for Rayleigh numbers larger than the critical value and less than 1·07 times the critical value. For a fluid depth of 5 mm, however, the formula (6.1) gives that cellular motion will be observed for Rayleigh numbers up to 1·54 times the critical value.

scholarly journals The global characteristics of the three-dimensional thermal convection inside a spherical shell

1997 ◽  
Vol 4 (1) ◽  
pp. 19-27 ◽  
Author(s):  
J. Arkani-Hamed
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Spherical Shell ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Horizontal Layer ◽  
Boundary Layer Theory ◽  
Physical Parameters ◽  
Rayleigh Numbers

Abstract. The Rayleigh number-Nusselt number, and the Rayleigh number-thermal boundary layer thickness relationships are determined for the three-dimensional convection in a spherical shell of constant physical parameters. Several models are considered with Rayleigh numbers ranging from 1.1 x 102 to 2.1 x 105 times the critical Rayleigh number. At lower Rayleigh numbers the Nusselt number of the three-dimensional convection is greater than that predicted from the boundary layer theory of a horizontal layer but agrees well with the results of an axisymmetric convection in a spherical shell. At high Rayleigh numbers of about 105 times the critical value, which are the characteristics of the mantle convection in terrestrial planets, the Nusselt number of the three-dimensional convection is in good agreement with that of the boundary layer theory. At even higher Rayleigh numbers, the Nusselt number of the three-dimensional convection becomes less than those obtained from the boundary layer theory. The thicknesses of the thermal boundary layers of the spherical shell are not identical, unlike those of the horizontal layer. The inner thermal boundary is thinner than the outer one, by about 30- 40%. Also, the temperature drop across the inner boundary layer is greater than that across the outer boundary layer.

scholarly journals Nonlinear Thermal Convection in a Layer with Imposed Energy Flux

1974 ◽  
Vol 27 (4) ◽  
pp. 481 ◽  
Author(s):  
R Van der Borght
Keyword(s):  
Boundary Conditions ◽  
Energy Flux ◽  
Thermal Convection ◽  
Average Energy ◽  
Finite Amplitude ◽  
Solar Granulation ◽  
Convective Motions ◽  
Rayleigh Numbers

Results are reported of an investigation into the effect of the chosen boundary conditions on the steady finite-amplitude convective motions in a layer in which the average energy flux is imposed. The boundary conditions are chosen with a view to the application of the results to solar granulation and supergranulation. It is shown that, at high Rayleigh numbers, solutions do in fact exist for which there is no modulation in the energy flux and little fluctuation in the temperature across the boundaries.

The Effect of a Magnetic Field on the Onset of Thermal Convection when Constant Flux Boundary Conditions Apply

1977 ◽  
Vol 3 (2) ◽  
pp. 164-165 ◽  
Author(s):  
J. O. Murphy
Keyword(s):  
Magnetic Field ◽  
Nuclear Energy ◽  
Radial Direction ◽  
Average Energy ◽  
Horizontal Layer ◽  
Heat Fluxes ◽  
Convective Zone ◽  
Flux Boundary Conditions ◽  
Convective Motions ◽  
Boussinesq Fluid

The energy passing through the boundaries of a convective zone in a star, in an outward radial direction per second, must in total be equal to the luminosity of the star, provided of course that this zone does not encompass nuclear energy producing regions. If, in an endeavour to establish the nature of the convective motions in this zone, a section of the zone is modelled by considering steady cellular convection in a horizontal layer of Boussinesq fluid, it is on the basis of an average energy flux being imposed. Moreover, the sum of the conductive and convective heat fluxes is represented by the Nusselt number, which is specified and constant for the zone.

Sign in / Sign up

Export Citation Format

Share Document