Turbulent thermal convection at high Rayleigh numbers for a Boussinesq fluid of constant Prandtl number

2005 ◽  
Vol 17 (12) ◽  
pp. 121701 ◽  
Author(s):  
G. Amati ◽  
K. Koal ◽  
F. Massaioli ◽  
K. R. Sreenivasan ◽  
R. Verzicco
Keyword(s):  
Prandtl Number ◽  
Thermal Convection ◽  
Boussinesq Fluid ◽  
Rayleigh Numbers

Relation between Nusselt number and Rayleigh number in turbulent thermal convection

1976 ◽  
Vol 73 (3) ◽  
pp. 445-451 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Thermal Convection ◽  
Similarity Theory ◽  
Unknown Constant ◽  
Velocity Defect ◽  
Fluid Layers ◽  
Rayleigh Numbers ◽  
Existing Data

A theory is developed for the dependence of the Nusselt number on the Rayleigh number in turbulent thermal convection in horizontal fluid layers. The theory is based on a number of assumptions regarding the behaviour in the molecular boundary layers and on the assumption of a buoyancy-defect law in the interior analogous to the velocity-defect law in flow in pipes and channels. The theory involves an unknown constant exponentsand two unknown functions of the Prandtl number. For eithers= ½ ors= 1/3, corresponding to two different theories of thermal convection, and for a given Prandtl number, constants can be chosen to give excellent agreement with existing data over nearly the whole explored range of Rayleigh numbers in the turbulent case. Unfortunately, comparisons with experiment do not permit a definite choice ofs, but consistency with the chosen form of the buoyancy-defect law seems to suggests= 1/3, corresponding to similarity theory.

scholarly journals Rotating turbulent thermal convection at very large Rayleigh numbers

2021 ◽  
Vol 912 ◽  
Author(s):  
Marcel Wedi ◽  
Dennis P.M. van Gils ◽  
Eberhard Bodenschatz ◽  
Stephan Weiss
Keyword(s):  
Thermal Convection ◽  
Rayleigh Numbers

Abstract

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.

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