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国际计算热科学期刊
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 0.7

ISSN 打印: 1940-2503
ISSN 在线: 1940-2554

国际计算热科学期刊

DOI: 10.1615/ComputThermalScien.2014006086
pages 113-127

VORTICITY SCALE AND INTEGRAL VALUES OF RAYLEIGH−BENARD CONVECTION

Igor B. Palymskiy
Siberian State University of Telecommunications and Information Sciences, 630102, Novosibirsk, Russia

ABSTRACT

The turbulent convection of liquid in a horizontal layer is simulated numerically for the case of heating from below. The liquid is assumed to be viscous and incompressible, and the layer's boundaries are assumed to be flat, isothermal, and free from shear stress. The Boussinesq approach without any semi-empirical relationships (direct numerical simulation) has been used and the flow is considered to be two-dimensional (2D) or three-dimensional (3D) and non-stationary. A special pseudo-spectral method with enough resolution and a Prandtl number equal to 10 is used. The present 3D simulation shows that the power law exponent at r ≥ 150 (here, r = Ra/Racr is supercriticality, where Ra and Racr = 657.5 are the Rayleigh number and its critical value) for temperature pulsations −2/15 coincides with the experimental result, and that the exponents of the power laws for vertical velocity pulsations 0.4 and Reynolds number 0.5 are close to the known experimental and numerical results. The same is also true for the kinetic energy and root-mean-square velocity. Meanwhile, the temperature and vertical velocity pulsations are represented correctly in 2D simulations only up to r ~ 250 because inherent in 2D simulations is an increase in the vorticity scale, and hence an increase in energy concentration on the large scale. The increase of the vorticity scale has been illustrated by the spectrum of the velocity, where the red (inverse) cascade of energy with power law − 5/3 is clearly seen.


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