Similarities between the structure functions of thermal convection and hydrodynamic turbulence

Shashwat Bhattacharya; Shubhadeep Sadhukhan; Anirban Guha; Mahendra K. Verma

doi:10.1063/1.5119905

Similarities between the structure functions of thermal convection and hydrodynamic turbulence

Shashwat Bhattacharya (Lead / Corresponding author), Shubhadeep Sadhukhan, Anirban Guha, Mahendra K. Verma

Civil Engineering

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Abstract

In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

Original language	English
Article number	115107
Pages (from-to)	1-12
Number of pages	12
Journal	Physics of Fluids
Volume	31
Issue number	11
Early online date	13 Nov 2019
DOIs	https://doi.org/10.1063/1.5119905
Publication status	Published - Nov 2019

ASJC Scopus subject areas

Computational Mechanics
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Fluid Flow and Transfer Processes

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Cite this

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abstract = "In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.",

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note = "This work was supported by Research Grant No. PLANEX/PHY/2015239 from Indian Space Research Organisation, India, and the Department of Science and Technology, India (Grant No. INT/RUS/RSF/P-03) for the Indo-Russian project.",

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AU - Guha, Anirban

AU - Verma, Mahendra K.

N1 - This work was supported by Research Grant No. PLANEX/PHY/2015239 from Indian Space Research Organisation, India, and the Department of Science and Technology, India (Grant No. INT/RUS/RSF/P-03) for the Indo-Russian project.

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N2 - In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

AB - In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

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Similarities between the structure functions of thermal convection and hydrodynamic turbulence

Abstract

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