Scaling in Internally Heated Convection: A Unifying Theory

Qi Wang; Detlef Lohse; Olga Shishkina

doi:10.1029/2020GL091198

Scaling in Internally Heated Convection: A Unifying Theory

Qi Wang, Detlef Lohse^*, Olga Shishkina^*

^*Corresponding author for this work

Research output: Contribution to journal › Letter › Academic › peer-review

29 Citations (Scopus)

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Abstract

We offer a unifying theory for turbulent, purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, https://doi.org/10.1017/S0022112099007545; 2001, https://doi.org/10.1103/PhysRevLett.86.3316) for Rayleigh-Bénard turbulence and of Shishkina et al. (2016, https://doi.org/10.1002/2015GL067003) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in respective boundary and bulk contributions. We obtain the mean temperature of the system and the Reynolds number (which are the response parameters) as function of the control parameters, namely the internal thermal driving strength (called, when nondimensionalized, the Rayleigh-Roberts number) and the Prandtl number. The results of the theory are consistent with our direct numerical simulations of the Boussinesq equations.

Original language	English
Article number	e2020GL091198
Journal	Geophysical research letters
Volume	48
Issue number	4
DOIs	https://doi.org/10.1029/2020GL091198
Publication status	Published - 28 Feb 2021

Keywords

UT-Hybrid-D
internal heating
convection

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Wang-2021-Scaling-in-internally-heated-convecFinal published version, 2.65 MBLicence: CC BY

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title = "Scaling in Internally Heated Convection: A Unifying Theory",

abstract = "We offer a unifying theory for turbulent, purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, https://doi.org/10.1017/S0022112099007545; 2001, https://doi.org/10.1103/PhysRevLett.86.3316) for Rayleigh-B{\'e}nard turbulence and of Shishkina et al. (2016, https://doi.org/10.1002/2015GL067003) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in respective boundary and bulk contributions. We obtain the mean temperature of the system and the Reynolds number (which are the response parameters) as function of the control parameters, namely the internal thermal driving strength (called, when nondimensionalized, the Rayleigh-Roberts number) and the Prandtl number. The results of the theory are consistent with our direct numerical simulations of the Boussinesq equations.",

keywords = "UT-Hybrid-D, internal heating, convection",

author = "Qi Wang and Detlef Lohse and Olga Shishkina",

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T2 - A Unifying Theory

AU - Wang, Qi

AU - Lohse, Detlef

AU - Shishkina, Olga

N1 - Wiley deal

PY - 2021/2/28

Y1 - 2021/2/28

N2 - We offer a unifying theory for turbulent, purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, https://doi.org/10.1017/S0022112099007545; 2001, https://doi.org/10.1103/PhysRevLett.86.3316) for Rayleigh-Bénard turbulence and of Shishkina et al. (2016, https://doi.org/10.1002/2015GL067003) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in respective boundary and bulk contributions. We obtain the mean temperature of the system and the Reynolds number (which are the response parameters) as function of the control parameters, namely the internal thermal driving strength (called, when nondimensionalized, the Rayleigh-Roberts number) and the Prandtl number. The results of the theory are consistent with our direct numerical simulations of the Boussinesq equations.

AB - We offer a unifying theory for turbulent, purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, https://doi.org/10.1017/S0022112099007545; 2001, https://doi.org/10.1103/PhysRevLett.86.3316) for Rayleigh-Bénard turbulence and of Shishkina et al. (2016, https://doi.org/10.1002/2015GL067003) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in respective boundary and bulk contributions. We obtain the mean temperature of the system and the Reynolds number (which are the response parameters) as function of the control parameters, namely the internal thermal driving strength (called, when nondimensionalized, the Rayleigh-Roberts number) and the Prandtl number. The results of the theory are consistent with our direct numerical simulations of the Boussinesq equations.

KW - UT-Hybrid-D

KW - internal heating

KW - convection

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JO - Geophysical research letters

JF - Geophysical research letters

IS - 4

M1 - e2020GL091198

ER -

Scaling in Internally Heated Convection: A Unifying Theory

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Keywords

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