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Scale-to-scale energy and enstrophy transport in two-dimensional Rayleigh–Taylor turbulence

Published online by Cambridge University Press:  02 December 2015

Quan Zhou ,
Yong-Xiang Huang ,
Zhi-Ming Lu ,
Yu-Lu Liu  and
Rui Ni
Quan Zhou*
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
Yong-Xiang Huang
Affiliation:
State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen 361102, China
Zhi-Ming Lu
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
Yu-Lu Liu
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
Rui Ni
Affiliation:
Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802-1412, USA
*
†Email address for correspondence: [email protected]
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Abstract

We apply a recently developed filtering approach, i.e. filter-space technique (FST), to study the scale-to-scale transport of kinetic energy, thermal energy, and enstrophy in two-dimensional (2D) Rayleigh–Taylor (RT) turbulence. Although the scaling laws of the energy cascades in 2D RT systems follow the Bolgiano–Obukhov (BO59) scenario due to buoyancy forces, the kinetic energy is still found to be, on average, dynamically transferred to large scales by an inverse cascade, while both the mean thermal energy and the mean enstrophy move towards small scales by forward cascades. In particular, there is a reasonably extended range over which the transfer rate of thermal energy is scale-independent and equals the corresponding thermal dissipation rate at different times. This range functions similarly to the inertial range for the kinetic energy in the homogeneous and isotropic turbulence. Our results further show that at small scales the fluctuations of the three instantaneous local fluxes are highly asymmetrically distributed and there is a strong correlation between any two fluxes. These small-scale features are signatures of the mixing and dissipation of fluids with steep temperature gradients at the fluid interfaces.

JFM classification

Convection: Buoyancy-driven instability Turbulent Flows: Turbulent convection Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , pp. 294 - 308
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Copyright
© 2015 Cambridge University Press 

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