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

  • Quan Zhou (a1), Yong-Xiang Huang (a2), Zhi-Ming Lu (a1), Yu-Lu Liu (a1) and Rui Ni (a3)...

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.

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Corresponding author

Email address for correspondence: qzhou@shu.edu.cn

References

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Abarzhi, S. I. 2010a On fundamentals of Rayleigh–Taylor turbulent mixing. Europhys. Lett. 91, 35001.
Abarzhi, S. I. 2010b Review of theoretical modelling approaches of Rayleigh–Taylor instabilities and turbulent mixing. Phil. Trans. R. Soc. Lond. A 368, 18091828.
Biferale, L., Mantovani, F., Sbragaglia, M., Scagliarini, A., Toschi, F. & Tripiccione, R. 2010 High resolution numerical study of Rayleigh–Taylor turbulence using a thermal lattice Boltzmann scheme. Phys. Fluids 22, 115112.
Boffetta, G. 2007 Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence. J. Fluid Mech. 589, 253260.
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427451.
Boffetta, G., de Lillo, F., Mazzino, A. & Musacchio, S. 2012 Bolgiano scale in confined Rayleigh–Taylor turbulence. J. Fluid Mech. 690, 426440.
Boffetta, G., Mazzino, A., Musacchio, S. & Vozella, L. 2009 Kolmogorov scaling and intermittency in Rayleigh–Taylor turbulence. Phys. Rev. E 79, 065301(R).
Boffetta, G., Mazzino, A., Musacchio, S. & Vozella, L. 2010 Statistics of mixing in three-dimensional Rayleigh–Taylor turbulence at low Atwood number and Prandtl number one. Phys. Fluids 22, 035109.
Boffetta, G. & Musacchio, S. 2010 Evidence for the double cascade scenario in two-dimensional turbulence. Phys. Rev. E 82, 016307.
Borue, V. & Orszag, S. A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 131.
Cabot, W. H. & Cook, A. W. 2006 Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae. Nat. Phys. 2, 562568.
Celani, A., Mazzino, A. & Vozella, L. 2006 Rayleigh–Taylor turbulence in two dimensions. Phys. Rev. Lett. 96, 134504.
Chen, S.-Y., Ecke, R. E., Eyink, G. L., Rivera, M., Wan, M.-P. & Xiao, Z.-L. 2006 Physical mechanism of the two-dimensional inverse energy cascade. Phys. Rev. Lett. 96, 084502.
Chen, S.-Y., Ecke, R. E., Eyink, G. L., Wang, X. & Xiao, Z.-L. 2003 Physical mechanism of the two-dimensional enstrophy cascade. Phys. Rev. Lett. 91, 214501.
Chertkov, M. 2003 Phenomenology of Rayleigh–Taylor turbulence. Phys. Rev. Lett. 91, 115001.
Chung, D. & Pullin, D. I. 2010 Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence. J. Fluid Mech. 643, 279308.
Clercx, H. J. H. & van Heijst, G. J. F. 2009 Two-dimensional Navier–Stokes turbulence in bounded domains. Appl. Mech. Rev. 62, 020802.
Dalziel, S. B., Linden, P. F. & Youngs, D. L. 1999 Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability. J. Fluid Mech. 399, 148.
Dimonte, G., Youngs, D. L., Dimits, A., Weber, S., Marinak, M., Wunsch, S., Garasi, C., Robinson, A., Andrews, M. J., Ramaprabhu, P. et al. 2004 A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration. Phys. Fluids 16, 16681693.
Eyink, G. L. 1995 Local energy flux and the refined similarity hypothesis. J. Stat. Phys. 78, 335351.
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325336.
Huang, Y.-X. & Zhou, Q. 2013 Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 737, R3.
Isobe, H., Miyagoshi, T., Shibata, K. & Yokoyama, T. 2005 Filamentary structure on the Sun from the magnetic Rayleigh–Taylor instability. Nature 434, 478481.
Kelley, D. H. & Ouellette, N. T. 2011 Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence. Phys. Fluids 23, 115101.
Liao, Y. & Ouellette, N. T. 2013 Spatial structure of spectral transport in two-dimensional flow. J. Fluid Mech. 725, 2812988.
Liao, Y. & Ouellette, N. T. 2014 Geometry of scale-to-scale energy and enstrophy transport in two-dimensional flow. Phys. Fluids 26, 045103.
Liu, J.-G., Wang, C. & Johnston, H. 2003 A fourth order scheme for incompressible Boussinesq equations. J. Sci. Comput. 18, 253285.
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83119.
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335364.
Matsumoto, T. 2009 Anomalous scaling of three-dimensional Rayleigh–Taylor turbulence. Phys. Rev. E 79, 055301(R).
Ni, R., Voth, G. A. & Ouellette, N. T. 2014 Extracting turbulent spectral transfer from under-resolved velocity fields. Phys. Fluids 26, 105107.
Qiu, X., Liu, Y.-L. & Zhou, Q. 2014 Local dissipation scales in two-dimensional Rayleigh–Taylor turbulence. Phys. Rev. E 90, 043012.
Rivera, M. K., Daniel, W. B., Chen, S. Y. & Ecke, R. E. 2003 Energy and enstrophy transfer in decaying two-dimensional turbulence. Phys. Rev. Lett. 90, 104502.
Soulard, O. 2012 Implications of the Monin–Yaglom relation for Rayleigh–Taylor turbulence. Phys. Rev. Lett. 109, 254501.
Soulard, O. & Griffond, J. 2012 Inertial-range anisotropy in Rayleigh–Taylor turbulence. Phys. Fluids 24, 025101.
Taleyarkhan, R. P., West, C. D., Cho, J. S. Jr, Lahey, R. T., Nigmatulin, R. I. & Block, R. C. 2002 Evidence for nuclear emissions during acoustic cavitation. Science 295, 18681873.
Vladimirova, N. & Chertkov, M. 2009 Self-similarity and universality in Rayleigh–Taylor, Boussinesq turbulence. Phys. Fluids 21, 015102.
Wan, M.-P., Xiao, Z.-L., Meneveau, C., Eyink, G. L. & Chen, S.-Y. 2010 Dissipation-energy flux correlations as evidence for the Lagrangian energy cascade in turbulence. Phys. Fluids 22, 061702.
Weinan, E. & Liu, J.-G. 1996 Vorticity boundary condition and related issues for finite difference schemes. J. Comput. Phys. 124, 368382.
Wilson, P. N. & Andrews, M. J. 2002 Spectral measurements of Rayleigh–Taylor mixing at small Atwood number. Phys. Fluids 14, 938945.
Xiao, Z., Wan, M., Chen, S. & Eyink, G. L. 2009 Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation. J. Fluid Mech. 619, 144.
Zhou, Q. 2013 Temporal evolution and scaling of mixing in two-dimensional Rayleigh–Taylor turbulence. Phys. Fluids 25, 085107.
Zhou, Y. 2001 A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Fluids 13, 538543.
Zingale, M., Woosley, S. E., Rendleman, C. A., Day, M. S. & Bell, J. B. 2005 Three-dimensional numerical simulations of Rayleigh–Taylor unstable flames in type Ia supernovae. Astrophys. J. 632, 10211034.
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