Hostname: page-component-7dd5485656-kp629 Total loading time: 0 Render date: 2025-10-27T09:40:10.017Z Has data issue: false hasContentIssue false
  • English
  • Français

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: qzhou@shu.edu.cn
Get access Rights & Permissions [Opens in a new window]

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

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , pp. 294 - 308
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abarzhi, S. I. 2010a On fundamentals of Rayleigh–Taylor turbulent mixing. Europhys. Lett. 91, 35001.Google Scholar
Abarzhi, S. I. 2010b Review of theoretical modelling approaches of Rayleigh–Taylor instabilities and turbulent mixing. Phil. Trans. R. Soc. Lond. A 368, 1809–1828.Google Scholar
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.Google Scholar
Boffetta, G. 2007 Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence. J. Fluid Mech. 589, 253–260.Google Scholar
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427–451.Google Scholar
Boffetta, G., de Lillo, F., Mazzino, A. & Musacchio, S. 2012 Bolgiano scale in confined Rayleigh–Taylor turbulence. J. Fluid Mech. 690, 426–440.Google Scholar
Boffetta, G., Mazzino, A., Musacchio, S. & Vozella, L. 2009 Kolmogorov scaling and intermittency in Rayleigh–Taylor turbulence. Phys. Rev. E 79, 065301(R).Google Scholar
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.Google Scholar
Boffetta, G. & Musacchio, S. 2010 Evidence for the double cascade scenario in two-dimensional turbulence. Phys. Rev. E 82, 016307.Google Scholar
Borue, V. & Orszag, S. A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.Google Scholar
Cabot, W. H. & Cook, A. W. 2006 Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae. Nat. Phys. 2, 562–568.Google Scholar
Celani, A., Mazzino, A. & Vozella, L. 2006 Rayleigh–Taylor turbulence in two dimensions. Phys. Rev. Lett. 96, 134504.Google Scholar
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.Google Scholar
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.Google Scholar
Chertkov, M. 2003 Phenomenology of Rayleigh–Taylor turbulence. Phys. Rev. Lett. 91, 115001.Google Scholar
Chung, D. & Pullin, D. I. 2010 Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence. J. Fluid Mech. 643, 279–308.CrossRefGoogle Scholar
Clercx, H. J. H. & van Heijst, G. J. F. 2009 Two-dimensional Navier–Stokes turbulence in bounded domains. Appl. Mech. Rev. 62, 020802.Google Scholar
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, 1–48.Google Scholar
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, 1668–1693.Google Scholar
Eyink, G. L. 1995 Local energy flux and the refined similarity hypothesis. J. Stat. Phys. 78, 335–351.Google Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.Google Scholar
Huang, Y.-X. & Zhou, Q. 2013 Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 737, R3.Google Scholar
Isobe, H., Miyagoshi, T., Shibata, K. & Yokoyama, T. 2005 Filamentary structure on the Sun from the magnetic Rayleigh–Taylor instability. Nature 434, 478–481.Google Scholar
Kelley, D. H. & Ouellette, N. T. 2011 Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence. Phys. Fluids 23, 115101.Google Scholar
Liao, Y. & Ouellette, N. T. 2013 Spatial structure of spectral transport in two-dimensional flow. J. Fluid Mech. 725, 281–2988.Google Scholar
Liao, Y. & Ouellette, N. T. 2014 Geometry of scale-to-scale energy and enstrophy transport in two-dimensional flow. Phys. Fluids 26, 045103.Google Scholar
Liu, J.-G., Wang, C. & Johnston, H. 2003 A fourth order scheme for incompressible Boussinesq equations. J. Sci. Comput. 18, 253–285.Google Scholar
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, 83–119.Google Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.Google Scholar
Matsumoto, T. 2009 Anomalous scaling of three-dimensional Rayleigh–Taylor turbulence. Phys. Rev. E 79, 055301(R).Google Scholar
Ni, R., Voth, G. A. & Ouellette, N. T. 2014 Extracting turbulent spectral transfer from under-resolved velocity fields. Phys. Fluids 26, 105107.Google Scholar
Qiu, X., Liu, Y.-L. & Zhou, Q. 2014 Local dissipation scales in two-dimensional Rayleigh–Taylor turbulence. Phys. Rev. E 90, 043012.Google Scholar
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.CrossRefGoogle ScholarPubMed
Soulard, O. 2012 Implications of the Monin–Yaglom relation for Rayleigh–Taylor turbulence. Phys. Rev. Lett. 109, 254501.Google Scholar
Soulard, O. & Griffond, J. 2012 Inertial-range anisotropy in Rayleigh–Taylor turbulence. Phys. Fluids 24, 025101.Google Scholar
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, 1868–1873.Google Scholar
Vladimirova, N. & Chertkov, M. 2009 Self-similarity and universality in Rayleigh–Taylor, Boussinesq turbulence. Phys. Fluids 21, 015102.Google Scholar
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.Google Scholar
Weinan, E. & Liu, J.-G. 1996 Vorticity boundary condition and related issues for finite difference schemes. J. Comput. Phys. 124, 368–382.Google Scholar
Wilson, P. N. & Andrews, M. J. 2002 Spectral measurements of Rayleigh–Taylor mixing at small Atwood number. Phys. Fluids 14, 938–945.Google Scholar
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, 1–44.Google Scholar
Zhou, Q. 2013 Temporal evolution and scaling of mixing in two-dimensional Rayleigh–Taylor turbulence. Phys. Fluids 25, 085107.Google Scholar
Zhou, Y. 2001 A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Fluids 13, 538–543.CrossRefGoogle Scholar
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, 1021–1034.Google Scholar