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Physics of Fluids / Volume 24 / Issue 2 / ARTICLES / Turbulent Flows

Phys. Fluids 24, 025101 (2012); http://dx.doi.org/10.1063/1.3680871 (25 pages)

Inertial-range anisotropy in Rayleigh-Taylor turbulence

Olivier Soulard and Jérôme Griffond

CEA, DAM, DIF, F-91297 Arpajon, France

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(Received 29 June 2011; accepted 19 December 2011; published online 14 February 2012)

In this work, the spectral equilibrium theory of Ishihara et al. [Phys. Rev. Lett. 88, 154501 (2002)10.1103/PhysRevLett.88.154501] is applied to Rayleigh-Taylor turbulence. With the help of Canuto and Dubovikov's model [V. Canuto and M. Dubovikov, Phys. Fluids 8, 571 (1996)10.1063/1.868842] closed expressions for the anisotropic spectra of velocity and density, valid in the inertial range, are derived. Based on this result, the main properties of Rayleigh-Taylor turbulence at small scales are discussed. These theoretical results are compared against a direct numerical simulation of a Rayleigh-Taylor mixing zone.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. GENERAL NOTATIONS AND MAIN ASSUMPTIONS
    1. General notations
    2. Spectral equilibrium assumptions
    3. Applicability of spectral equilibrium assumptions to Rayleigh-Taylor flows
  3. DERIVATION OF AN EQUILIBRIUM SPECTRUM
    1. Asymptotic solution of the Canuto and Dubovikov model
    2. Properties of the equilibrium spectra
    3. Realizability and validity conditions
  4. COMPARISON WITH DNS
    1. Flow configuration
    2. Validity of the equilibrium assumptions and realizability
    3. 3D spectra for axisymmetric inhomogeneous turbulence
    4. Time evolution of 3D modulus spectra
    5. Angular spectra
    6. 1D and 2D spectra
  5. CONCLUSIONS

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KEYWORDS, PACS, and IPC

Keywords

flow simulation, mixing, numerical analysis, Rayleigh-Taylor instability, turbulence

PACS

  • 47.20.Ma

    Interfacial instabilities (e.g., Rayleigh-Taylor)

  • 47.27.E-

    Turbulence simulation and modeling

  • 47.51.+a

    Mixing

  • 02.60.Cb

    Numerical simulation; solution of equations

  • 45.70.Mg

    Granular flow: mixing, segregation and stratification

International Patent Classification (IPC)

  • B01F3/00

    Mixing, e.g. dispersing, emulsifying, according to the phases to be mixed

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3680871

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    T. Ishihara, K. Yoshida, and Y. Kaneda, “Anisotropic velocity correlation spectrum at small scales in a homogeneous turbulent shear flow,” Phys. Rev. Lett. 88, 154501 (2002).

    V. Canuto and M. Dubovikov, “A dynamical model for turbulence. I. General formalism,” Phys. Fluids 8, 571 (1996)PHFLE6000008000002000571000001.

    Y. Zhou, “A scaling analysis of turbulent flows driven by Rayleigh-Taylor and Richtmyer-Meshkov instabilities,” Phys. Fluids 13, 538 (2001)PHFLE6000013000002000538000001.

    M. Chertkov, “Phenomenology of Rayleigh-Taylor turbulence,” Phys. Rev. Let. 91, 115001 (2003).

    O. Poujade, “Rayleigh-Taylor turbulence is nothing like Kolmogorov turbulence in the self-similar regime,” Phys. Rev. Lett. 97, 185002 (2006).

    G. Boffetta, A. Mazzino, S. Musachino, and L. Vozella, “Kolmogorov scaling and intermittency in Rayleigh-Taylor turbulence,” Phys. Rev. E 79, 065301 (2009).

    T. Ishida and Y. Kaneda, “Small-scale anisotropy in magnetohydrodynamic turbulence under a strong uniform magnetic field,” Phys. Fluids 19, 075104 (2007)PHFLE6000019000007075104000001.

    K. Yoshida, T. Ishihara, and Y. Kaneda, “Anisotropic spectrum of homogeneous turbulent shear flow in a Lagrangian renormalized approximation,” Phys. Fluids 15, 2385 (2003)PHFLE6000015000008002385000001.

    V. Canuto, M. Dubovikov, and A. Dienstfrey, “A dynamical model for turbulence. IV. Buoyancy-driven flows,” Phys. Fluids 9, 2118 (1997)PHFLE6000009000007002118000001.

    C. Cambon and R. Rubinstein, “Anisotropic developments for homogeneous shear flows,” Phys. Fluids 18, 085106 (2006)PHFLE6000018000008085106000001.

    D. I. Pullin and T. S. Lundgren, “Axial motion and scalar transport in stretched spiral vortices,” Phys. Fluids 13, 2553 (2001)PHFLE6000013000009002553000001.

    C. Gibson, “Fine structure of scalar fields mixed by turbulence. I. Zero-gradient points and minimal gradient surfaces,” Phys. Fluids 11, 2305 (1968)PFLDAS000011000011002305000001.


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