Energy spectrum of buoyancy-driven turbulence

Abhishek Kumar, Anando G. Chatterjee, Mahendra K. Verma

    Research output: Contribution to journalArticle

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    Abstract

    Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux Πu, we demonstrate that, for stably stratified flows, the kinetic energy spectrum Eu(k)∼k-11/5, the potential energy spectrum Eθ(k)∼k-7/5, and Πu(k)∼k-4/5 are consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence Eu(k) follows Kolmogorov's spectrum with a constant energy flux. For Rayleigh-Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing Πu(k) with k, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant Πu(k) and Eu(k)∼k-5/3 for a narrow band of wave numbers. © 2014 American Physical Society.
    Original languageEnglish
    Article number023016
    Number of pages9
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume90
    DOIs
    Publication statusPublished - 25 Aug 2014

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    Buoyancy
    Energy Spectrum
    Kinetic energy
    buoyancy
    Turbulence
    energy spectra
    kinetic energy
    turbulence
    Scaling
    scaling
    Energy
    potential energy
    Stratified Flow
    stratified flow
    direct numerical simulation
    Rayleigh
    Convection
    narrowband
    convection
    High Resolution

    Cite this

    Energy spectrum of buoyancy-driven turbulence. / Kumar, Abhishek; Chatterjee, Anando G.; Verma, Mahendra K.

    In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 90, 023016 , 25.08.2014.

    Research output: Contribution to journalArticle

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    AB - Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux Πu, we demonstrate that, for stably stratified flows, the kinetic energy spectrum Eu(k)∼k-11/5, the potential energy spectrum Eθ(k)∼k-7/5, and Πu(k)∼k-4/5 are consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence Eu(k) follows Kolmogorov's spectrum with a constant energy flux. For Rayleigh-Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing Πu(k) with k, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant Πu(k) and Eu(k)∼k-5/3 for a narrow band of wave numbers. © 2014 American Physical Society.

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