Statistical features of rapidly rotating decaying turbulence: Enstrophy and energy spectra and coherent structures

Manohar K. Sharma, Abhishek Kumar, Mahendra K. Verma, Sagar Chakraborty

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    Abstract

    In this paper, we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modeling. We find that as the turbulent flow evolves in time, the Rossby number decreases to ∼10−3, and the flow becomes quasi-two-dimensional with strong coherent columnar structures arising due to the inverse cascade of energy. We establish that a major fraction of energy is confined in Fourier modes (±1, 0, 0) and (0, ±1, 0) that correspond to the largest columnar structure in the flow. For wavenumbers (k) greater than the enstrophy dissipation wavenumber (kd), our phenomenological arguments and numerical study show that the enstrophy flux and spectrum of a horizontal cross section perpendicular to the axis of rotation are given by ϵωexp(−C(k/kd)2) and Cϵ2/3ωk−1exp(−C(k/kd)2), respectively; for this 2D flow, ϵω is the enstrophy dissipation rate, and C is a constant. Using these results, we propose a new form for the energy spectrum of rapidly rotating decaying turbulence: E(k)=Cϵ2/3ωk−3exp(−C(k/kd)2). This model of the energy spectrum is based on wavenumber-dependent enstrophy flux, and it deviates significantly from power law energy spectrum reported earlier.
    Original languageEnglish
    Article number045103
    Number of pages14
    JournalPhysics of Fluids
    Volume30
    Early online date4 Apr 2018
    DOIs
    Publication statusPublished - Apr 2018

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    vorticity
    energy spectra
    turbulence
    dissipation
    axes of rotation
    turbulent flow
    cascades
    energy
    cross sections
    simulation

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    Statistical features of rapidly rotating decaying turbulence: Enstrophy and energy spectra and coherent structures. / Sharma, Manohar K.; Kumar, Abhishek; Verma, Mahendra K.; Chakraborty, Sagar.

    In: Physics of Fluids, Vol. 30, 045103, 04.2018.

    Research output: Contribution to journalArticle

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    AU - Chakraborty, Sagar

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    N2 - In this paper, we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modeling. We find that as the turbulent flow evolves in time, the Rossby number decreases to ∼10−3, and the flow becomes quasi-two-dimensional with strong coherent columnar structures arising due to the inverse cascade of energy. We establish that a major fraction of energy is confined in Fourier modes (±1, 0, 0) and (0, ±1, 0) that correspond to the largest columnar structure in the flow. For wavenumbers (k) greater than the enstrophy dissipation wavenumber (kd), our phenomenological arguments and numerical study show that the enstrophy flux and spectrum of a horizontal cross section perpendicular to the axis of rotation are given by ϵωexp(−C(k/kd)2) and Cϵ2/3ωk−1exp(−C(k/kd)2), respectively; for this 2D flow, ϵω is the enstrophy dissipation rate, and C is a constant. Using these results, we propose a new form for the energy spectrum of rapidly rotating decaying turbulence: E(k)=Cϵ2/3ωk−3exp(−C(k/kd)2). This model of the energy spectrum is based on wavenumber-dependent enstrophy flux, and it deviates significantly from power law energy spectrum reported earlier.

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