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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2505.09537 |
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| _version_ | 1866913837149585408 |
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| author | Patel, Pratik Yadav, Sharad K Miura, Hideaki Pandit, Rahul |
| author_facet | Patel, Pratik Yadav, Sharad K Miura, Hideaki Pandit, Rahul |
| contents | We carry out extensive pseudospectral direct numerical simulations (DNSs) of decaying three-dimensional (3D) Hall magnetohydrodynamics (3D HMHD) plasma turbulence at three magnetic Prandtl numbers $Pr_{m}=0.1$, $1.0$ and $10.0$. Our DNSs have been designed to uncover the dependence of the statistical properties of 3D HMHD turbulence on $Pr_m$ and to bring out the subtle interplay between three lengths, the kinetic and magnetic dissipation length scales $η_u$, and $η_b$ and the ion-inertial scale $d_i$, below which we see the manifestations of the Hall term. This interplay, qualitatively apparent from isosurface plots of the moduli of the vorticity and the current density, is exposed clearly by the kinetic-energy and magnetic-energy spectra, $E_u(k)$ and $E_b(k)$, respectively. We find two different inertial regions, In the first inertial region $k<k_{i}\sim1/d_i$, both the kinetic-energy and magnetic-energy spectra, $E_u(k)$ and $E_b(k)$, respectively, display power-law regions with an exponent that is consistent with Kolmogorov-type $-5/3$ scaling, at all values of $Pr_m$. In the second inertial region $k > k_{i}$, the scaling of $E_b(k)$ depends upon $Pr_M$: At $Pr_{m}=0.1$, the spectral-scaling exponent is $-17/3$, but for $Pr_{m}=1$ and $10$ this exponent is $-11/3$. We then show theoretically that
$E_u(k) \sim k^2 E_b(k)$ for $Pr_m \ll 1$ and $E_b(k) \sim k^2 E_u(k)$ for $Pr_m \gg 1$; our DNS results are consistent with our theoretical predictions. We examine, furthermore, left- and right-polarised fluctuations of the fields that lead, respectively, to the dominance of ion-cyclotron or whistler waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncovering the Varieties of Three-dimensional Hall-MHD Turbulence Patel, Pratik Yadav, Sharad K Miura, Hideaki Pandit, Rahul Space Physics Plasma Physics We carry out extensive pseudospectral direct numerical simulations (DNSs) of decaying three-dimensional (3D) Hall magnetohydrodynamics (3D HMHD) plasma turbulence at three magnetic Prandtl numbers $Pr_{m}=0.1$, $1.0$ and $10.0$. Our DNSs have been designed to uncover the dependence of the statistical properties of 3D HMHD turbulence on $Pr_m$ and to bring out the subtle interplay between three lengths, the kinetic and magnetic dissipation length scales $η_u$, and $η_b$ and the ion-inertial scale $d_i$, below which we see the manifestations of the Hall term. This interplay, qualitatively apparent from isosurface plots of the moduli of the vorticity and the current density, is exposed clearly by the kinetic-energy and magnetic-energy spectra, $E_u(k)$ and $E_b(k)$, respectively. We find two different inertial regions, In the first inertial region $k<k_{i}\sim1/d_i$, both the kinetic-energy and magnetic-energy spectra, $E_u(k)$ and $E_b(k)$, respectively, display power-law regions with an exponent that is consistent with Kolmogorov-type $-5/3$ scaling, at all values of $Pr_m$. In the second inertial region $k > k_{i}$, the scaling of $E_b(k)$ depends upon $Pr_M$: At $Pr_{m}=0.1$, the spectral-scaling exponent is $-17/3$, but for $Pr_{m}=1$ and $10$ this exponent is $-11/3$. We then show theoretically that $E_u(k) \sim k^2 E_b(k)$ for $Pr_m \ll 1$ and $E_b(k) \sim k^2 E_u(k)$ for $Pr_m \gg 1$; our DNS results are consistent with our theoretical predictions. We examine, furthermore, left- and right-polarised fluctuations of the fields that lead, respectively, to the dominance of ion-cyclotron or whistler waves. |
| title | Uncovering the Varieties of Three-dimensional Hall-MHD Turbulence |
| topic | Space Physics Plasma Physics |
| url | https://arxiv.org/abs/2505.09537 |