Kolmogorov Scaling for Total Energy and Cross Helicity in Magnetohydrodynamic Turbulence
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| Format: | Preprint |
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2026
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| _version_ | 1866917293373521920 |
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| author | Verma, Manthan Jha, Abhishek K. Verma, Mahendra K. |
| author_facet | Verma, Manthan Jha, Abhishek K. Verma, Mahendra K. |
| contents | The problem of scaling in isotropic magnetohydrodynamic (MHD) turbulence has remained unresolved, with competing predictions of $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. In this paper, we address this long-standing controversy using high-resolution numerical simulations on $8192^2$ and $1536^3$ grids. We show that the total energy and cross helicity spectra are closer to $k^{-5/3}$ than $k^{-3/2}$. The fluxes and structure functions of the total energy and cross helicity also demonstrate robust support for Kolmogorov scaling. The magnetic energy shows $k^{-5/3}$ spectrum, but the kinetic energy exhibits $k^{-3/2}$ spectrum; the latter spectrum is due to the energy transfers from the magnetic field to the velocity field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21271 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kolmogorov Scaling for Total Energy and Cross Helicity in Magnetohydrodynamic Turbulence Verma, Manthan Jha, Abhishek K. Verma, Mahendra K. Plasma Physics The problem of scaling in isotropic magnetohydrodynamic (MHD) turbulence has remained unresolved, with competing predictions of $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. In this paper, we address this long-standing controversy using high-resolution numerical simulations on $8192^2$ and $1536^3$ grids. We show that the total energy and cross helicity spectra are closer to $k^{-5/3}$ than $k^{-3/2}$. The fluxes and structure functions of the total energy and cross helicity also demonstrate robust support for Kolmogorov scaling. The magnetic energy shows $k^{-5/3}$ spectrum, but the kinetic energy exhibits $k^{-3/2}$ spectrum; the latter spectrum is due to the energy transfers from the magnetic field to the velocity field. |
| title | Kolmogorov Scaling for Total Energy and Cross Helicity in Magnetohydrodynamic Turbulence |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2602.21271 |