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Large-scale dynamos driven by shear-flow-induced jets

Nature volume 649, pages 848–852 (2026)Cite this article

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Abstract

At every scale they occupy, magnetic fields affect various phenomena, including star formation, cosmic-ray transport, charged-particle acceleration, space weather, transport in planetary atmospheres and laboratory plasmas. These fields are often generated and sustained by turbulent flows in a process called the dynamo. In 1955, E. N. Parker parameterized the effects of small-scale turbulence to propose a mean-field dynamo theory1. The widely used theory reproduces observed large-scale fields but suffers from difficulty in tuning parameters as they are not justified from first principles: studies of turbulent flows show tangled magnetic fields, which are folded and fragmented into small-scale structures owing to shear-flow straining2,3. Here, considering a shear flow that is unstable and driven, we develop analytic theory and perform three-dimensional, advanced computer simulations of turbulence with up to 4,096 × 4,096 × 8,192 grid points, showing ab initio generation of quasi-periodic, large-scale magnetic fields. The generation occurs via the mean-vorticity effect—an additional mean-field dynamo process postulated4 in 1990. Crucial to this dynamo is the prior generation of large-scale three-dimensional jets, robustly produced as topologically protected and exact nonlinear solutions of the magnetohydrodynamic equations. The jet-driven dynamo applies to shear-driven laboratory and astrophysical systems. These include binary neutron star mergers5,6, where the reported dynamo probably operates on microsecond timescales to produce in milliseconds some of the strongest magnetic fields in the Universe7, providing signals for multi-messenger astronomy8.

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Fig. 1: Long-time evolution of the MHD-KH dynamo, showing phases of turbulent generation of flows and magnetic fields.
Fig. 2: Properties of the KH-instability-induced jets and dynamo.
Fig. 3: Mechanism of the jet-driven ϒ-dynamo.
Fig. 4: Dominance of cross-helicity.

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Data availability

Any data needed to evaluate the conclusions of this article are present in the article or Methods or available via Zenodo at https://doi.org/10.5281/zenodo.17162239 (ref. 56). Simulation files, post-processing scripts, additional materials, data used to produce figures, and details of numerical implementation are available via Zenodo at https://doi.org/10.5281/zenodo.17162239 (ref. 56). Upon request, the corresponding author will share additional details on analysis methods.

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Acknowledgements

We thank J. R. Beattie, A. M. Beloborodov, A. Bhattacharjee, K. J. Burns, F. Ebrahimi, R. Habegger, D. Lecoanet, B. Miquel, E. R. Most, J. S. Oishi, S. Patil and B. Ripperda for discussions. This work used Anvil at Purdue University through allocation TG-PHY130027 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) programme, which is supported by National Science Foundation grants 2138259, 2138286, 2138307, 2137603 and 2138296. We acknowledge staff support from Anvil and additional computing resources from Bridges-2. This material is based on work funded by the National Science Foundation (NSF) under award 2409206 and Department of Energy (grant number DE-SC0022257) through the DOE/NSF Partnership in Basic Plasma Science and Engineering. A.E.F. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2402142.

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Author notes

  1. B. Tripathi

    Present address: Columbia University, New York, NY, USA

Authors and Affiliations

  1. University of Wisconsin–Madison, Madison, WI, USA

    B. Tripathi, P. W. Terry, E. G. Zweibel & R. Fan

  2. University of Colorado, Boulder, CO, USA

    A. E. Fraser

  3. Dutch Institute for Fundamental Energy Research, Eindhoven, The Netherlands

    M. J. Pueschel

  4. Eindhoven University of Technology, Eindhoven, The Netherlands

    M. J. Pueschel

  5. Department of Physics and Astronomy, Ruhr-Universität Bochum, Bochum, Germany

    M. J. Pueschel

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  1. B. Tripathi
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  4. E. G. Zweibel
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Contributions

B.T. led the research, conceptualized the idea for the reported dynamo, developed analytic theory and schematic diagrams, modified numerical codes, performed simulations, acquired and analysed data, and wrote the first draft of the article. A.E.F. substantially contributed by helping develop research ideas, participating in the discussion of research methods, interpreting data, and editing and reviewing the article. P.W.T. substantially contributed by helping develop research ideas, participating in the discussion of research methods, interpreting data, and editing and reviewing the article. E.G.Z. substantially contributed by helping develop research ideas, participating in the discussion of research methods, interpreting data, and editing and reviewing the article. M.J.P. substantially contributed by helping develop research ideas, participating in the discussion of research methods, interpreting data, and editing and reviewing the article. R.F. substantially contributed by helping develop research ideas, participating in the discussion of research methods, interpreting data, and editing and reviewing the article.

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Correspondence to B. Tripathi.

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Extended data figures and tables

Extended Data Fig. 1 Anisotropic growth rate spectrum of the KH instability, along with the spectra of energies.

The mean flow is directed along x and varies along z. The spectrum of the linear growth rate γKH of the KH instability is anisotropic. The growth rate is the largest around k = (±0.5, 0), which represents the 2D KH instability. The growth rate is zero for kx = 0 and ky ≠ 0. The square boxes in the upper half of the figure show time-averaged spectra of energies in horizontal field E(bx) and horizontal flow E(ux) (the contribution of the initial mean flow is removed). These spectra share the upper right-hand logarithmic colour bar, extending from yellow to black. The square boxes in the lower half of the figure show time-averaged spectra of energies in vertical field E(bz) and vertical flow E(uz). These share the lower right-hand linear colour bar, extending from white to blue. The center of each square box represents the wavenumber resolved in the nonlinear simulation (only a small part of the wavenumber range is shown, as the KH instability exists at large scales |ka| ≱ 1). The special square box centred at k = (0,0) is shared by four quadrants. All quantities are measured using a and U0.

Extended Data Fig. 2 Cascade of kinetic and magnetic energies from large scales to small scales.

Nonlinear energy flux through spectral space is measured in a simulation with 4096 × 4096 × 8192 grid points. Here, \(k={({k}_{x}^{2}+{k}_{y}^{2})}^{1/2}\). The energy flux is integrated over the z-axis. A constant energy flux in k-space indicates an inertial range. Energy injected externally to the mean flow (shown with a white-headed arrow on the left margin) is cascaded to small scales, as shown by \(\Pi \)uu, which measures energy flux due to transfer of energy between two velocity fluctuations. Magnetic-to-magnetic energy flux \(\Pi \)bb shows a prominent small-scale cascade over two decades of inertial range. This analysis shows that the ϒ-dynamo arising in KH-unstable shear flow is not due to an inverse cascade of energy. The ϒ-dynamo is due to energy transfer from large-scale jets to the mean field, as demonstrated in Extended Data Fig. 3.

Extended Data Fig. 3 Spectrum of nonlinear energy transfer to the mean magnetic field via turbulent field-line stretching.

This figure confirms that the large-scale velocity fluctuations give energy to the mean magnetic field (red)—and that the small-scale velocity fluctuations receive energy from the mean magnetic field (blue). The quantity shown is T(k″), which represents the rate of nonlinear energy transfer to the mean field \(\hat{b}\)x(kx = 0, ky = 0). Mathematically, T(k″) = ⟨\(\hat{b}\)x*(0,0) [\(\hat{{\bf{b}}}\)(k′) · ∇\(\hat{u}\)x(k″)]⟩z, where k″ = (kx″,ky″) is the horizontal wavenumber of the velocity u, and k′ = (kx′,ky′) is the horizontal wavenumber of the magnetic field b; the wavenumber-triad constraint imposes (0,0) = k′ + k″. The quantities \(\hat{{\bf{b}}}\)(k′) and \(\hat{u}\)x(k″) represent the horizontally Fourier-transformed coefficients of magnetic fields and velocity with wavenumbers k′ and k″, respectively; these quantities are retained in the physical domain z before integrating the transfer function along z. The quantity \(\hat{b}\)x*(0,0) is the horizontally-Fourier-transformed, complex-conjugated, x-directed mean magnetic field, whose energy is around two orders of magnitude larger than the y-directed mean field in the nonlinear phase. The mean field \(\hat{b}\)x(0,0) is inhomogeneous in z (as is the mean flow); the operation ⟨·⟩z averages the nonlinear transfer function in z. The transfer function is time-averaged over the saturated phase (t = 1000–4000). Of particular note is the extraordinary contribution of the large-scale jets, especially with wavenumber (kx″a,ky″a) = (0,0.2), which contribute the largest in the mean-field generation. This is consistent with Fig. 3. The square box at kx″ = ky″ = 0 is white because the mean flow does not directly couple to the mean field in this system (the so-called \(\varOmega \)-effect32 is zero).

Extended Data Fig. 4 Comparison of three-dimensional unit vectors (shown with carets) of different components of the mean turbulent EMF \(\boldsymbol{\mathcal{E}}\) from a KH-instability-driven dynamo simulation in a and from the Madison Dynamo Laboratory Experiment37 in b.

With respect to \({\mathcal{E}}\), the β-diffusion term is anti-aligned, and the α-term is orthogonal (indicating the non-helical nature of dynamo). A near-identical orthogonal orientation of the α-term was measured in the Madison Dynamo Experiment37 in panel b. In the Madison Dynamo Experiment, the vorticity is considerably large in the radial direction38. This is consistent with the dominance of the observed radial EMF, suggesting the important role of the large-scale vorticity-effect4 in the turbulent EMF. Similarly, the ϒ-term in panel a is perfectly co-aligned with the mean EMF \({\mathcal{E}}\). Here, the novel jet-driven ϒ-dynamo, arising from the large-scale vorticity, is confirmed to be the source of the dynamo. Diagram in b reproduced with permission from ref. 37, AAS.

Extended Data Fig. 5 PDF of cosine of angle between u, b, ω(= ∇ × u), and j(= ∇ × b), in a simulation with 4096 × 4096 × 8192 grid points.

The turbulent flow and fields measured at the shear layer are non-helical and close to pure Alfvénic states (orange curve), which explains why the ϒ-effect dominates in the mean EMF. For the pure Alfvénic states, α is zero; β and ϒ are similar and are not impacted by the non-kinematic (flow-evolution) effect in the same manner as the α is (see last paragraph of “Analytic quasilinear EMF model” in Methods). A large-scale steady shear flow induces an “imbalanced” MHD turbulence (asymmetry of the orange curve) and thus drives the dynamo via the non-zero ϒ-coefficient. Similar PDFs of dominant cross-helicity and non-helical flows were recently detected in the magnetosheath turbulence observed by the Magnetospheric Multiscale Spacecraft49.

Extended Data Table 1 A list of commonly used symbols and meanings
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Tripathi, B., Fraser, A.E., Terry, P.W. et al. Large-scale dynamos driven by shear-flow-induced jets. Nature 649, 848–852 (2026). https://doi.org/10.1038/s41586-025-09912-0

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