Exact von-Kármán-Howarth relations for the Hosking integral in decaying, non-helical magnetically-dominated turbulence

ORAL

Abstract

The Hosking integral (Hosking & Schekochihin 2021, PRX 11, 041005) has recently been recognised as a key invariant that constrains the decay of magnetic fields that are statistically homogeneous, isotropic and non-helical, such as would have existed in the early Universe under certain primordial magnetogenesis scenarios. In this talk, we present new von-Karman-Howarth-Monin relations and corresponding exact scaling relations for the two-point magnetic-helicity-density correlation function in both incompressible and compressible magnetohydrodynamic (MHD) turbulence. We demonstrate with high-resolution numerical simulations of such turbulence that the condition of rapid decorrelation of the velocity and magnetic fields that — according to our new relations — is required for the conservation of the Hosking integral is, indeed, satisfied. Thus, we provide new evidence in support of the importance of the Hosking integral in constraining turbulent MHD decay.

*J. K. J. H. acknowledges funding via the ANU Chancellor's International Scholarship, the Space Plasma, Astronomy and Astrophysics Research Award and the Boswell Technologies Endowment Fund. C. F. acknowledges funding provided by the Australian Research Council (Future Fellowship FT180100495), and the Australia-Germany Joint Research Cooperation Scheme (UA-DAAD). We further acknowledge high-performance computing resources provided by the Leibniz Rechenzentrum and the Gauss Centre for Supercomputing (grants pr32lo, pr48pi and GCS Large-scale project 10391), the Australian National Computational Infrastructure in the framework of the National Computational Merit Allocation Scheme, ANU Merit Allocation Scheme (grant ek9), and the ANU Startup Scheme (grant xx52), as well asthe Pawsey Supercomputing Centre (grant pawsey0810).

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Publication: Exact von-Kármán-Howarth scaling relations for the Hosking integral in non-helical magnetohydrodynamic turbulence. (J.K.J. Hew, D.N. Hosking, C. Federrath, J.R. Beattie, A. Seta & N. Kriel): planned paper

Non-helical inverse transfer of magnetic energy in decaying compressible MHD turbulence. (J.K.J. Hew, D.N. Hosking, C. Federrath, J.R. Beattie, A. Seta & N. Kriel): planned paper

Hew, Justin Kin Jun, and Christoph Federrath. "Lagrangian statistics of a shock-driven turbulent dynamo in decaying turbulence." Monthly Notices of the Royal Astronomical Society 520, no. 4 (2023): 6268-6282.

Presenters

  • Justin Kin Jun Hew

    • Australian National University

Authors

  • Justin Kin Jun Hew

    • Australian National University

  • David N Hosking

    • Princeton University

  • Christoph Federrath

    • Australian National University