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

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.