Conservation of magnetic helicity fluctuations by spatial decorrelations in freely decaying, strongly magnetised turbulence

Abstract: he Hosking integral (Hosking and Schekochihin 2021, PRX 11, 041005) has recently been recognised as a key invariant constraining the decay of magnetic fields that are statistically homogeneous, isotropic and non-helical. In this paper, we construct von-Karman-Howarth-Monin relations for the Hosking correlator (i.e., the two-point correlation function of the magnetic-helicity density) and provide exact scaling relations for its behaviour in both incompressible and compressible magnetohydrodynamic (MHD) turbulence. We show that under the conditions of rapid decorrelation of velocity and magnetic fields, the Hosking integral becomes the conserved quantity of ideal, non-helical incompressible magnetohydrodynamic (MHD) turbulence. Furthermore, we provide explicit forms of the relevant fourth and fifth-order two-point correlation functions. Keywords: Magnetohydrodynamics, turbulence, von-Karman-Howarth relations, isotropic turbulence