Assessment of refined similarity hypothesis in magnetohydrodynamic turbulence

The Kolmogorov’s refined similarity hypothesis (RSH), which plays a fundamental role in studying turbulence intermittency, establishes a connection between locally averaged energy dissipation rates and statistics of velocity increments. This work extends the RSH framework from hydrodynamic (HD) turbulence to magnetohydrodynamic (MHD) turbulence. In analogy to the form of the RSH in HD turbulence and the third-order law in MHD turbulence (Politano & Pouquet, Geophys. Res. Lett. , vol. 25, 1998, pp. 273–276), simple and mixed forms of RSH in MHD turbulence are proposed. These two forms are systematically verified and compared with datasets from direct numerical simulations. The results reveal that the simple form satisfies the predictions of Kolmogorov’s RSH, with respect to the scaling exponents of the local variables and the probability density functions (PDFs) of the Elsässer increments. The range of the local Reynolds number over which the RSH is satisfied is wider for the simple form than for the mixed form. The PDFs of the normalised Elsässer increments reasonably follow Gaussian and Rayleigh distributions for the simple and mixed forms, respectively. The effects of the external forcing and mean magnetic fields are studied, and these do not alter the performance of the two forms. However, cross-helicity can change the RSH constant for the simple form, while this constant for the mixed form does not vary. This study advances understanding of intermittency, multifractality, anomalous scaling and cascade dynamics in MHD turbulence.