A-priori study of the subgrid energy transfers for small-scale dynamo in kinematic and saturation regimes

TL;DR

This study analyzes the statistical properties of subgrid energy transfers in small-scale dynamos across different regimes using high-resolution simulations, providing insights for improved subgrid-scale modeling in magnetohydrodynamics.

Contribution

It offers an a priori analysis of subgrid energy transfers during various dynamo stages, highlighting their intermittency and differences in inertial, Lorentz, and magnetic induction effects.

Findings

All SGS energy transfers show intermittency with scale-dependent PDFs.

Intermittency decreases in inertial transfers during saturated dynamo.

The analysis guides subgrid-scale modeling in MHD dynamos.

Abstract

The statistical properties of the subgrid energy transfers of homogeneous small-scale dynamo are investigated during the kinematic, nonlinear and statistically saturated stages. We carry out an a priori analysis of data obtained from an ensemble of direct numerical simulations on $512^3$ grid points and at unity magnetic Prandtl number. In order to provide guidance for subgrid-scale (SGS) modelling of different types of energy transfer that occur in magnetohydrodynamic dynamos, we consider the SGS stress tensors originating from inertial dynamics, Lorentz force and the magnetic induction separately. We find that all SGS energy transfers display some degree of intermittency as quantified by the scale-dependence of their respective probability density functions. Concerning the inertial dynamics, a depletion of intermittency occurs in presence of a saturated dynamo.