Impact of pressure anisotropy on the cascade rate of Hall-MHD turbulence with biadiabatic ions

TL;DR

This study investigates how ion pressure anisotropy influences the energy cascade rate in Hall-MHD turbulence through 3D simulations, revealing that anisotropy can significantly alter cascade dynamics depending on scale.

Contribution

It introduces a detailed analysis of pressure anisotropy effects on cascade rates in Hall-MHD turbulence and presents a new Fourier-based method for computing exact laws in simulations.

Findings

Pressure anisotropy can enhance or reduce the cascade rate.

Anisotropy effects are scale-dependent and more pronounced with initial anisotropy.

A new numerical method for analyzing turbulence in full increment space is proposed.

Abstract

The impact of ion pressure anisotropy on the energy cascade rate of Hall-MHD turbulence with biadiabatic ions and isothermal electrons is evaluated in three-dimensional direct numerical simulations, using the exact (or third-order) law derived in \citet{simon_exact_2022}. It is shown that pressure anisotropy can enhance or reduce the cascade rate, depending on the scales, in comparison with the prediction of the exact law with isotropic pressure, by an amount that correlates well with pressure anisotropy $a_p=\frac{p_\perp}{p_\parallel}\neq1$ that develops in simulations initialized with an isotropic pressure (${a_p}_0=1$). A simulation with initial pressure anisotropy, ${a_p}_0=4$, confirms this trend, exhibiting a stronger impact on the cascade rate, both in the inertial range and at larger scales, close to the forcing scales. Furthermore, a Fourier-based numerical method, to compute exact laws in numerical simulations in the full $(\ell_\perp,\ell_\parallel)$ increment plane, is presented.