Phenomenologies of intermittent Hall MHD turbulence

Mimi Dai

doi:10.3934/dcdsb.2021285

Article Contents

2022, Volume 27, Issue 10: 5535-5560. Doi: 10.3934/dcdsb.2021285

This issue Previous Article Dynamics for the 3D incompressible Navier-Stokes equations with double time delays and damping Next Article Stability of positive steady-state solutions to a time-delayed system with some applications

Phenomenologies of intermittent Hall MHD turbulence

Mimi Dai^,

851 S Morgan St, Chicago, IL 60607, USA

^*Corresponding author: Mimi Dai
^*Corresponding author: Mimi Dai

Received: March 31, 2021

Early access: December 2021

Published: October 2022

The author is supported by NSF grants DMS–1815069 and DMS–2009422. She is grateful to the Institute for Advanced Study for its hospitality

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Abstract

We introduce the concept of intermittency dimension for the magnetohydrodynamics (MHD) to quantify the intermittency effect. With dependence on the intermittency dimension, we derive phenomenological laws for intermittent MHD turbulence with and without the Hall effect. In particular, scaling laws of dissipation wavenumber, energy spectra and structure functions are predicted. Moreover, we are able to provide estimates for energy spectra and structure functions which are consistent with the predicted scalings.

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Mathematics Subject Classification: Primary: 35Q35, 76D03; Secondary: 76W05.

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Figure 1. Structure function exponent as a function of p for EMHD with different intermittency level

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Figure 2. Second (red) and third (blue) order structure functions for homogeneous isotropic self-similar EMHD turbulence

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Figure 3. Second (red) and third (blue) order structure functions for extremely anisotropic EMHD turbulence

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Figure 4. Magnetic energy spectra of Hall MHD when $ \delta_u = \delta_b = 3 $ (blue lines) and when $ \delta_u = \delta_b = 0 $ (red lines)

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Figure 5. Negative exponent $\gamma$ of perpendicular energy spectrum with dependence on intermittency dimension $ \delta_{\perp} $

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Figure 6. Energy spectra of perpendicular cascade under different assumptions

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