# American Institute of Mathematical Sciences

doi: 10.3934/dcdsb.2021285
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## Phenomenologies of intermittent Hall MHD turbulence

 851 S Morgan St, Chicago, IL 60607, USA

*Corresponding author: Mimi Dai

Received  April 2021 Early access December 2021

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

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.

Citation: Mimi Dai. Phenomenologies of intermittent Hall MHD turbulence. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021285
##### References:

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##### References:
Structure function exponent as a function of p for EMHD with different intermittency level
Second (red) and third (blue) order structure functions for homogeneous isotropic self-similar EMHD turbulence
Second (red) and third (blue) order structure functions for extremely anisotropic EMHD turbulence
Magnetic energy spectra of Hall MHD when $\delta_u = \delta_b = 3$ (blue lines) and when $\delta_u = \delta_b = 0$ (red lines)
Negative exponent $\gamma$ of perpendicular energy spectrum with dependence on intermittency dimension $\delta_{\perp}$
Energy spectra of perpendicular cascade under different assumptions
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