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Abstract A particular type of dyadic model for the magnetohydrodynamics (MHD) with dominating forward energy cascade is studied. The model includes intermittency dimension $$\delta $$ in the nonlinear scales. It is shown that when $$\delta $$ is small, positive solution with large initial data for either the dyadic MHD or the dyadic Hall MHD model develops blowup in finite time. Moreover, for a class of positive initial data with large velocity components and small magnetic field components, we prove that there exists a positive solution that blows up at a finite time.
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Phenomenologies of intermittent Hall MHD turbulence
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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- PAR ID:
- 10340704
- Date Published:
- Journal Name:
- Discrete & Continuous Dynamical Systems - B
- Volume:
- 0
- Issue:
- 0
- ISSN:
- 1531-3492
- Page Range / eLocation ID:
- 0
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/dcdsb.2021285
