Mathematical Geosciences Seminar - Adrian Fraser

Dr. Adrian Fraser, Hale Postdoctoral Fellow, LASP, University of Colorado Boulder

Non-ideal instabilities in sinusoidal shear flows with a streamwise magnetic field.

We investigate the linear stability of a sinusoidal shear flow with an initially uniform streamwise magnetic field in the framework of incompressible magnetohydrodynamics (MHD) with finite resistivity and viscosity. This flow is known to be unstable to the Kelvin- Helmholtz instability in the hydrodynamic case. The same is true in ideal MHD, where dissipation is neglected, provided the magnetic field strength does not exceed a critical threshold beyond which magnetic tension stabilizes the flow. Here, we demonstrate that including viscosity and resistivity introduces two new modes of instability. One of these modes, which we refer to as an Alfvénic Dubrulle-Frisch instability, exists for any nonzero magnetic field strength as long as the magnetic Prandtl number Pm < 1. We present a reduced model for this instability that reveals its excitation mechanism to be the negative eddy viscosity of periodic shear flows described by Dubrulle & Frisch (1991). Finally, we demonstrate numerically that this mode saturates in a quasi-stationary state dominated by counter-propagating solitons.

Dial-In Information

https://cuboulder.zoom.us/j/93373630169

Tuesday, September 20 at 11:00am to 12:00pm

Engineering Center, ECOT 317
1111 Engineering Drive, Boulder, CO 80309

Event Type

Colloquium/Seminar

Interests

Science & Technology, Research & Innovation

Audience

Faculty, Students, Graduate Students, Postdoc

College, School & Unit

Engineering & Applied Science

Group
Applied Mathematics
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