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Stability of Magnetohydrodynamic Shear Flow Boundaries: Kelvin-Helmholtz Instabilities and Emission of Magnetosonic Waves Open Access


Other title
MHD Shear Flow Instabilities
Magnetosonic Wave Emission
Kelvin-Helmholtz Instability
Type of item
Degree grantor
University of Alberta
Author or creator
Turkakin, Hava
Supervisor and department
Ian Robert Mann (Department of Physics)
Robert Rankin (Department of Physics)
Examining committee member and department
David Knudsen (External examiner)
Frank Hegmann (Department of Physics)
Richard Marchand (Departmet of Physics)
Department of Physics

Date accepted
Graduation date
Doctor of Philosophy
Degree level
boundaries for the Kelvin-Helmholtz Instability (KHI) is investigated. We have focused our attention on the emission of magnetosonic waves from the Kelvin-Helmholtz (K-H) unstable shear flow boundaries of MHD plasmas. We have shown for the first time that the Kelvin-Helmholtz Instability is a mechanism for fast and slow MHD wave, i.e. magnetosonic wave, generation along MHD shear flow boundaries. Our results is significant in showing that the emission of MHD waves from an unstable MHD shear flow boundary is possible and these waves may provide a efficient mean of energy transportation in between two MHD media. The Kelvin - Helmholtz generated fast/slow waves are introduced in the context of the primary/secondary KHI. First, the primary and secondary K-H surface wave modes on the Earth’s magnetopause are studied. The primary KHI is caused by fast MHD waves while the secondary KHI is caused slow MHD waves. The secondary KHI usually is possible at smaller shear flow speeds and have smaller growth rates than the primary KHI. The Earth’s magnetopause is considered as an infinitely thin MHD shear flow boundary. Phase velocity diagrams are presented that allow us to identify the excited MHD waves that correspond to growing modes of the KHI under different conditions of the regions on both sides of the magnetopause boundary. The relation between the primary and the secondary KHI to magnetosonic wave interactions under different solar wind conditions is revealed through these diagrams. Using the observational values of the KHI relevant waves and the results of our study, general behavior of the primary and the secondary KHI relevant waves along the K-H unstable magnetopause is provided. A relation between the KHI waves and Negative Energy Waves (NEWs) is also shown. Following, the KHI of the Earth’s magnetotail flow channels associated with bursty bulk flows (BBFs) is investigated. The BBF channel boundary is also considered as an infinitely thin MHD shear flow boundary and an inner boundary is assumed in the middle of the channel. MHD oscillations of the BBF channels in both kink and sausage modes are investigated for the KHI. Both the primary and the secondary KHI are found to cause the emission of magnetosonic waves along these boundaries. These instabilities are shown to be important for stopping the BBFs where the KHI removes energy from the flow. We have provided a model that can explain, for the first time, the generation mechanism for the observations of waves propagating towards both flanks of the Earth’s magnetopause and emitted from BBF channels in the central magnetotail. Results shown in this section was published in Geophysical Research Letters and the paper was chosen as a spotlight paper with innovative ideas by American Geophysical Union. Then a finite width boundary layer is added and emission of magnetosonic waves due to KHI from superfast relative flows across MHD plasma boundaries are investigated. While previous studies have focused their attention on the most unstable KHI waves, we have shown that the most significant modes are not the fastest growing modes. In contrast, the KHI wave growth resulting in emission of magnetosonic waves, which usually does not efficiently take place for the fastest growing modes, is the main source of energy transport. With the results obtained, the processes of the KHI and magnetosonic wave emission along various MHD shear flow boundaries in the Earth’s magnetosphere and the solar corona is discussed. We have concluded that while the KHI would be more favorable on the day-side magnetopause and Coronal Mass Ejection (CME) boundaries, emission of magnetosound would dominate along the nightside magnetopause, BBFs in the inner plasmasheet and Supra-Arcade Downflows (SADs) in the solar corona. Finally, nonlinear evolution of the KHI and emission of magnetosound due to the action of the KHI are investigated using the FLASH code which is provided by Flash Center at the University of Chicago. The same parameter space as the linear calculations for finite transition thickness is used to study the nonlinear KHI along MHD shear flow boundaries. Results obtained from the FLASH code were in very good agreement with the linear results. Emission of magnetosound from MHD shear flow boundaries in the linear stages of the KHI is confirmed.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
Turkakin, H., R. Rankin, and I. R. Mann, Primary and secondary compressible Kelvin- Helmholtz surface waves instabilities on the earth’s magnetopause, J. Geop. Res., 118 , 2013.Turkakin, H., I. R. Mann, and R. Rankin, Kelvin-Helmholtz unstable magnetotail flow channels: Deceleration and radiation of MHD waves, Geop. Res. Lett., 41 , 2014.

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