Kelvin-Helmholtz instability in a rotating ideally conducting inhomogeneous plasma

Pramana ◽  
2004 ◽  
Vol 62 (4) ◽  
pp. 899-909
Author(s):  
Vinod Kumar ◽  
K. M. Srivastava ◽  
Nagendra Kumar ◽  
Himanshu Sikka
Keyword(s):  
Inhomogeneous Plasma ◽  
Helmholtz Instability

scholarly journals A theory of MHD instability of an inhomogeneous plasma jet

2010 ◽  
Vol 77 (3) ◽  
pp. 315-337 ◽  
Author(s):  
ANATOLY S. LEONOVICH
Keyword(s):  
Shear Flow ◽  
Plasma Flow ◽  
Flow Instability ◽  
Inhomogeneous Plasma ◽  
Plasma Jet ◽  
Wkb Approximation ◽  
Tangential Discontinuity ◽  
Radial Coordinate ◽  
Helmholtz Instability ◽  
The Stability

AbstractA problem of the stability of an inhomogeneous axisymmetric plasma jet in a parallel magnetic field is solved. The jet boundary becomes, under certain conditions, unstable relative to magnetosonic oscillations (Kelvin–Helmholtz instability) in the presence of a shear flow at the jet boundary. Because of its internal inhomogeneity the plasma jet has resonance surfaces, where conversion takes place between various modes of plasma magnetohydrodynamic (MHD) oscillations. Propagating in inhomogeneous plasma, fast magnetosonic waves drive the Alfven and slow magnetosonic (SMS) oscillations, tightly localized across the magnetic shells, on the resonance surfaces. MHD oscillation energy is absorbed in the neighbourhood of these resonance surfaces. The resonance surfaces disappear for the eigenmodes of SMS waves propagating in the jet waveguide. The stability of the plasma MHD flow is determined by competition between the mechanisms of shear flow instability on the boundary and wave energy dissipation because of resonant MHD-mode coupling. The problem is solved analytically, in the Wentzel, Kramers, Brillouin (WKB) approximation, for the plasma jet with a boundary in the form of a tangential discontinuity over the radial coordinate. The Kelvin–Helmholtz instability develops if plasma flow velocity in the jet exceeds the maximum Alfven speed at the boundary. The stability of the plasma jet with a smooth boundary layer is investigated numerically for the basic modes of MHD oscillations, to which the WKB approximation is inapplicable. A new 'unstable mode of MHD oscillations has been discovered which, unlike the Kelvin–Helmholtz instability, exists for any, however weak, plasma flow velocities.

Simulations of the shock-driven Kelvin–Helmholtz instability in inclined gas curtains

2021 ◽  
Vol 33 (6) ◽  
pp. 064103
Author(s):  
Brian Romero ◽  
Svetlana V. Poroseva ◽  
Peter Vorobieff ◽  
Jon M. Reisner
Keyword(s):  
Helmholtz Instability

Error analysis of higher order trace finite element methods for the surface Stokes equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Jankuhn ◽  
Maxim A. Olshanskii ◽  
Arnold Reusken ◽  
Alexander Zhiliakov
Keyword(s):  
Finite Element ◽  
Stokes System ◽  
Parametric Representation ◽  
Higher Order ◽  
Optimal Order ◽  
Helmholtz Instability ◽  
Surface Stability ◽  
Instability Problem ◽  
Convergence Results ◽  
Optimal Order Convergence

AbstractThe paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in ℝ3. The method employs parametric Pk-Pk−1 finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin--Helmholtz instability problem on the unit sphere.

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