| dc.description.abstract | Magnetic fields are present in the solar system and astrophysical bodies (e.g. the Sun's field, the Earth's field, and the fields of giant planets, stars and galaxies). Our research examines the effect of magnetic fields on these systems, extending the work of Meshalkin and Sinai (1961) & Manfroi and Young (2002). The results will be useful for understanding the effects of the magnetic field in more turbulent regimes, although this study is concerned with the instabilities associated with classical laminar flow. We aim to investigate the role played by the magnetic field in modifying the stability properties of planar-forced fluid flows. In the absence of magnetic fields, the flow found by a body force, and nonlinear interactions with Rossby waves result in the generation of strong zonal flows. However, we find that the presence of a weak magnetic field suppresses the zonal jet generation.
Here we study the instabilities of the Kolmogorov flow. We consider u_0=(0,sin x ) as a 2D incompressible flow. In the presence of a mean magnetic field, the dynamics are governed by the Navier–Stokes equations and the induction equation. We perform a classical linear analysis, in which growth rate, stability criteria, and MHD effects are derived. Instabilities are investigated associated with two magnetic field orientations, which can be x-directed (horizontal) or y-directed (vertical}) in our two-dimensional system to give an MHD version of Kolmogorov flow. In a basic equilibrium state magnetic field lines are straight for the case of vertical field and sinusoidal for horizontal field with an additional component of the external force balancing the resulting Lorentz force. | en_GB |
