Magnetohydrodynamic (MHD) Stability of Oscillating Fluid Cylinder with Magnetic Field

Abstract

The magnetohydrodynamic (MHD) stability of oscillating fluid with longitudinal magnetic field has been discussed. The problem is formulated and the (MHD) basic equations are solved. By using the computer procedure from different values of the acting magnetic field the stable and unstable regions are identified. This phenomenon is interest, academically and during the geological drilling in the crust of the earth as we have superposed gas-oil layer mixture fluids. A general eigenvalue relation is derived studied analytically and results are confirmed numerically. The oscillating liquid has stabilizing tendency, in the absence of the effect of the electromagnetic field in the liquid and gas cylinder region, so the model is only subject to the capillary force. It has been found that the model is unstable in the region 0 < x < 1, while it is stable in the region 1 ≤ x < ∞ where x is the longitudinal dimensionless wave number. This means that the model is just unstable in small domains of axisymmetric perturbation but it stables in all domains. For very high intensity of magnetic field the model is completely stable for all values of wavelengths. The capillary force is destabilizing only in a small axisymmetric domain while it is stabilizing in all other axisymmetric perturbations. The stability behavior of the model comes after destabilizing behavior of the model when it be reduced and suppressed.