Three-dimensional magnetohydrodynamic Kelvin–Helmholtz instability of cylindrical flow with permeable boundaries

• Published in: Physics of plasmas Vol. 21; no. 3
• Main Author: Kumar Awasthi, Mukesh
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.03.2014
• Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AXIAL SYMMETRY; Boundaries; Conducting fluids; CYLINDRICAL CONFIGURATION; Flow stability; Fluid dynamics; Fluid flow; FLUIDS; HEAT TRANSFER; Incompressible flow; Interface stability; INTERFACES; Kelvin-Helmholtz instability; MAGNETIC FIELDS; Magnetic permeability; Magnetohydrodynamics; MASS TRANSFER; Plasma physics; POROUS MATERIALS; Porous media; Stability analysis; Stability criteria; Suction
• ISSN: 1070-664X; 1089-7674
• DOI: 10.1063/1.4869728

We study the linear magnetohydrodynamic Kelvin–Helmholtz instability of the interface between two viscous, incompressible, and electrically conducting fluids. The phases are enclosed between two coaxial cylindrical porous layers with the interface through which mass and heat transfer takes place. The fluids are subjected to a constant magnetic field parallel to the streaming direction, and the suction/injection velocities for the fluids at the permeable boundaries are also taken into account. Here, we use an irrotational theory in which the motion and pressure are irrotational, and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. We consider both asymmetric and axisymmetric disturbances in our analysis. A quadratic dispersion relation is deduced and stability criterion is given in terms of a critical value of relative velocity, as well as, magnetic field. It has been observed that in the case of permeable boundaries, heat and mass transfer phenomena play a dual in the stability analysis. The flow through porous medium is more stable than the pure flow.