Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids

Abstract

The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schrödinger equations (l-NLS) with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoretically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.

Nonlinear EHD Instability of Two-Superposed Walters’ B Fluids Moving through Porous Media

“…He found that the presence of both streaming and tangential electric field had an effect on the disturbances. A nonlinear stability of surface wave between two conducting fluids was examined by Zakaria et al [11]. Based on the multiple scale approach, they derived a nonlinear Schrödinger equation with complex coefficients.…”

Non Darcian Approach to MHD Flow of Stratified Incompressible Viscous Fluid Between Two Semi-Infinite Parallel Plates Partially Filled With Highly Porous Medium

“…Vajravelu et al [10] have discussed the effect of magnetic field on unsteady flow of two immiscible conducting fluids between two permeable beds. Transciet couette flow in a rotating non-Darcian porous medium parallel plate configuration is studied by Anwarbeg et al [11] Kandryzakaria et al [12] discussed magneto hydrodynamics instability of interfacial waves between two immiscible cylindrical fluids.…”

Non Darcian Approach to Flow of Stratified Incompressible Viscous Fluid Between Two Semi-Infinite Parallel Plates Partially Filled With Highly Porous Medium

“…Vajravelu et al [10] have discussed the effect of magnetic field on unsteady flow of two immiscible conducting fluids between two permeable beds. Transciet couette flow in a rotating non-Darcian porous medium parallel plate configuration is studied by Anwarbeg et al [11] Kandryzakaria et al [12] discussed magneto hydrodynamics instability of interfacial waves between two immiscible cylindrical fluids. Earlier Narasimhacharyulu et al [13] studied the problem of two phase fluid flow between parallel plates with porous lining and Narasimhacharyulu et al [14] examined the flow of micropolar fluid between parallel plates coated with porous lining.…”