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Abstract
The plan of the research is mainly concerned with the study of the interfacial waves between incompressible immiscible fluids using the equations of motion with the appropriate boundary conditions. This thesis is divided into four chapters as follows: Chapter 1 is a general introduction. This chapter includes a
classification for Newtonian fluids, equations of motion and boundary
conditions, magnetohydrodynamics, mathematical background, concepts, and tools we need in our research and a survey of some previous studies related to the subject of the research. The problems of nonlinear instability of interfacial waves between two or more
immiscible conducting cylindrical fluids are shown. Some approximate methods like Runge-Kutta,exponential stability, the method of strained parameter,and the method of multiple scales are explained. The equations of motion for some modeling of fluid are discussed and their applications. In chapter 2, the study of analysis of nonlinear instability of the
nonlinear dynamics of interfacial waves at the interface of swirling
streaming inviscid jet is established. The investigations are based on the concept of the perturbations. The mechanism by which the growth of small-amplitude perturbations yields nonlinear waves is illustrated. For
the purpose of comparing the numerical results with laboratory observations, we account for viscous dissipation in the bulk of the fluids in terms of phenomenological damping coefficient included in the equation of motion