Abstract
The scope of the present paper is to determine how ion electrostatic wave perturbations in plasma flows are influenced by the presence of a kinematically complex velocity shear. For this purpose we consider a model based on the following set of physical equations: the equation of motion, the continuity equation and the Poisson equation for the electric potential governing the evolution of the system. After linearizing the equations, we solve them numerically. We find out that for a variety of specific values of parameters the system may exhibit quite interesting dynamic behaviour. In particular, we demonstrate that the system exhibits two different kinds of shear flow instabilities: (a) when the wave vectors evolve exponentially, the ion sound modes become unstable as well; while, (b) on the other hand, one can find areas in a parametric space where, when the wave vectors vary periodically, the physical system is subject to a strongly pronounced parametric instability. We also show the possibility of the generation of beat wave phenomena, characterized by a noteworthy quasi-periodic temporal behaviour. In the conclusion, we discuss the possible areas of applications and further directions of generalization of the presented work.
Highlights
It is well known that plasma flows in different astrophysical, geophysical and laboratory situations are characterized by spatially inhomogeneous velocity fields and the presence of this velocity shear may significantly influence the modes of collective behaviour fostered in these flows
The goal of the present study was to consider ion-sound waves influenced by kinematic complexity and to study the role of the latter in the dynamical evolution of these waves
In the framework of the method developed by [10] we have considered the full set of equations, consisting of the momentum conservation equation, the mass conservation equation and the Poisson equation, and we linearized these around an equilibrium state
Summary
It is well known that plasma flows in different astrophysical, geophysical and laboratory situations are characterized by spatially inhomogeneous velocity fields (shear flows) and the presence of this velocity shear may significantly influence the modes of collective behaviour fostered in these flows. The existence of such shear flows with kinematic complexity might strongly influence the plasma processes in a number of realistic astrophysical scenarios. In last two decades it has been realized that collective phenomena in shear flows are characterized by so-called non-modal processes, which in turn are related with non-normality of the involved mathematical operators [7]. In the framework of this method, the system of partial differential equations governing the dynamical evolution of modes of collective behavior is reduced to the inspection of a set of ordinary differential equations (ODEs) in time, i.e., to the solution of a relatively simple initial value problem
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