  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.
