Steady-state flows of inviscid incompressible fluid and related particle dynamics in rectangular channels

In this paper, we investigate inviscid incompressible fluid flow in a 2D channel of finite length described by Euler's equation with Yudovich's boundary conditions. A border of the channel includes inlet with prescribed vorticity and normal velocity, an outlet with only normal velocity defined and two horizontal impermeable walls. Using analytic and numerical methods we obtained a set of steady-state flows contains both flow-through and recirculation zones, characterized by various distributions of vorticity and stream function. The properties and structure of flows and the effect on it of parameters such as channel length and velocity of fluids in inlet and outlet of the channel is studied. Steady-state flows linear instability and perturbation response was evaluated using spectral approach and long-time numerical simulation by the vortex-in-cell method for a non-steady problem. The second part of the paper is devoted to the investigation of Lagrangian dynamics of a fluid particle in steady-state and periodically driven flows. The factors affecting on stay time of the particle in the flow-through zone of the channel were investigated.