It has been long established that Reynolds number effects can lead to flow instabilities and/or transition from laminar to turbulent flow regimes. The nature of free shear jets is well understood and heavily covered in the fluid mechanics literature. On the other hand, the study of wall bounded or confined jets presents some challenges and is still a developing area of research that requires further attention. In this work, we deal with quasi-impinging jets, such as the ones feeding into a virtual impactor, which are used for micron-size solid particle collection and separation. Two dimensional direct numerical simulations are performed using a finite volume code at three Reynolds numbers that cover laminar, transition, and turbulent flow regimes. The simulations demonstrate the presence of a Kelvin-Helmholtz instability associated with jet flapping and vortex shedding. In addition, the stability characteristics of the free boundary layer are compared and analyzed. The study of the transport of aerosol particles in such systems is initiated in a way that is completely different from previous time-averaged calculations. It is shown that the particle behavior is strongly influenced by the frequency of fluctuations and its motion is affected by the fluid's coherent structures. The three dimensional features of the flow are then investigated by Large Eddy Simulation (LES). The Lagrangian dynamic subgrid scale turbulence model (Meneveau et al., J. of Fluid Mechanics, v. 319, pp. 353) is implemented and validated in two canonical turbulent flow problems before it is applied to the virtual impaction jet. The LES results confirm the presence of a self-sustained shear layer instability, and are consequently used to investigate the mechanism of particle dispersion and preferential concentration.