Two-Dimensional Incompressible Rotational Impinging Jets Issuing From a Finite Nozzle

Abstract

This study is devoted to the well-posedness of a two-dimensional incompressible rotational impinging jet issuing from a finite nozzle. More precisely, for a given vertical velocity and a constant vorticity at the nozzle entrance, it is shown that there exists a unique incompressible rotational impinging jet with the free boundary joining smoothly to the endpoint of the nozzle. The crucial difficulty in our analysis is to overcome the smoothness loss of the solution at the corners of the nozzle entrance. Furthermore, we establish the negativity of the vertical velocity and the asymptotic behavior of the flow far downstream.