On incompressible oblique impinging jet flows.

The object of this work is to investigate the fluid mechanics of oblique impinging jet flows and to this end some existence and nonexistence results are initiated. First, we established the existence of incompressible oblique impinging jet plane flows with two asymptotic directions. More precisely, given a two-dimensional semi-infinitely long nozzle and a wall behind the nozzle, for any given mass flux in the inlet of the nozzle, then there exists a smooth incompressible oblique impinging jet flow with two asymptotic directions. The impinging jet develops two free streamlines, which initiate smoothly at the endpoints of the semi-infinitely long nozzle, and the speed on free streamlines remains a constant, which can be determined by the impinging jet flow itself. The asymptotic behaviors of the oblique impinging jet flows at the far fields, the position of the stagnation points, convexity of the free boundaries and other properties are also considered. On another side, it is showed in this paper that there does not exist an oblique impinging jet flow with one asymptotic direction generally. [ABSTRACT FROM AUTHOR]