Incompressible impinging jet flow with gravity

TL;DR

This paper studies the steady flow of an incompressible, inviscid fluid from a nozzle under gravity, establishing existence, boundary properties, and asymptotic behavior of impinging jets with free surfaces.

Contribution

It proves the existence of two-dimensional incompressible impinging jets with gravity for given pressure and flux, and analyzes their boundary and asymptotic properties.

Findings

Existence of impinging jet solutions under specified conditions.

Smooth initiation and horizontal downstream free surfaces.

Asymptotic behavior characterized upstream and downstream.

Abstract

In this paper, we investigate steady two-dimensional free-surface flows of an inviscid and incompressible fluid emerging from a nozzle, falling under gravity and impinging onto a horizontal wall. More precisely, for any given atmosphere pressure $p_{atm}$ and any appropriate incoming total flux $Q$, we establish the existence of two-dimensional incompressible impinging jet with gravity. The two free surfaces initiate smoothly at the endpoints of the nozzle and become to be horizontal in downstream. By transforming the free boundary problem into a minimum problem, we establish the properties of the flow region and the free boundaries. Moreover, the asymptotic behavior of the impinging jet in upstream and downstream is also obtained.