On the non-circular hydraulic jump for an impinging inclined jet

When a laminar inclined circular jet impinges on a horizontal surface, it forms a non-circular hydraulic jump resulting from the non-axisymmetric flow. In this study, we develop an integral approach in the boundary-layer (near impingement) and thin-film regions to theoretically analyze the flow field and the hydraulic jumps structure. We particularly explore the interplay among inertia, gravity, viscosity, and the effective inclination angle on the non-axisymmetric flow. The boundary-layer height exhibits an azimuthal dependence at a strong gravity level only; however, the thin film thickness as well as the hydraulic jump profile shows a strong non-axisymmetric behavior at all gravity levels. In contrast to the existing literature, the present study accounts for the presence of the boundary layer near impingement and the azimuthal flow. We demonstrate that the azimuthal flow component cannot be neglected in the presence of gravity. The theory is validated against existing experimental results for the inclined jet of water.