Conservation of “Partial Vorticity” with Application on Hydraulic Jumps

Abstract

In two preceding works, the idea of partial conservation theorems was introduced and conservation equations for partial energy and partial angular momentum were established. A similar conservation theorem for partial vorticity of incompressible fluids is established here. The vorticity vector is divided into two elements (both denoted “partial vorticity”) and their conservation equations established separately. They show that, in addition to terms similar to the terms of the conservation equation for total vorticity, the conservation equation for partial vorticity has a term that describes the transfer of vorticity between the partial vorticities, i.e. Without affecting the vorticity vector. A simple example of an application is included. It shows that the vortex in the vicinity of a hydraulic jump is located above the surface level of the incoming flow.