A discontinuous conically symmetric flow of an ideal incompressible fluid

The Euler equations are considered in spherical coordinates to describe the steady flow of an ideal incompressible fluid. An exact conically symmetric solution based on the source/sink and strong conic discontinuity with an apex in zero of the coordinate system is obtained. The northern region of the flow is situated in the finite vicinity of the symmetry axis, i.e., within a discontinuity cone, where the solution is regular and vortex-free. On the other side of the discontinuity, the flow adjoins the permeable equator plane. In this region, the flow is vortex-like, and its properties are determined by a density jump. The fluid flowing through the discontinuity is governed by the increase of entropy principle. The thermal field corresponding to the flow is presented. It shows that the spatial heterogeneity of temperature results from the interaction between the azimuth vorticity component and the meridional velocity component. A strong discontinuity cone angle is revealed to be a significant parameter of the problem. A comparative analysis of the source and sink properties is performed. The considered flows qualitatively differ in terms of pressure and velocity behavior.