Wall jet on a hemi-spherical shell: conserved quantities and group invariant solution. (English) Zbl 1176.35139

Summary: The variational derivative approach is used to derive the conservation laws for the system of equations for the velocity components as well as for the third-order partial differential equation for the stream function governing flow outside and inside of a hemi-spherical shell. One of the conserved vectors for the stream function equation is used to derive the conserved quantity for the wall jet. A symmetry is associated with that conserved vector and then this symmetry is used to generate a group invariant solution for the wall jet formed on the outside or inside of the shell.


35Q35 PDEs in connection with fluid mechanics
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76M30 Variational methods applied to problems in fluid mechanics