The dynamics of an ideal fluid flow into an inclined cavity of a paraboloid form

The present paper is a theoretical study of the motion of an inclined cavity of a paraboloid form filled with an ideal and incompressible fluid. The cavity is placed in the gravity field and its roto-translation motion is unknown. We look for determining the translation and rotation velocities of the cavity, the velocity potential of the fluid particles as well as the form of the fluid free surface. To this end, we shall use both the analytical and numerical methods. Numerical examples are presented in tables and graphs to elucidate the accuracy and efficiency of the proposed method.