Flow equations being nonlinear are notoriously difficult to solve analytically. In this work we show that through the three independent

functions variational formalism for stationary barotropic flows one can obtain new analytical solutions of the flow equations.

This family of flows is constructed such that they flow on predetermined Bernoullian surfaces from which the rest of the variational

variables are derived. The flows obtained has non zero helicity and some of them are self-gravitating. Through the technique described

above the existence of a new astrophysical object; the self-gravitating torus was derived.

Bibliography

[1] Asher Yahalom "Using fluid variational variables to obtain new analytic solutions of self-gravitating flows with nonzero helicity"

Procedia IUTAM 7 (2013) 223 – 232.