Fluid flow versus Geometric Dynamics

Dragos Isvoranu, Constantin Udriste
This paper investigates the way in which geometric dynamics on Riemannian manifolds can be applied to fluid flow. The equations of motion from fluid mechanics (momentum equations), expressed on general curvilinear coordinates, are compared with the equations of motion in a gyroscopic field of forces. Attempts are made to seek conditions under which both describe the same motion, especially in the case when trajectories are not field lines. It is proved that all pathlines and streamlines are
more » ... streamlines are geodesics in the least square sense and, in some circumstances, other trajectories included in geometric dynamics have physical support. Mathematics Subject Classification: 37N10, 76B75, 93C15, 34H05, 34B60.