AN UNCONSTRAINED HAMILTONIAN-FORMULATION FOR INCOMPRESSIBLE FLUID-FLOW

The equations governing the time evolution of an ideal fluid in materi al coordinates are expressed as an unconstrained canonical Hamiltonian system. The incompressibility of the flow is consequent upon certain first integrals of the motion. The variable conjugate to the configura tion field is not the usual linear momentum, but is instead a quantity that is related to linear momentum through an auxiliary scalar field whose time derivative is the pressure. The definition of the Hamiltoni an involves a minimization with respect to this auxiliary field. The m ethod of derivation may be generally applied to obtain unconstrained H amiltonian descriptions of Lagrangian held equations subject to pointw ise constraints.