Energy-Dissipation Theorem and Detailed Josephson Equation for Ideal Incompressible Fluids

Abstract

The dissipation of energy in the flow of an ideal incompressible fluid is described by a theorem whose derivation relies upon the exact three-dimensional Magnus formula discussed in the previous paper. The theorem, which explicitly demonstrates the role of vortex motion in the process of energy dissipation, can be used to calculate the trajectories of vortices. Also derived is a detailed Josephson equation - an extension of Anderson's "new corollary in classical hydrodynamics" - which provides an exact non-time-average relation between chemical potentials and vortex motion.