Fluid dynamical Lorentz force law and Poynting theorem—derivation and implications

Abstract

Fluid dynamical analogs of the electrodynamical Lorentz force law and Poynting theorem are derived and their implications analyzed. The companion paper by Scofield and Huq 2014 Fluid. Dyn. Res. 46 055513 gives a heuristic introduction to the present results. The fluid dynamical analogs are consequences of a new causal, covariant, geometrodynamical theory of fluids (GTF). Compared to the Navier–Stokes theory, GTF shows the existence of new causal channels of stress-energy propagation and dissipation due to the action of transverse modes of flow. These channels describe energy-dissipation and transport along curved stream tubes common in turbulent flows.