“The Josephson-Anderson Relation and the Origin of Turbulent Drag”

Gregory Eynik (Johns Hopkins Whiting School of Engineering) will present at the 2022 Simons Collaboration on Wave Turbulence Annual Meeting on December 1st and 2nd in New York.

“The Josephson-Anderson Relation and the Origin of Turbulent Drag”:

The Josephson-Anderson relation provides the modern understanding for energy dissipation in quantum superfluids and superconductors, relating drag to motion of quantized vortex lines across the background potential superflow.  The same relation has been recently shown to apply widely to classical fluid flows described by the incompressible Navier-Stokes equation. Here it connects dissipation with flux of continuously distributed vorticity across the streamlines of the smooth potential Euler solution. We shall concisely review these concepts and explain how they give a new resolution of the classical d’Alembert paradox, connecting it with Onsager’s theory of high Reynolds number turbulence. The theory explains experimental puzzles about the wall conditions of solid bodies necessary for anomalous dissipation. The Josephson-Anderson relation is valid, however, at any Reynolds number and explains the origin of drag in flows ranging from low-Reynolds-number Stokes flow to transitional and fully-developed turbulence. As such, it provides a sharp, precise tool with which to address the theoretical and practical issue of drag reduction. We shall review our initial efforts to apply the Josephson-Anderson relation to turbulent channel flow and to resolve the 75-year-old open problem of drag reduction by polymer additives.