First observation of the Josephson-Anderson relation in experiments on hydrodynamic drag

TL;DR

This study experimentally verifies the Josephson-Anderson relation in classical fluids by measuring the velocity field around an accelerating plate in water, confirming theoretical predictions about the decomposition of drag into potential and vortical parts.

Contribution

First experimental verification of the Josephson-Anderson relation in classical hydrodynamics using particle image velocimetry around an accelerating flat plate.

Findings

Excellent agreement between measured drag and theoretical prediction.

Added mass contribution remains significant even in vortical flow.

Potential flow analysis accurately predicts the vortical flux of vorticity.

Abstract

We verify a recent prediction (Eq. 3.50 in G. L. Eyink, Phys. Rev. X 11, 031054 (2021)) for the drag on an object moving through a fluid. In this prediction the velocity field is decomposed into a nonvortical (potential) and vortical contribution, and so is the associated drag force. In the Josephson-Anderson relation the vortical contribution of the drag force follows from the flux of vorticity traversing the streamlines of the corresponding potential flow. The potential component is directly determined by the plate acceleration and its added mass. The Josephson-Anderson relation is derived from the quantum description of superfluids, but remarkably applies to the classical fluid in our experiment. In our experiment a flat plate is accelerated through water using a robotic arm. This geometry is simple enough to allow analytic potential flow streamlines. The monitored plate position shows an oscillatory component of the acceleration, which adds an additional test of the Josephson-Anderson relation. The instantaneous velocity field is measured using particle image velocimetry. It enables us to evaluate Eq. 3.50 from [1] and compare its prediction to the measured drag force. We find excellent agreement, and, most remarkably find that the added mass contribution to the drag force still stands out after the flow has turned vortical. We finally comment on the requirements on the experimental techniques for evaluating the Josephson-Anderson relation.