Wave-crests around obstacles in odd viscous liquids

TL;DR

This paper theoretically investigates wave-crest formations around obstacles in odd viscous liquids, providing a framework to determine odd-viscosity coefficients through analysis of wave shapes.

Contribution

It introduces a theoretical method to relate wave-crest shapes to odd-viscosity coefficients, aiding experimental measurement of these coefficients.

Findings

Derived parametric relations for odd-viscosity coefficients

Predicted wave-crest shapes in 2D and 3D odd viscous liquids

Established a framework for experimental determination of odd viscosity

Abstract

The values of liquid odd-viscosity coefficients remain largely unknown, with only a single experimental measurement reported to date [Nature Physics 15, 1188 (2019)]. In this work, inspired by the well-known consequences of dispersion surfaces in classical liquids from the work of Lighthill, we theoretically determine the shapes of constant-phase wave crests formed around obstacles moving at constant velocity in two- and three-dimensional odd viscous liquids, which may or may not undergo rigid rotation. From this analysis, we derive parametric relations that the odd-viscosity coefficients must satisfy, providing a framework for their experimental determination.