Non-Reciprocal Capillary Waves

TL;DR

This paper demonstrates that odd viscosity in chiral fluids breaks the reciprocity of capillary waves, leading to novel wave behaviors, boundary layers, and flow reversals, with potential applications in fluidic waveguiding.

Contribution

It reveals how odd viscosity induces non-reciprocal capillary wave behavior and flow phenomena, a novel insight into chiral fluid surface dynamics.

Findings

Discovered two inequivalent branches of odd capillary waves.

Identified wave-induced flow reversal and anti-Stokes drift.

Showed control of wave propagation via parity-breaking effects.

Abstract

Capillary waves are a classical free-surface phenomenon in fluid mechanics, yet their behavior in chiral fluids remains largely unexplored. We show that odd viscosity breaks the reciprocity of capillary waves. Using linear theory together with fully nonlinear direct numerical simulations, we find that surface tension creates two inequivalent branches of odd capillary waves: a dispersive branch and a quasi-acoustic branch absent in the capillarity-free limit. Their unequal propagation and attenuation transform standing waves into traveling waves and produce an anomalously deep vortical boundary layer. Above a threshold odd viscosity, nonlinear accumulation of vorticity near the surface reverses the induced shear current and drives bulk particles opposite to the wave motion, giving rise to an anti-Stokes drift with no counterpart in conventional fluids. Our results show how combining capillarity with broken parity can be used to control wave propagation and transport at fluid interfaces, opening a route toward one-way fluidic waveguiding and chirality-programmed interfacial flows.