Slanted snaking of localized Faraday waves

TL;DR

This paper investigates the phenomenon of slanted snaking in localized Faraday waves through experiments, theory, and simulations, revealing the role of conserved volume and introducing a universal coupled model.

Contribution

It presents the first combined experimental, theoretical, and numerical analysis of slanted snaking in Faraday waves, emphasizing the influence of volume conservation.

Findings

Experimental evidence of hysteresis in wave transition

Observation of localized waves extending outside hysteresis

Model successfully reproduces slanted snaking behavior

Abstract

We report on an experimental, theoretical and numerical study of slanted snaking of spatially localized parametrically excited waves on the surface of a water-surfactant mixture in a Hele-Shaw cell. We demonstrate experimentally the presence of a hysteretic transition to spatially extended parametrically excited surface waves when the acceleration amplitude is varied, as well as the presence of spatially localized waves exhibiting slanted snaking. The latter extend outside the hysteresis loop. We attribute this behavior to the presence of a conserved quantity, the liquid volume, and introduce a universal model based on symmetry arguments, which couples the wave amplitude with such a conserved quantity. The model captures both the observed slanted snaking and the presence of localized waves outside the hysteresis loop, as demonstrated by numerical integration of the model equations.