# Wind-sustained viscous solitons

## TL;DR

This study investigates wind-sustained viscous solitons in high-viscosity liquids, revealing their subcritical formation, propagation dynamics, and how increased wind velocity affects their emission and interactions.

## Contribution

It provides experimental evidence of viscous solitons' subcritical nature and characterizes their dynamics and bifurcation behavior in a wind-tunnel setup.

## Key findings

- Viscous solitons are emitted in high shear stress regions and sustained by wind in lower stress zones.
- Their velocity results from a balance between aerodynamic and viscous drag.
- Higher wind speeds increase soliton emission frequency, affecting downstream interactions.

## Abstract

When wind blows at the surface of a liquid of sufficiently high viscosity, a wave packet of small amplitude is first generated, which sporadically forms large-amplitude fluid bumps that rapidly propagate downstream. These nonlinear structures, first observed by Francis [Philos. Mag. 42, 695 (1954)], have an almost vertical rear facing the wind and a weak slope at the front. We call them viscous solitons. We investigate their dynamics in a wind-tunnel experiment using silicon oil of kinematic viscosity 1000 mm^2 s^-1 by means of laser sheet profilometry and particle image velocimetry. We give evidence of their subcritical nature: they are emitted in a region of large shear stress but, once formed, they are sustained by the wind and propagate in a region of lower stress. Their propagation velocity is given by the balance between aerodynamic drag in the air and viscous drag in the liquid. The stable soliton branch of the subcritical bifurcation diagram is reconstructed from the measured soliton amplitude at various wind velocities and distances along the channel. At large wind velocity, the emission frequency of solitons increases, resulting in a long-range sheltering of downstream mature solitons by newly formed upstream solitons, which limits their course.