Effect of wind turbulence on wave generation over a viscous liquid

TL;DR

This study investigates how free-stream turbulence affects wave formation on a viscous liquid surface, revealing that turbulence increases wrinkle amplitude and lowers the critical wind speed for wave transition, with a constant friction velocity at transition.

Contribution

It provides new experimental insights into turbulence effects on wave generation over viscous liquids and develops a qualitative wave energy balance model.

Findings

Turbulence increases wrinkle amplitude.

Turbulence reduces the critical wind speed for wave onset.

Friction velocity remains approximately constant at the transition.

Abstract

When wind blows over the surface of a viscous liquid, a clear transition from irregular small-amplitude streamwise-oriented wrinkles to well-defined nearly two-dimensional regular waves is observed at a critical wind velocity. We examine how free-stream turbulence in the air influences the growth of wrinkles and regular waves, as well as the transition between these two regimes. Experiments are carried out in a wind tunnel, in which air is blown over a tank filled with silicone oil whose viscosity is fifty times higher than that of water. The free-stream turbulence is enhanced using upstream grids, achieving relative turbulence intensities up to 8%. Surface deformations are measured using Free-Surface Synthetic Schlieren with micrometer accuracy. Velocity measurements are performed using hot-wire anemometry above the interface and particle image velocimetry in the liquid. Results reveal two primary effects of grid-enhanced free-stream turbulence: an increase in the wrinkle amplitude, and a reduction in the critical wind speed at the onset of regular waves. Nevertheless, the wrinkle-wave transition still corresponds to an approximately constant friction velocity. Similar to a classical boundary layer over a flat plate, the friction velocity is found to decrease with fetch. From a wave energy balance, we develop a qualitative model explaining why, with the highly viscous liquid considered here, this decrease in the friction velocity results in a non-monotonic variation of the wave amplitude with the fetch.