[Paper Review] Effect of wind turbulence on wave generation over a viscous liquid

Romain Mathis, Sébastien Cazin+5 more|arXiv (Cornell University)|Jan 28, 2026

Ocean Waves and Remote Sensing0 citations

TL;DR

The paper experimentally examines how free-stream turbulence enhances wrinkles and lowers the onset wind speed for wave formation on a highly viscous liquid, showing that the wrinkle-wave transition occurs at a nearly constant friction velocity but shifts with turbulence levels.

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.

Motivation & Objective

• Investigate how free-stream turbulence in air affects wrinkle growth and the transition to regular waves on a viscous liquid surface.
• Determine how grid-generated turbulence modifies the onset conditions and surface deformation amplitudes.
• Quantify the role of friction velocity at the air-liquid interface in the wrinkle-wave transition.
• Develop a qualitative energy-balance perspective to explain observed fetch-dependent behavior.

Proposed method

• Wind tunnel experiments with air blowing over a silicone oil layer (viscosity 50x that of water).
• Two grids (G32 and G64) generate controlled free-stream turbulence levels up to ~8%.
• Measurement of air velocity and turbulence with hot-wire anemometry above the interface.
• PIV in the liquid to determine interface shear and friction velocity via interface stress continuity.
• Free-Surface Synthetic Schlieren to map surface deformations with micrometer accuracy.
• Analysis of surface height data to extract zeta_rms and its relation to u* and U_a.

Experimental results

Research questions

• RQ1 How does free-stream turbulence intensity influence wrinkle amplitude and the onset of wave generation on a viscous liquid?
• RQ2 Does the wrinkle-wave transition depend on fetch, and if so, how is it related to the friction velocity u*?
• RQ3 How does grid-induced turbulence modify boundary-layer properties and the critical conditions for wave onset?
• RQ4 Can a wave-energy-balance framework explain the observed non-monotonic evolution of wave amplitude with fetch?

Key findings

• Free-stream turbulence increases wrinkle amplitude and lowers the critical wind speed for the wrinkle-to-wave transition.
• The transition occurs at approximately constant friction velocity u* (about 0.33–0.35 m/s) across inlet conditions, but the corresponding wind speed U_a decreases with higher turbulence (8.0 m/s NG; 5.9 m/s G32; 5.1 m/s G64).
• Friction velocity decays with fetch following a Schlichting-like law, and grids shift the virtual origin and pre-factor, affecting u* vs x.
• Wave amplitudes scale with u* in the wrinkle regime and jump sharply at transition, with zeta_rms ≈ 16 ± 4 μm at transition.
• The measured zeta_rms at transition relative to viscous scale delta_nu = nu_a / u* is about 0.36 ± 0.1, larger than prior experiments, potentially due to lower surface tension of the silicone oil used.
• The large turbulence-induced increase in wrinkle amplitude accounts for the reduced U_ac in grid cases.