Viscosity effects in wind wave generation

TL;DR

This study experimentally examines how liquid viscosity influences wind wave generation, revealing distinct regimes, scaling laws, and a new regime at high viscosity, extending previous research over a broad viscosity range.

Contribution

It extends prior work by systematically analyzing viscosity effects on wind-induced surface deformations, identifying new regimes and proposing a scaling model for wrinkles.

Findings

Wrinkles amplitude scales as ν^{-1/2} u^{* 3/2}

Transition from wrinkles to waves becomes abrupt at high viscosity

A new regime with periodic fluid bumps appears at ν > 100-200×10^{-6} m^2/s

Abstract

We investigate experimentally the influence of the liquid viscosity on the problem of the generation of waves by a turbulent wind at the surface of a liquid, extending the results of Paquier, Moisy and Rabaud [Phys. Fluids {\bf 27}, 122103 (2015)] over nearly three decades of viscosity. The surface deformations are measured with micrometer accuracy using the Free-Surface Synthetic Schlieren method. We recover the two regimes of surface deformations previously identified: the wrinkles regime at small wind velocity, resulting from the viscous imprint on the liquid surface of the turbulent fluctuations in the boundary layer, and the regular wave regime at large wind velocity. Below the wave threshold, we find that the characteristic amplitude of the wrinkles scales as $\nu^{-1/2} u^{* 3/2}$ over nearly the whole range of viscosities, whereas their size are essentially unchanged. We propose a simple model for this scaling, which compares well with the data. We finally show that the critical friction velocity $u^*$ for the onset of regular waves slowly increases with viscosity as $\nu^{0.2}$. Whereas the transition between wrinkles and waves is smooth at small viscosity, including for water, it becomes rather abrupt at large viscosity. Finally, a new regime is found at $\nu > 100-200 \times 10^{-6}$~m$^2$~s$^{-1}$, characterized by a slow, nearly periodic emission of large-amplitude isolated fluid bumps.