Wind-wave growth over a viscous liquid

TL;DR

This study investigates how increased liquid viscosity affects wind-wave growth, using experiments with silicon oil and advanced optical measurements to compare results with existing theoretical models.

Contribution

It provides the first detailed experimental analysis of wind-wave growth over viscous liquids and evaluates Miles' model applicability in such conditions.

Findings

Viscosity significantly influences wave growth rates.

Miles' model reasonably predicts growth over viscous liquids.

Critical friction velocity scales with liquid viscosity.

Abstract

Experimental and theoretical studies on wind-wave generation have focused primarily on the air-water interface, where viscous effects are small. Here we characterize the influence of the liquid viscosity on the growth of mechanically generated waves. In our experiment, wind is blowing over a layer of silicon oil, of viscosity 20 and 50 times that of water, and waves of small amplitude are excited by an immersed wave-maker. We measure the spatial evolution of the wave slope envelope using Free-Surface Synthetic Schlieren, a refraction-based optical method. Through spatiotemporal band-pass filtering of the surface slope, we selectively determine the spatial growth rate for each forcing frequency, even when the forced wave is damped and coexists with naturally amplified waves at other frequencies. Systematic measurements of the growth rate for various wind velocities and wave frequencies are obtained, enabling precise determination of the marginal stability curve and the onset of wave growth. We show that Miles' model, which is commonly applied to water waves, offers a reasonable description of the growth rate for more viscous liquids. We finally discuss the scaling of the growth rate of the most amplified wave and the critical friction velocity with the liquid viscosity.