Growth of surface wind-waves in water of finite depth: A laboratory experiment

This paper reports on laboratory experiment results on wind-driven surface waves in finite depth and their comparison with theoretical predictions and experimental in-situ studies. We introduce the Miles theory’s extension to the case of finite depth, as well as the rules transforming theoretical expressions to formulae commonly used in experimental routines, in particular the important rules transforming theoretical growth rates to experimental ones. Wind waves depend strongly on boundary marine layer parameters, namely, the aerodynamic roughness length, the Charnock constant, as well as the drag coefficient. Consequently, this work gives detailed measurements of these parameters in finite depths. Experiments conducted in the IRPHÉ/Pythéas wind-wave tank (Marseille, France), reveal that for a given wind speed, these values are higher in finite depth than in deep water. In the limit case of fully developed surface, due to depth, theoretical and empirical formulas relating the critical values of wave age to the non-dimensional depth have been experimentally verified. Plots of non-dimensional peak frequency, non-dimensional energy, and the inverse of wave age, against non-dimensional depth are presented. The plots clearly show that these quantities admit a limit due to the depth influence. All data obey the range of empirical values established in field experiments. Experimental data, obtained in the facility, agree with the theoretical family of depth-dependent wave growth rate as a function of wave age in finite depth. The non-dimensional growth-rate data obtained in our laboratory, as a function of the inverse of wave age, are consistent with the theoretical predictions of Miles theory in finite depth (Montalvo et al., 2013a,b, Latifi et al.. 2017), as well as measurements from other laboratories.