Shear flow instability analysis of young wind waves: coupled air–water Orr–Sommerfeld framework guided by experiment

The generation and growth of wind waves are re-examined using linear viscous shear flow instability theory by solving the coupled in-air and in-water Orr–Sommerfeld equations. To enable comparison with the available laboratory observations, model simulations are performed for a wide range of wavelengths spanning the gravity–capillary and gravity wave regimes typical of such experiments. The sensitivity of the results to key modelling assumptions is investigated, including the friction velocity, the surface drift velocity at the air–water interface as well as the shapes of velocity profiles in air and in water, which are modelled using the mixing-length approach. Airflows both over an initially smooth surface and over a surface modified by the emergence of fast-growing short ripples, and thus effectively rough, are considered. A detailed energy budget analysis, based on eigenfunctions of the coupled Orr–Sommerfeld equations across different wavelengths, provides further insight into the mechanisms governing energy transfer from wind to water waves under diverse flow conditions.