Wind-Ocean Surface Wave Interactions: Growth of Bound and Free Waves under Wind Forcing

We present an analysis of wind-ocean surface wave interactions using direct numerical simulations with the Basilisk Solver, following the work from Wu, Popinet, and Deike (2022). Surface waves are initialized as third-order Stokes waves with steepness (ak), ranging from 0.15 to 0.3, and are forced by a turbulent boundary layer characterized by the ratio of the wind friction velocity and the phase speed of the carrier wave (u∗/c), ranging from 0.1 to 0.5. While Wu et al. (2022) analyzed the growth of the carrier wave, we delve into the multi-scale behaviors of surface waves, including millimeter-sized capillary waves.

We perform a comparative study by exploring various scenarios with different values of (ak) and (u∗/c), and carrier wavelength. We perform a space-time Fourier transform analysis, computing the wave spectrum E(k, ω). The analysis of the spectrum in space E(k) at different instances in time allows us to measure the respective growth rate β(k) for each wavenumber, while the analysis of the space-time Fourier spectrum E(k, ω) provides the angular frequency ω of each growing mode at a given k. We identify modes that are bound to the carrier wave as they grow at the same phase speed c = ω/k as the carrier wave, as well as the development of free modes traveling at a speed given by the dispersion relation of gravity-capillary waves. Results of the growth rate as a function of the wave age (u∗/c) are discussed and compared to previous results.

This comparative analysis allowed us to gain a comprehensive understanding of wind-ocean surface wave dynamics under varying conditions.