A numerical and theoretical study of wind over fast-propagating water waves

Effects of fast-propagating water waves on the overlying wind are investigated using simulation and theoretical analysis. By performing a large eddy simulation (LES) of turbulent wind over water waves with high wave age, we observe that the perturbation to wind velocity and pressure by the waves, or the wave-induced airflow, is mainly induced by the vertical movement of the wave surface. We perform scaling analysis to show that the turbulent stress effects on fast wave-induced airflow are negligible. Moreover, we find that the curvilinear model developed for opposing wave effects on wind by Cao et al. (J. Fluid Mech., vol. 901, 2020, p. A27) provides predictions that agree well with the present LES results of wind following fast waves. Our analyses of the results indicate that the fast wave-induced airflow is a quasilinear process. To elucidate the mechanisms for fast wave effects, we split the curvilinear model into two equations corresponding to wave kinematics and forcing by wave elevation, respectively. Using these equations, we illustrate that the vertical component of wave orbital velocity induces a strong airflow perturbation, which produces the dominant components of fast wave-induced airflow and determines its overall spatial structure. Furthermore, we discover that the weak components of fast wave-induced airflow are forced by the dominant components via viscous stress and by the forcing induced by wave elevation, and generate the form drag on the wave surface.