doi:10.1017/S0022112008004060 Printed in the United Kingdom 1 Direct numerical simulation of wind-wave

An air–water coupled model is developed to investigate wind-wave generation processes at low wind speed where the surface wind stress is about 0.089 dyn cm−2 and the associated surface friction velocities of the air and the water are u∗a ∼ 8.6 cm s−1 and u∗w ∼ 0.3 cm s−1, respectively. The air–water coupled model satisfies continuity of velocity and stress at the interface simultaneously, and hence can capture the interaction between air and water motions. Our simulations show that the wavelength of the fastest growing waves agrees with laboratory measurements (λ ∼ 8–12 cm) and the wave growth consists of linear and exponential growth stages as suggested by theoretical and experimental studies. Constrained by the linearization of the interfacial boundary conditions, we perform simulations only for a short time period, about 70 s; the maximum wave slope of our simulated waves is ak ∼ 0.01 and the associated wave age is c/u∗a ∼ 5, which is a slow-moving wave. The effects of waves on turbulence statistics above and below the interface are examined. Sensitivity tests are carried out to investigate the effects of turbulence in the water, surface tension, and the numerical depth of the air domain. The growth rates of the simulated waves are compared to