ALBERT

Description: 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 ua* ∼ 8.6 cm s-1 and uw* ∼ 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 70s; the maximum wave slope of our simulated waves is ak ∼ 0.01 and the associated wave age is c/ua * ∼ 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 a previous theory for linear growth and to experimental data and previous simulations that used a prescribed wavy surface for exponential growth. In the exponential growth stage, some of the simulated wave growth rates are comparable to previous studies, but some are about 2-3 times larger than previous studies. In the linear growth stage, the simulated wave growth rates for these four simulation runs are about 1-2 times larger than previously predicted. In qualitative agreement with previous theories for slow-moving waves, the mechanisms for the energy transfer from wind to waves in our simulations are mainly from turbulence-induced pressure fluctuations in the linear growth stage and due to the in-phase relationship between wave slope and wave-induced pressure fluctuations in the exponential growth stage. © 2008 Cambridge University Press.

Description: A new analytical model is developed for the equilibrium range of the spectrum of wind-forced ocean surface gravity waves. We first show that the existing model of Phillips (1985) does not satisfy overall momentum conservation at high winds. This constraint is satisfied by applying recent understanding of the wind forcing of waves. Waves exert a drag on the air flow so that they support a fraction of the applied wind stress, which thus leaves a smaller turbulent stress near the surface to force growth of shorter wavelength waves. Formulation of the momentum budget accounting for this sheltering constrains the overall conservation of momentum and leads to a local turbulent stress that reduces as the wavenumber increases. This local turbulent stress then forces wind-induced wave growth. Following Phillips (1985), the wind sea is taken to be a superposition of linear waves, and equilibrium is maintained by a balance between the three sources and sinks of wave action. These assumptions lead to analytical formulae for the local turbulent stress and the degree of saturation, B(k), of waves in the equilibrium range. We identify a sheltering wavenumber, ks, over which the local turbulent stress is significantly reduced by longer waves. At low wavenumbers or at low winds, when k ≪ ks, the sheltering is weak and B(k) has a similar form to the model of Phillips (1985). At higher wavenumbers or at higher winds, k ≫ ks, B(k) makes a transition to being proportional to k0. The additional constraint of conservation of momentum also yields a formula for the coefficient that appears in the solution for B(k). The spectra for mature seas are calculated from the model and are shown to agree with field observations. In particular, our model predicts more realistic spectral levels toward the high wavenumber limit compared to the previous model of Phillips (1985). We suggest that the model may explain the overshoot phenomena observed in the spectral energy levels as the fetch increases.