Waves and the Air–Sea Momentum Budget: Implications for Ocean Circulation Modeling

The influence of waves on the mean flow is derived on a rotating earth in the form of interaction stresses and a mass flux in the averaged momentum balance and mass conservation equations, respectively, using Hasselmann's formalism and keeping only the vertical component f of the Coriolis parameter. These stresses, easily computed from a spectral wave model, arise from both spatial gradients in the wave field and the bufferlike role of waves that store a small fraction of the air–sea momentum flux in the initial growth stages (young seas) and restore this momentum to the mean currents, atmosphere, or solid earth when wave energy is dissipated. The practical importance of these wave-induced stresses on the depth-integrated mean circulation is evaluated from wind-wave growth curves and a third-generation spectral wave model. In steady conditions, waves are shown to induce stresses opposed to the wind stress for wave growth stages that may represent up to 10% of the wind stress for short fetches. Assuming simple mean flow responses, wave-induced stresses shall translate into mean sea level variations, which are typically less than 1 mm in the middle of ocean basins but are much larger and significant in shallow areas like continental shelves. The present formulation is consistent with previous studies on wave-driven inertial oscillations and nearshore circulation, cases for which wave effects are known to be much stronger.