A simple model of the atmospheric boundary layer over the ocean where the swell impact on the atmosphere is explicitly accounted for is suggested. The model is based on Ekman's equations, where the stress in the wave boundary layer is split into two parts: the turbulent and wave-induced stress. The turbulent stress is parameterized traditionally via the eddy viscosity proportional to the generalized mixing length. The wave-induced stress directed upward (from swell to the atmosphere) is parameterized using the formalism of the wind-over-waves coupling theory. The model can be seen as an extension of the model by Kudryavtsev and Makin (J Phys Oceanogr 34:934-949, 2004) to the scale of the entire atmospheric boundary layer by including the Coriolis force into the momentum conservation equation and generalizing the definition of the mixing length. The regime of low winds for swell propagating along the wind direction is studied. It is shown that the impact of swell on the atmosphere is governed mainly by the swell parameter--the coupling parameter that is the product of the swell steepness and the growth rate coefficient. When the coupling parameter drops below - 1 the impact of swell becomes significant and affects the entire atmospheric boundary layer. The turbulent stress is enhanced near the surface as compared to the no-swell case, and becomes negative above the height of the inner region. The wind profile is characterized by a positive gradient near the surface and a negative gradient above the height of the inner region forming a characteristic bump at the height of the inner region. Results of the model agree at least qualitatively with observations performed in the atmosphere in presence of swell.
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