Observations of swell dissipation across oceans reveal a significant loss of energy that can bethe result of many of processes. Among these candidate mechanisms, this paper examines the properties ofthe viscous air-sea boundary layer driven by swells in order to characterize the induced atmospheric flowregime and its associated viscous dissipation over swells. A series of 3-D numerical experiments is carriedout with a RANS model and appropriate turbulence closure. These experiments reveal a laminar to turbulenttransition in the near free-surface region for a common range of characteristic amplitudes and periods ofswells under stationary conditions. At low Reynolds number, laminar conditions prevail and computeddecay rates conform to the analytical formulation lm of the Stokes interfacial boundary layer for this problem. The turbulent regimes are characterized as well, and the new decay rates follow a nondimensional parametric relation above Re=5. 1e5 (e.g., amplitude larger than 1.1 m for a 14 s monochro- matic wave period). Typical decay rates are up to 4 times above the laminar values, which is a factor 10 less?than the largest rates estimated for oceanic conditions. A sensitivity analysis is finally conducted to evaluate the influence of the stationary hypothesis. It demonstrates a short setup length and low relative variations of the unsteady decay rates for laminar, transitioning and developed turbulent conditions, which confirms the evaluation of steady decay rates.