Bulk, Spectral and Deep Water Approximations for Stokes Drift: Implications for Coupled Ocean Circulation and Surface Wave Models

Abstract Surface waves modify upper ocean dynamics through Stokes drift related processes. Stokes drift estimated from a discrete wave spectrum is compared to Stokes drift approximations as a monochromatic profile based on bulk surface wave parameters, and to two additional superexponential functional forms. The impact of these different methods on ocean processes is examined in two test‐bed cases of a wave‐current coupled system: (1) a wind‐free shallow water inlet test case and (2) an idealized deep water hurricane case with high varying winds. In case (1), tidal currents and bathymetry can modify the waves and significantly affect Stokes drift computed from the wave spectrum. In case (2), rapid variation in atmospheric stress at high wind speed generates large departures from fully developed equilibrium seas. In both cases, large deviations in ocean current response are produced when the Stokes drift is approximated monochromatically from bulk wave parameters, rather than from integration over the wave spectra. Deep water simulations using the two superexponential approximations are in better agreement with those estimated from wave spectra than are those using the monochromatic, exponential profile based on bulk wave parameters. In order to represent the impact of Stokes drift at resolved scales, we recommend that for studies of nearshore processes and deep water events, like wave‐current interactions under storms, the Stokes drift should be calculated from full wave spectra. For long simulations of open ocean dynamics, methods using superexponential profiles to represent equilibrium wind seas might be sufficient, but appear to be marginally more computationally efficient.