Langmuir Turbulence in Swell

The problem is posed and solved for the oceanic surface boundary layer in the presence of wind stress, stable density stratification, equilibrium wind-waves, and remotely generated swell-waves. The addition of swell causes an amplification of the Lagrangian-mean current and rotation toward the swell-wave direction, a fattening of the Ekman velocity spiral and associated vertical Reynolds stress profile, an amplification of the inertial current response, an enhancement of turbulent variance and buoyancy entrainment rate from the pycnocline, and—for very large swell—an upscaling of the coherent Langmuir circulation patterns. Implications are discussed for the parameterization of Langmuir turbulence influences on the mean current profile and the material entrainment rate in oceanic circulation models. In particular, even though the turbulent kinetic energy monotonically increases with wave amplitude inversely expressed by the turbulent Langmuir number La, the Lagrangian shear eddy viscosity profile κL(z) is a nonmonotonic function of La, first increasing with increasing wave amplitude up to approximately the wind-wave equilibrium level, then decreasing with additional swell-wave amplitude. In contrast, the pycnocline entrainment rate is a monotonic function ~La−2.