Relationship between Wave-Induced Diffusion Tensor and Stokes Drift for Unstable Waves

Abstract:

In the presence of waves, the mean fluid velocity is different depending on whether the mean is taken along a coordinate fixed in space (Eulerian mean) or along a coordinate fixed to fluid particles (Lagrangian mean). The difference (Lagrangian mean minus Eulerian mean) in the velocity is called the Stokes drift (velocity), of which theoretically precise definition was given by Andrews and McIntyre (JFM;1978). Here we give simple and intuitive graphic illustrations explaining the relationship between the wave-induced diffusion tensor and the Stokes drift. The symmetric part of the diffusion tensor is related to the temporal and spatial change of wave amplitude, while the antisymmetric part is related to the spatial change of the amplitude of gyrating motion of fluid particles. The divergence of the diffusion tensor induces an additional transport velocity in the Eulerian mean transport equation. However, the direction of the additional velocity is opposite (identical) to the Stokes drift velocity for the symmetric (antisymmetric) part. This relationship is exemplified for the theoretical Eady wave and for atmospheric eddies simulated by a GCM.