On the distortion of diffusion by non-breaking waves

Scalars in the upper ocean are transported by surface gravity waves. Their net transport is often attributed to the advective Stokes drift, however, this assumption neglects potential effects of waves on diffusion. In this study, we conduct a fully Lagrangian analysis of the advection–diffusion equation to show that non-breaking waves influence diffusion in two ways: (i) the unsteady strain from the wave orbital motion causes diffusion to vary as a function of wave phase, maximising horizontal diffusion under the crests and minimising it under the troughs, and conversely for vertical diffusion, (ii) the Lagrangian mean water level induces a mean vertical strain which yields a net enhancement of the horizontal diffusion. These effects are driven by the normal strain of the wave and therefore represent a mechanism distinct from the drift-induced shear dispersion, which we refer to as ‘distortion’. This means that the net transport of diffusive scalars under surface waves differs from that under only the wave-averaged Stokes drift, and similarly that the net transport under a standing wave differs from diffusion in a quiescent fluid. Asymptotic expressions for the diffusivity distortion are derived for monochromatic progressive waves, standing waves and a wave spectrum, which are then validated with numerical simulations. Finally, we also investigate the influence of the Lagrangian mean water level on buoyant particle distributions, showing how it can skew the interpretation of vertical transport models commonly used for studying ocean microplastics.