Eulerian Description of Wave-Induced Stokes Drift Effect on Tracer Transport

The wave-induced Stokes drift plays a significant role on mass/tracer transport in the ocean and the evolution of coastal morphology. The tracer advection diffusion equation needs to be modified for Eulerian ocean models to properly account for the surface wave effects. The Eulerian description of Stokes drift effect on the tracer transport is derived in this study to show that this effect can be accounted for automatically in the wave-averaged advection-diffusion equation. The advection term in this equation is the wave-averaged concentration flux produced by the interaction between fluctuations of linear wave orbital velocity and tracer concentration, and the advection velocity is the same as the Stokes drift velocity. Thus, the effective dispersion of tracers by surface gravity waves is calculated due to the Stokes drift effect and the corresponding dispersion coefficient in the depth-integrated equation is then derived. The Eulerian description of Stokes drift effect of tracer concentration is illustrated by the direct numerical simulation of the advection–diffusion equation under simple linear waves. The equivalence between both the Eulerian and Lagrangian descriptions is also verified by particle tracking method. The theoretical analysis is found to agree well with the wave-induced dye drift velocity observed outside the surf zone in a longshore current experiment.

Wave-Filtered Surf Zone Circulation under High-Energy Waves Derived from Video-Based Optical Systems

This paper examines the potential of an optical flow video-based technique to estimate wave-filtered surface currents in the nearshore where wave-breaking induced foam is present. This approach uses the drifting foam, left after the passage of breaking waves, as a quasi-passive tracer and tracks it to estimate the surface water flow. The optical signature associated with sea-swell waves is first removed from the image sequence to avoid capturing propagating waves instead of the desired foam motion. Waves are removed by applying a temporal Fourier low-pass filter to each pixel of the image. The low-pass filtered images are then fed into an optical flow algorithm to estimate the foam displacement and to produce mean velocity fields (i.e., wave-filtered surface currents). We use one week of consecutive 1-Hz sampled frames collected during daylight hours from a single fixed camera located at La Petite Chambre d’Amour beach (Anglet, SW France) under high-energy conditions with significant wave height ranging from 0.8 to 3.3 m. Optical flow-computed velocities are compared against time-averaged in situ measurements retrieved from one current profiler installed on a submerged reef. The computed circulation patterns are also compared against surf-zone drifter trajectories under different field conditions. Optical flow time-averaged velocities show a good agreement with current profiler measurements: coefficient of determination (r2)= 0.5–0.8; root mean square error (RMSE) = 0.12–0.24 m/s; mean error (bias) =−0.09 to −0.17 m/s; regression slope =1±0.15; coherence2 = 0.4–0.6. Despite an underestimation of offshore-directed velocities under persistent wave breaking across the reef, the optical flow was able to correctly reproduce the mean flow patterns depicted by drifter trajectories. Such patterns include rip-cell circulation, dominant onshore-directed surface flow and energetic longshore current. Our study suggests that open-source optical flow algorithms are a promising technique for coastal imaging applications, particularly under high-energy wave conditions when in situ instrument deployment can be challenging.