Abstract
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.
Highlights
The Stokes drift velocity, which is the time mean velocity of a fluid particle in water waves [1,2], may play a significant role on the mass/tracer transport in the ocean and the evolution of coastal morphology
The Lagrangian Stokes drift cannot be detected directly by current measurements at a fixed position, it is suggested to be explicitly considered in the models that attempt to predict the transport of organisms and solutes in the nearshore environment as a surface wave effect
Reniers et al [5] showed that when Stokes drift was considered in the model of the computed drifter trajectories, good agreement was found with the observed retention of surf zone material on a rip-channel beach
Summary
The Stokes drift velocity, which is the time mean velocity of a fluid particle in water waves [1,2], may play a significant role on the mass/tracer transport (e.g., larval, plankton, oil, plastic pollution, etc.) in the ocean and the evolution of coastal morphology. Stokes drift near the water surface could be stronger than measured Eulerian currents on the inner shelf, and it is necessary to include the Stokes drift to explain an observed shoreward migration of a dye plume trajectory. Reniers et al [5] showed that when Stokes drift was considered in the model of the computed drifter trajectories, good agreement was found with the observed retention of surf zone material on a rip-channel beach. Without Stokes drift considered, the estimated results overpredicted the number of observed drifter exits by almost an order of magnitude during the drifter deployments. This emphasizes the importance of including Stokes drift when calculating the transport of floating materials on the ocean surface. The tracer advection equation has been modified for Eulerian ocean models to account for Stokes drift effect by McWilliams et al [9], but they did not consider the diffusion terms
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