Horizontal dispersion of ocean tracers in internal wave shear

The horizontal dispersion of ocean tracers due to the interaction of vertical diffusion and the vertical shear from internal waves is examined using a Lagrangian particle-tracking model. For idealized, sinusoidal horizontal velocity profiles of unbounded vertical extent, the irreversible horizontal dispersion of particle clouds is maximal when the timescale of particle diffusion across the velocity variations and the period of shear oscillation are comparable. For measured velocity profiles from the thermocline in the Gulf of Aqaba (Red Sea), the total dispersion and irreversible dispersion of particle clouds both tend to increase with vertical diffusion, cloud height, and cloud age. The total and irreversible horizontal cloud variances typically grow with time (t) like t⁰ to t³ and t¹ to t³, respectively. Estimates of the irreversible horizontal dispersivity from an existing analytical model based on vertically constant, oscillating shear agree remarkably well with estimates from the particle-tracking model, with differences dependent on the vertical variability in vertical diffusion and shear that are not incorporated in the analytical model.