Particle dynamics due to interaction between a breaking-induced vortex and a nearbed vortex

One single regular wave, traveling over a submerged abrupt discontinuity, can generate a pair of counter-rotating vortices. A nearbed vortex is generated by the flow separation that occurs at the bed, while a surface vortex can be generated by either a direct (co-rotating vortex) or a backward (counter-rotating vortex) breaking. Starting from recent laboratory test results, which highlighted the role of wave nonlinearity on the interaction between the counter-rotating vortices and led to the identification of three different regimes [Brocchini et al., “Interaction between breaking-induced vortices and near-bed structures: Part 1—Experimental and theoretical investigation,” J. Fluid Mech. 940, A44 (2022)], the present work illustrates the main findings obtained from the optical analysis of the flow field induced by three different wave conditions, each belonging to a specific nonlinear regime. For each test, the measured domain has been seeded with virtual particles to obtain long-lasting trajectories driven by the Eulerian flow field recovered through the particle tracking velocimetry analysis, to be studied by means of single-particle and multi-particle statistics. Both absolute and relative statistics confirm that a ballistic regime exists just after particle release (⁠ ⁠) at each location of the domain. At times larger than the Lagrangian timescale (⁠ ⁠), the absolute statistics suggest a sub-diffusive regime both within the vortices and between such areas (i.e., in correspondence of the breaking-induced jet), followed by a superdiffusive regime, dominated by rotation and particle release. Differently, the relative diffusivity suggests the occurrence of a superdiffusive regime at ⁠, corresponding to an enstrophy cascade and exponential growth, followed by a Richardson regime and then by an oscillatory behavior, during which particles are periodically trapped and released by vortices.