Vorticity dynamics in the presence of shallow water waves

We present a theoretical and numerical investigation of the interaction of a circular Rankine vortex and a surface gravity wavefield with length and time scales applicable to surfzone vortices. An approximate solution first given by Coste et al. [11] using a wave equation that accounts for the Doppler shift and diffraction by the vortical current is presented. Here, we calculate time-averaged wave quantities such as the radiation stress and wave momentum as a function of the vortex circulation. The Craik-Leibovich [12] wave-mean flow interaction equations predict a net drift of the vortex in the direction of the refracted waves at the core, with a velocity on the order of the Stokes drift.;The approximate analytical wave solution agrees well with the numerical results from the parabolic wave model REF-DIF as well as the fully nonlinear wave model, FUNWAVE. Differences in FUNWAVE are primarily due to the steepening (and speeding up) of the wave near the vortex core. The results of a full numerical simulation of the combined wave-current interaction in a rectangular domain and flat bottom with a wave absorbing layer at the domain boundary are given. Here it is shown that the dynamics of the vortex consists of steady translation in the upwave direction due to an 'anti-Stokes drift', deformation and rotation from wave-induced flows near the core as well as shear-type vorticity filaments that wind around the vortex boundary as seen in Melander et al. [37]. This is compared to a vortex subjected to random velocity perturbation in the absence of waves.