We restrict attention to axially symmetric solutions and consider models with and without vortices.
The role of these potentials is to hold down the vortices from moving as a result of mutual interactions.
Owing to the induced velocity field, the three vortices start to rotate around each other.
The final state comprises two counter-rotating vortices which dissipate.
In these works the waves and vortices were assumed to be uncorrelated.
The vorticity is modelled as point vortices, vortex sheets, and finite area vortex regions.
Upon returning to the stationary frame of reference, these cells are precisely the viscous vortices oscillating to and fro high above the ripples.
This result indicated that the vortex merging process suppressed the activity of the streamwise vortices and made the mixing layer more two-dimensional.
