Vortex ring connecting to a free surface:
Interaction of a vortex ring with a freely deformable surface. Panels (a)-(f) show 6 representative stages when the ring connects to the surface. Contours of instantaneous surface elevation are plotted on the surface. For better visualization, the surface is artificially shifted up.
Direct numerical simulation of free-surface turbulence:
Surface deformation generated by complex vortical structures in the turbulence underneath the surface. The surface-connected vortices O1—O5 are indicated. Contours of the vertical vorticity omega_z and the surface divergence du/dx+dv/dy are plotted in (a) and (b), respectively. In (b), the velocity vectors (u,v) are also plotted for every four grid points. In (c), the vortices are represented by the lambda_2 method. More details of the simulation can be found in Yang & Shen (2011, J. Comput. Phys.).