https://www.researchgate.net/publication/342247893
A rectilinear vortex with a core filled with air models a plunging breaking wave whose tip has pinched off a pocket of air. For a rectilinear vortex moving parallel to the free surface, air is entrained as the free surface wraps around the axial vorticity. The amount of air that is entrained depends on a Froude number that is based on the circulation of vorticity. Cross-axis vorticity is formed as a result of instabilities in the axial vorticity. Roll-wave instabilities form on the outer face of the sheet of water that wraps around the axial vorticity. For sufficiently high Froude numbers, both the axial and cross-axis vortex tubes entrain air. The air that is entrained is driven by pressure gradients toward the centers of the axial and cross-axis vortex tubes where the pressures are minimal.