Vorticity dynamics

Does there exist any boundary condition for vorticity which corresponds to no-sleep ones - zero velocity on the boundary of the solid. In a playful way we can say that dolphins know the answer on this question, but keep silence. Dolphin’s skin can read vorticity distribution in order to prevent turbulent flow.

Vorticity layer

Vorticity function simplifies dynamics system and decreases the number of equations and unknown functions (continuity equation, divergence-free, etc.):

No-slip condition. Biot-Savar Law.

No-slip condition V=0 on the streamlined object via Biot-Savar Law has rather complicated integral formula for vorticity.

Boundary condition for vorticity

At infinity we have zero-boundary condition

An actual question - what happens on the boundary of the object.

Does there exist no-slip boundary condition for vorticity?

Yes. Dirichlet no-slip boundary condition can be written as Robin boundary ones for vorticity. No integral relations from Biot-Savar Law and other sophisticated conditions!