Lamb surface

In fluid dynamics, Lamb surfaces are smooth, connected orientable two-dimensional surfaces, which are simultaneously stream-surfaces and vortex surfaces, named after the physicist Horace Lamb. Lamb surfaces are orthogonal to the Lamb vector $$\boldsymbol{\omega}\times\mathbf{u}$$ everywhere, where $$\boldsymbol{\omega}$$ and $$\mathbf{u}$$ are the vorticity and velocity field, respectively. The necessary and sufficient condition are


 * $$(\boldsymbol{\omega}\times\mathbf{u})\cdot[\nabla\times(\boldsymbol{\omega}\times\mathbf{u})]=0, \quad \boldsymbol{\omega}\times\mathbf{u}\neq 0.$$

Flows with Lamb surfaces are neither irrotational nor Beltrami. But the generalized Beltrami flows has Lamb surfaces.