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.^[1][2][3] Lamb surfaces are orthogonal to the Lamb vector ${\displaystyle {\boldsymbol {\omega }}\times \mathbf {u} }$ everywhere, where ${\displaystyle {\boldsymbol {\omega }}}$ and ${\displaystyle \mathbf {u} }$ are the vorticity and velocity field, respectively. The necessary and sufficient condition are

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

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

• Beltrami flow