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.

See also

• Beltrami flow