Physics:Lamb surface

Short description: Smooth, connected 2D surfaces in fluid dynamics

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 [math]\displaystyle{ \boldsymbol{\omega}\times\mathbf{u} }[/math] everywhere, where [math]\displaystyle{ \boldsymbol{\omega} }[/math] and [math]\displaystyle{ \mathbf{u} }[/math] are the vorticity and velocity field, respectively. The necessary and sufficient condition are

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

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

See also

• Beltrami flow