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.[1][2][3] Lamb surfaces are orthogonal to the Lamb vector
everywhere, where
and
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.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/953b2b7970acc3c8587e19a3b6bcb4b1c3ddc817)
Flows with Lamb surfaces are neither irrotational nor Beltrami. But the generalized Beltrami flows has Lamb surfaces.
- ^ Lamb, H. (1932). Hydrodynamics, Cambridge Univ. Press,, 134–139.
- ^ Truesdell, C. (1954). The kinematics of vorticity (Vol. 954). Bloomington: Indiana University Press.
- ^ Sposito, G. (1997). On steady flows with Lamb surfaces. International journal of engineering science, 35(3), 197–209.