Lamb vector

In fluid dynamics, Lamb vector is the cross product of vorticity vector and velocity vector of the flow field, named after the physicist Horace Lamb. The Lamb vector is defined as

where ${\displaystyle \mathbf {u} }$ is the velocity field and ${\displaystyle \mathbf {\omega } =\nabla \times \mathbf {u} }$ is the vorticity field of the flow. It appears in the Navier–Stokes equations through the material derivative term, specifically via convective acceleration term,

In irrotational flow, Lamb vector is zero, as in Beltrami flow. The concept of Lamb vector is widely used in turbulent flows. The Lamb vector is analogous to electric field, when Navier–Stokes equation is compared with Maxwell's equations.

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