Question: Consider a velocity field with non vanishing curl. Define a locally orthonormal basis at a point in the velocity field, so that one basis vector,

Consider a velocity field with non vanishing curl. Define a locally orthonormal basis at a point in the velocity field, so that one basis vector, e_x, is parallel to the vorticity. Now imagine the remaining two basis vectors as being frozen into the fluid. Show that they will both rotate about the axis defined by e_x and that the vorticity will be the sum of their angular velocities (i.e., twice the average of their angular velocities).

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