The curl of the velocity field $\bar V(\bar x,t )$ is known to be related to the local angular velocity $\bar \omega (\bar x,t) $ by the expression

$$\bar \omega = \frac{1}{2}\nabla \times \bar V $$

Is the curl of the vorticity related to any or all of the local acceleration $a = \partial_{t} \bar V $, the local angular acceleration $\alpha = \partial_{t} \bar \omega$ and/or the local gyroscopic/angular precession $\bar L (\bar x,t)$ ?

If so, is there a general expressions similar to the above to describe such a relationship?

$$\nabla \times \bar \omega = ?$$

  • $\begingroup$ The answer is in another MSE question. $\endgroup$
    – Kurt G.
    Jul 24, 2021 at 4:53


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