I just got a new book on turbomachinery that uses some notation I'm not familiar with.

$$ \nabla \lor \vec{W} = -2\vec{\Omega} $$

The del-(something)-vector format makes me think its vector calculus. From context (rotating equipment), maybe its vector calculus in a cylindrical coordinate system? Or the list of symbols says the V-like symbol is "vector product", so is this just non-standard notation for curl?

For context, W is the relative velocity between the rotating equipment and the fluid, and omega is the angular speed (this bit is also confusing since speed is not a vector, but this equation identifies it as one).

What does $\nabla \lor \text{vector}$ mean?

  • $\begingroup$ I think it is a rotational, but you should provide more context: what is $W$? What is $\Omega$? $\endgroup$ – FGSUZ Apr 24 at 16:44
  • $\begingroup$ $\vec{\nabla} \lor \vec{W}$, $\vec{\nabla} \times \vec{W}$, $\text{curl } \vec{W}$ all mean the same thing. $\endgroup$ – Thomas Fritsch Apr 24 at 17:04
  • $\begingroup$ Research Clifford algebra. It extends vector calculus to multi-dimensions. $\endgroup$ – Bill N Apr 24 at 17:07
  • $\begingroup$ @ThomasFritsch, while that is comment length, it seems to answer the whole questiion. So if you'd like to make it an answer, I'd accept. Thanks! $\endgroup$ – ericksonla Apr 24 at 17:28
  • 1
    $\begingroup$ @levitopher Yeah, Clifford is a particular exterior algebra. Related to the question, I have actually never seen the upside-down wedge used anywhere. Who uses that notation? exterior algebra uses $\wedge$. $\endgroup$ – Bill N Apr 24 at 17:49

There are several notations in use for the curl of a vector field $\vec{W}$:

  • $\vec{\nabla} \lor \vec{W}$
  • $\vec{\nabla} \times \vec{W}$
  • $\text{curl } \vec{W}$

And they all mean the same thing.


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