# Vector calculus notation, maybe?

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?

• I think it is a rotational, but you should provide more context: what is $W$? What is $\Omega$? – FGSUZ Apr 24 at 16:44
• $\vec{\nabla} \lor \vec{W}$, $\vec{\nabla} \times \vec{W}$, $\text{curl } \vec{W}$ all mean the same thing. – Thomas Fritsch Apr 24 at 17:04
• Research Clifford algebra. It extends vector calculus to multi-dimensions. – Bill N Apr 24 at 17:07
• @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! – ericksonla Apr 24 at 17:28
• @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 $\wedge$. – Bill N Apr 24 at 17:49

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