# Q and R

Q and R are two invariants of the velocity gradient tensor. Following (mostly) the notation used in Davidson, these are defined as:

where

and is the i-th component of vorticity. Note, most authors define R with a negative as

By the definitions of viscous dissipation, , and enstrophy, , and using the relation between and the rotation tensor, we can write

which is a very useful formulation for computing Q.

Where Q is large and positive the flow has intense enstrophy, whereas large negative Q is a region of strong strain. The precise meaning of large is not yet fully known.

The value of R specifies regions of vortex stretching (positive R) and compression (negative R). Combined, R and Q will specify the type of vortex stretching or strain.

See Davidson for more information.