In the stability of continuously stratified parallel shear flows the ratio of (the squares of) the buoyancy frequency to the background velocity gradient is known as the (gradient) Richardson number.
Here is the reference density and is the background density field.
- Hunt, J C R (1998), Lewis Fry Richardson and his contributions to mathematics, meteorology, and models of conflict, Annual Review of Fluid Mechanics, Vol. 30, 1998, pp. xiii–xxxvi.