# Richardson number

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.

$Ri = \frac{N^2}{U_z^2}$

$N = \mbox{Buoyancy frequncy} = -\frac{g}{\rho_0} \frac{\partial \bar{\rho}}{\partial z}$

Here $\rho_0$ is the reference density and $\bar{\rho}$ is the background density field.

## References

• 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.