# Richardson number

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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.