# Richardson number

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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.