Richardson number

Summary

The Richardson number is the dimensionless number that compares the stabilising effect of a stable density stratification with the destabilising effect of velocity shear. In its gradient form it is the square of the Brunt–Väisälä frequency divided by the square of the shear. When it is large, buoyancy suppresses overturning and turbulence; when it is small, shear can roll the layers up into Kelvin–Helmholtz billows. The Miles–Howard theorem makes the threshold $1/4$ precise for inviscid parallel flows.