Oceanography
In oceanography, the Richardson number has a more general form which takes stratification into account. It is a measure of relative importance of mechanical and density effects in the water column, as described by the Taylor–Goldstein equation, used to model Kelvin–Helmholtz instability which is driven by sheared flows.
where N is the Brunt–Väisälä frequency.
The Richardson number defined above is always considered positive. A negative value of N² (i.e. complex N) indicates unstable density gradients with active convective overturning. Under such circumstances the magnitude of negative Ri is not generally of interest. When Ri is small (typically considered below 1/4), then velocity shear is considered sufficient to overcome the tendency of a stratified fluid to remain stratified, and some mixing will generally occur. When Ri is large, turbulent mixing across the stratification is generally suppressed.
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