Richardson Number (3 types)

Richardson number that is also called the mixing efficiency of stratified turbulence. It is important in determining the flows like ocean circulation, air-sea transport or air turbulence. A lower value indicates a higher degree of turbulence.

Flux Richardson Number

In a static stable environment, turbulent vertical motions are acting against the restoring force of gravity. Thus buoyancy tends to suppress turbulence, while wind shears tend to generate turbulence mechanically. The ratio of buoyant production of the TKE budget to the mechanical production is called the flux Richardson number. (R_f). The Richardson number is dimensionless.

• R_f = +1 is a critical value, as the mechanically production rate balances the buoyant consumption of TKE.
• Flow is turbulent (dynamically unstable) when, R_f < +1
• Flow is turbulent (statically unstable) when, R_f < 0, (denominator is negative)
• Flow is statically stable when, R_f > 0
• Flow is laminar (dynamically stable) when, R_f > +1

Gradient Richardson Number

When investigator refer to a Richardson number without specifying which one, they usually mean the Gradient Richardson number. The gradient Richardson number is the ratio of vertical gradient of potential temperature and wind speed.

• R_c (Critical Richardson number) = 0.21-0.25
• R_T (Turbulence Richardson number) = 1
• Laminar flow becomes Turbulence when , R_i < R_c (creation of KH wave)
• Turbulence flow becomes Laminar when, R_i > R_T

Bulk Richardson Number

The Bulk Richardson number is widely used in the meteorology, because rawinsonde data and numerical weather forecasts supply wind and temperature measurements at discrete points in space. It is the ratio of buoyancy to vertical shear.