Richardson Number

Description

The Richardson number is used as a rough measure of expected air turbulence. A lower value indicates a higher degree of turbulence. Values in the range 10 to 0.1 are typical, with values below unity indicating significant turbulence.

Definition

The Richardson number, Ri, is the dimensionless ratio of buoyant suppression of turbulence to shear generation of turbulence and is defined as:

where g is the acceleration of gravity, β a representative vertical convective stability (commonly ∂θ/∂z, where θ is potential temperature), and ∂u/∂z (the change of wind speed with height) is a characteristic vertical shear of the wind. It is used as a dynamic stability measure to determine if turbulence will exist. The Richardson number is a component of the Graphical Turbulence Guidance product available on the U.S. National Oceanic and Atmospheric Administration (NOAA) Aviation Weather Center website.

Richardson number and turbulence

The Richardson number is used as a rough measure of expected air turbulence. A lower score indicates a higher degree of turbulence (wind speed factor greater than convective stability factor). Values in the range 10 to 0.1 are typical, with values below unity indicating significant turbulence.

Richardson number and stability

The Richardson number is a turbulence indicator and also an index of stability. Meteorologists classify atmospheric stability in the surface layer as unstable, neutral, and stable. Strongly negative Richardson numbers indicate that convection predominates, winds are weak, and there is a strong vertical motion characteristic of an unstable atmosphere. Smoke leaving a source spreads rapidly vertically and horizontally. As mechanical turbulence increases, the Richardson number approaches zero, and the dispersion of a smoke plume decreases, approaching neutral stability where (∂θ/∂z) = 0. Finally, as the Richardson number becomes positive, vertical mixing ceases, and mechanical turbulence is dampened. The atmosphere becomes stably stratified, and very little vertical dispersion of a smoke plume occurs.

 

Stability ClassificationRichardson numberComment
Stable> 0.25No vertical mixing, winds weak, strong inversion, mechanical turbulence dampened, negligible spreading of smoke plume
Stable0 < Ri < 0.25Mechanical turbulence weakened by stable stratification
NeutralRi = 0Mechanical turbulence only
Unstable−0.03 < Ri < 0Mechanical turbulence and convection
UnstableRi < −0.04Convection predominant, winds weak, strong vertical motion, smoke rapidly spreading vertically and horizontally

Richardson number and stability

 

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