﻿

# Richardson number

The Richardson number is named after Lewis Fry Richardson (1881 &ndash; 1953). It is the dimensionless number that expresses the ratio of potential to kinetic energy [Modellers will be more familiar with the reciprocal of the square root of the Richardson number, known as the Froude number.]

:$Ri = \left\{ghover u^2\right\}$

where "g" is the acceleration due to gravity, "h" a representativevertical lengthscale, and "u" a representative speed.

When considering flows in which density differences are small (the
Boussinesq approximation), it is common to use the reduced gravity"g' " and the relevant parameter is the densimetric Richardson number

:$Ri=\left\{g\text{'} hover u^2\right\}$

which is used frequently when considering atmospheric or oceanic flows.

If the Richardson number is much less than unity, buoyancy is unimportantin the flow. If it is much greater than unity, buoyancy is dominant (inthe sense that there is insufficient kinetic energy to homogenize the fluids).

If the Richardson number is of order unity, then the flow is likely tobe buoyancy-driven: the energy of the flow derives from the potential energy in the system originally.

Aviation

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

Thermal convection

In thermal convection problems, Richardson number represents the importance of natural convection relative to the forced convection. The Richardson number in this context is defined as

:

where "g" is the gravitational acceleration, is the thermal expansion coefficient, $T_ ext\left\{hot\right\}$ is the hot wall temperature, $T_ ext\left\{ref\right\}$ is the reference temperature, $L$ is the characteristic length, and $V$ is the characteristic velocity.

The Richardson number can also be expressed by using a combination of the Grashof number and Reynolds number,

: $mathit\left\{Ri\right\} = frac\left\{Gr\right\}\left\{Re^2\right\}.$

Typically, the natural convection is negligible when $Ri < 0.1$, forced convection is negligible when $Ri > 10$, and neither is negligible when $0.1 < Ri < 10$. It may be noted that usually the forced convection is large relative to natural convection except in the case of extremely low forced flow velocities.

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.

:$Ri = N^2/\left(du/dz\right)^2$

where "N" is the Brunt-Väisälä frequency.

The Richardson number defined above is always considered positive. An imaginary "N" indicates unstable density gradients with active convective overturning. Under such circumstances, "N" does not have an accepted physical meaning and 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. A good reference on this subject is J.S. Turner, "Buoyancy Effects in Fluids", Cambridge University Press, 1973.

Notes

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Richardson number — ▪ meteorology       parameter that can be used to predict the occurrence of fluid turbulence and, hence, the destruction of density currents in water or air. It was defined by the British meteorologist Lewis Fry Richardson (Richardson, Lewis Fry) …   Universalium

• Bulk Richardson number — DefinitionThe Bulk Richardson Number (BRN) is a dimensionless number in meteorology relating vertical stability and vertical shear (generally, stability divided by shear). It represents the ratio of thermally produced turbulence and turbulence… …   Wikipedia

• Richardson — is an English surname, and may also refer to:In places: *Richardson, Australian Capital Territory *Richardson, Saskatchewan, Canada *Richardson, Texas, USA *Richardson Beach, Hawaii, USA *Richardson County, Nebraska, USA *Richardson Township,… …   Wikipedia

• RICHARDSON L F — UNITED KINGDOM (see also List of Individuals) 11.10.1881 Newcastle/UK 30.9.1953 Kilmun/UK Lewis Fry Richardson graduated in natural sciences from King s College, Cambridge in 1903. After a short stay as an assistant at the National Physical… …   Hydraulicians in Europe 1800-2000

• Richardson , Lewis Fry — (1881–1953) British meteorologist and physicist Richardson, the son of a farmer, was born in Newcastle upon Tyne and educated at Durham College and Cambridge University, graduating in 1903. In 1913 he became superintendent of the meteorological… …   Scientists

• Richardson, Lewis Fry — ▪ British physicist born Oct. 11, 1881, Newcastle upon Tyne, Northumberland, Eng. died Sept. 30, 1953, Kilmun, Argyll, Scot.       British physicist and psychologist who was the first to apply mathematical techniques to predict the weather… …   Universalium

• Number 96 (TV series) — Number 96 Title card from a 1975 episode of Number 96. Where the cliff hanger resolution that followed this shot at the start of the episode took place in one of the building s flats, the shot of the building would zoom in on that flat as the… …   Wikipedia

• Number 10 (TV series) — Number 10 was a 1983 British television series originally aired on ITV and lasting for 7 episodes from 13 February to 27 March 1983. It depicted the personal and political lives of seven British Prime Ministers, ranging from the 1780s to the… …   Wikipedia

• Richardson, Texas — Infobox Settlement official name = Richardson, Texas settlement type = City nickname = The Telecom Corridor imagesize = image caption = image mapsize = 250px map caption = Location within Dallas County and the state of Texas mapsize1 = map… …   Wikipedia

• Richardson's Bay — Geobox|Estuary name = Richardson s Bay native name = other name = category = image caption =The outlet of Coyote Creek, which drains Tam Valley into upper Richardson s Bay official name = etymology = after William A. Richardson motto = nickname …   Wikipedia