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In atmospheric science, several different expressions for the Richardson number are commonly used: the flux Richardson number (which is fundamental), the gradient Richardson number, and the bulk Richardson number. The flux Richardson number is the ratio of buoyant production (or suppression) of turbulence kinetic energy to the production of ...
The Bulk Richardson Number (BRN) is a dimensionless number relating vertical stability and vertical wind shear (generally, stability divided by shear). It represents the ratio of thermally-produced turbulence and turbulence generated by vertical shear. Practically, its value determines whether convection is free or forced.
Richardson numbers higher than indicate that the flow problem is pure natural convection and the influence of forced convection can be neglected. [ 3 ] Like for natural convection, the nature of a mixed convection flow is highly dependent on heat transfer (as buoyancy is one of the driving mechanisms) and turbulence effects play a significant role.
The Bulk Richardson Number (BRN) is an approximation of the Gradient Richardson number. [1] The BRN is a dimensionless ratio in meteorology related to the consumption of turbulence divided by the shear production (the generation of turbulence kinetic energy caused by wind shear) of turbulence.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The most important feature of baroclinic instability is that it exists even in the situation of rapid rotation (small Rossby number) and strong stable stratification (large Richardson's number) typically observed in the atmosphere. [citation needed] The energy source for baroclinic instability is the potential energy in the environmental flow.
The most generally used dimensionless number would be the Richardson number and Rayleigh number. The mathematics of the flow is therefore simpler because the density ratio ρ 1 / ρ 2 , a dimensionless number , does not affect the flow; the Boussinesq approximation states that it may be assumed to be exactly one.
The Obukhov length (), a characteristic length scale of surface layer turbulence derived by Obukhov in 1946, [4] is used for non-dimensional scaling of the actual height. M–O similarity theory marked a significant landmark of modern micrometeorology , providing a theoretical basis for micrometeorological experiments and measurement techniques.