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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 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.
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 ratio of the Grashof number to the square of the Reynolds number may be used to determine if forced or free convection may be neglected for a system, or if there's a combination of the two. This characteristic ratio is known as the Richardson number (Ri). If the ratio is much less than one, then free convection may be ignored.
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.
Though initially thought to be a constant, recent work has shown that the entrainment coefficient varies with the local Richardson number. [9] Typical values for the entrainment coefficient are of about 0.08 for vertical jets and 0.12 for vertical, buoyant plumes while for bent-over plumes, the entrainment coefficient is about 0.6.
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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.