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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's notion of turbulence was that a turbulent flow is composed by "eddies" of different sizes. The sizes define a characteristic length scale for the eddies, which are also characterized by flow velocity scales and time scales (turnover time) dependent on the length scale.
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.
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.
Schematic illustration of production, energy cascade and dissipation in the energy spectrum of turbulence. The largest motions, or eddies, of turbulence contain most of the kinetic energy, whereas the smallest eddies are responsible for the viscous dissipation of turbulence kinetic energy. Kolmogorov hypothesized that when these scales are well ...
Richardson was also interested in atmospheric turbulence and performed many terrestrial experiments. The Richardson number, a dimensionless parameter of the theory of turbulence, is named for him. He famously summarised turbulence in rhyming verse in Weather Prediction by Numerical Process (p 66): [12]
Throughout the early 20th Century, the ideas of Kelvin-Helmholtz instabilities were applied to a range of stratified fluid applications. In the early 1920s, Lewis Fry Richardson developed the concept that such shear instability would only form where shear overcame static stability due to stratification, encapsulated in the Richardson Number.