This decomposition of a flow variable into a mean value and a turbulent fluctuation was originally proposed by Osborne Reynolds in 1895, and is considered to be the beginning of the systematic mathematical analysis of turbulent flow, as a sub-field of fluid dynamics.
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The new " inner length scale " \ eta is a viscous length scale, and is of order \ frac { \ nu } { u _ * }, with u _ * being the velocity scale of the turbulent fluctuations, in this case a friction velocity.
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