In fluid dynamics and turbulence, Reynolds decomposition is a mathematical technique to separate the average and fluctuating parts of a quantity. For example, for a quantity u the decomposition woud be: Fluid dynamics is the subdiscipline of fluid mechanics that studies fluids in motion. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by semi-random, stochastic property changes. ...
where denotes the time average of (often called the steady component), and the fluctuating part (or perturbations). The perturbations are defined such that their time average equals zero.
This allows us to simplify the Navier-Stokes equations by substituting in the sum of the steady component and perturbations to the velocity profile and taking the mean value. The resulting equation contains a nonlinear term known as the Reynolds stress which gives rise to turbulence. The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances like liquids and gases. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by semi-random, stochastic property changes. ...
In 1868 he became a professor of engineering at Owens College in Manchester (a predecessor of the Victoria University of Manchester, merged with the UMIST in 2004 to become the University of Manchester), and was only the second to hold this role in England.
Reynolds famously studied the conditions in which the flow of fluid in pipes transitioned from laminar to turbulent.
Reynolds also proposed what is now known as Reynolds-averaging of turbulent flows, where quantities such as velocity are expressed as the sum of mean and fluctuating components.
denotes the time average of 
(often called the steady component), and 
the fluctuating part (or perturbations). The perturbations are defined such that their time average equals zero.
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