Reynolds decomposition

In fluid dynamics and the theory of turbulence, Reynolds decomposition is a mathematicaltechnique to separate the average and fluctuating parts of a quantity.For example, for a quantity $scriptstyle\; u$ the decomposition would be

:$u(x,y,z,t)\; =\; overline\{u(x,y,z)\}\; +\; u\text{'}(x,y,z,t)$

where $scriptstyleoverline\{u\}$ denotes the time average of $scriptstyle\; u,$ (often called the steady component), and$u\text{'},$ 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 stresses which gives rise to turbulence.

ee also

*Reynolds-averaged Navier-Stokes equations
*Turbulence