Fluid dynamics

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:

$$

u(x,y,z,t) = \overline{u(x,y,z)} + u'(x,y,z,t) where $\backslash overline\{u\}$ denotes the time average of $u\backslash ,$ (often called the steady component), and $u\text{'}\backslash ,$ 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.

See also

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• Reynolds-averaged Navier-Stokes equations
• Turbulence