### Reynolds decomposition

(mathematical separation of average and fluctuating parts of a quantity)

**Reynolds decomposition** is a mathematical separation of a quantity
(an evolving field, i.e., a field as a function
of time)
into its time-averaged and its fluctuating parts. For example:

________
u(x,y,z,t) = u(x,y,z) + u'(x,y,z,t)

- u - a quantity: a function of x,y,z, and t
- u overbar - time-averaged u
- u' - fluctuating part of u

Reynolds decomposition is a technique for dealing with the Navier-Stokes equations.
In that case, the fluctuating component includes a non-linear
component which is called the **Reynolds stress** or **Reynolds stresses**,
which account(s) for turbulence.
In analysis of fluid motions (e.g., atmospheres),
this sort of decomposition (a **partitioning** of fluid motion
into the mean motion versus the fluctuations) might be done for a single
directional component, e.g., specifically for the meridional flow.

(*mathematics,fluid dynamics,field*)
**Further reading:**

http://en.wikipedia.org/wiki/Reynolds_decomposition

**Referenced by pages:**

dynamo

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