Astrophysics (Index) About

### 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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