Reynolds decomposition
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In
Decomposition
For example, for a quantity the decomposition would be
The expected value, , is often found from an ensemble average which is an average taken over multiple experiments under identical conditions. The expected value is also sometime denoted , but it is also seen often with the over-bar notation.[3]
Direct numerical simulation, or resolution of the Navier–Stokes equations completely in , is only possible on extremely fine computational grids and small time steps even when Reynolds numbers are low, and becomes prohibitively computationally expensive at high Reynolds' numbers. Due to computational constraints, simplifications of the Navier-Stokes equations are useful to parameterize turbulence that are smaller than the computational grid, allowing larger computational domains.[4]
Reynolds decomposition allows the simplification of the Navier–Stokes equations by substituting in the sum of the steady component and perturbations to the velocity profile and taking the
See also
References
- ^ Müller, Peter (2006). The Equations of Oceanic Motions. p. 112.
- S2CID 122145330.
- ISBN 978-0-12-405935-1.
- )