Introduction to turbulence/Homogeneous turbulence
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</math> | </math> | ||
</td><td width="5%">(1)</td></tr></table> | </td><td width="5%">(1)</td></tr></table> | ||
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| + | This is often written (especially for isotropic turbulence) as: | ||
| + | |||
| + | <table width="70%"><tr><td> | ||
| + | :<math> | ||
| + | \frac{d}{dt} \left[ \frac{3}{2} u^{2} \right] = - \epsilon | ||
| + | </math> | ||
| + | </td><td width="5%">(2)</td></tr></table> | ||
| + | |||
| + | where | ||
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| + | <table width="70%"><tr><td> | ||
| + | :<math> | ||
| + | k \equiv \frac{3}{2} u^{2} | ||
| + | </math> | ||
| + | </td><td width="5%">(3)</td></tr></table> | ||
Revision as of 07:16, 12 March 2008
A first look at decaying turbulence
Look, for example, at the decay of turbulence which has already been generated. If this turbulence is homogeneous and there is no mean velocity gradient to generate new turbulence, the kinetic energy equation reduces to simply:
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| (1) |
This is often written (especially for isotropic turbulence) as:
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| (2) |
![\frac{d}{dt} \left[ \frac{3}{2} u^{2} \right] = - \epsilon](/W/images/math/a/c/2/ac251958c2df0a8a260f8f83d2645da2.png)
where
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| (3) |
