# Introduction to turbulence/Homogeneous turbulence

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 Revision as of 06:59, 12 March 2008 (view source)Michail (Talk | contribs) (→A first look at decaying turbulence)← Older edit Revision as of 07:16, 12 March 2008 (view source)Michail (Talk | contribs) (→A first look at decaying turbulence)Newer edit → Line 8: Line 8: [/itex] [/itex]
(1)
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+ + This is often written (especially for isotropic turbulence) as: + +
+ :$+ \frac{d}{dt} \left[ \frac{3}{2} u^{2} \right] = - \epsilon +$ + (2)
+ + where + +
+ :$+ k \equiv \frac{3}{2} u^{2} +$ + (3)

## 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:

 $\frac{d}{dt} k = - \epsilon$ (1)

This is often written (especially for isotropic turbulence) as:

 $\frac{d}{dt} \left[ \frac{3}{2} u^{2} \right] = - \epsilon$ (2)

where

 $k \equiv \frac{3}{2} u^{2}$ (3)