# Introduction to turbulence/Homogeneous turbulence

## 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)