= Reynolds averaging
{c}
{title2=$f=\overline f+f',\quad\overline{f'}=0$}
<Reynolds averaging> separates a resolved mean from zero-mean fluctuations. The idealized averaging operation is linear and idempotent, commutes with the <derivatives> under consideration and treats resolved mean factors as constant inside its averaging scale. Products then satisfy $\overline{fg}=\overline f\,\overline g+\overline{f'g'}$. Actual finite spatial filters need scale separation or corrections when these rules are only approximate.
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