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Commutation of differentiation and averaging operations

by plasmoid
Tags: average, calculus, turbulence
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Apr3-11, 02:08 PM
P: 15
I've been studying Turbulence, and there's a lot of averaging of differential equations involved. The books I've seen remark offhandedly that differentiation and averaging commute

for eg. < [tex]\frac{df}{dt}[/tex] > = [tex]\frac{d<f>}{dt}[/tex]

Here < > is temporal averaging. If the differentiation is w.r.t. a spatial coordinate it makes sense, but could someone help me with the above equation?
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