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The mean of the product of a flow variable and the mean component of another flow variable is ____________

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The mean of the product of a flow variable and the mean component of another flow variable is ____________

(a) the product of their mean components

(b) the product of their fluctuating components

(c) the mean of the product of their mean components

(d) the mean of the product of their fluctuating components

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My question is from Turbulence Modelling topic in division Turbulence Modelling of Computational Fluid Dynamics

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Right option is (a) the product of their mean components

Explanation: Consider two flow variables which can be decomposed as a=A+a’ and b=B+b’. The mean of the product of one flow variable and the mean component of another flow variable is represented as

aB=(A+a’)B

aB=AB+a’B

As a’B=0 and AB=AB,

aB=AB.

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