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The mean of the space-based integral of a flow variable is equal to ____________

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The mean of the space-based integral of a flow variable is equal to ____________

(a) the summation of its mean component

(b) the space-based integral of its fluctuating component

(c) the space-based integral of its mean component

(d) the summation of its fluctuating components

This question was addressed to me in my homework.

Question is taken from Turbulence Modelling topic in chapter Turbulence Modelling of Computational Fluid Dynamics

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Correct answer is (c) the space-based integral of its mean component

Easy explanation: As the mean of the fluctuating component is zero and the mean of the mean component is the mean component itself, the mean of the space-based integral of a flow variable is equal to the space-based integral of its mean component alone.

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