The instantaneous streamwise velocity of turbulent flow is given by u(x,y,z,t)= u(x,y,z)+u(x,y,z,t). The time average of the fluctuating velocity u is .

GATE 2016 ME (ME1) – Question 23

Fluid Mechanics · Viscous flow, boundary layer and elementary turbulent flow · 1 mark · Multiple choice

The instantaneous streamwise velocity of turbulent flow is given by $u(x,y,z,t)=\bar u(x,y,z)+u\prime(x,y,z,t)$. The time average of the fluctuating velocity $u\prime$ is ______.

$u\prime/2$
$-\bar u/2$
Zero
$\bar u/2$

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Correct answer: (C) Zero

Explanation

Reynolds decomposition defines u=u-mean+u-prime. Taking the time mean gives mean(u-prime)=mean(u)−u-mean=0. Thus **zero, C**. The source’s separator resembles a dot; the intended operation is the additive Reynolds decomposition, not multiplication.