Correct Answer - Option 2 : increase in u' in x-direction followed by increase in v' in negative y-direction
Concept:
The time-averaged velocity components and the fluctuating components, each satisfy the continuity equation for incompressible flow. Hence we can write
\(\frac{{du'}}{{dx}} + \frac{{dv'}}{{dy}} + \frac{{dw'}}{{dz}} = 0\)
Now, let us consider a two-dimensional flow in which the turbulent components are independent of the z-direction. Therefore the above equation will take the form
\(\frac{{du'}}{{dx}} + \frac{{dv'}}{{dy}} = 0\)
On the basis of the condition mentioned in the above equation it can be stated that if at an instant there is an increase in u' in the x-direction, it will be followed by an increase in v' in the negative y-direction.