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\(Q = \frac{{\partial u'}}{{\partial x}} = - \frac{{\partial v'}}{{\partial y}}\) for a turbulent flow signifies


1. conservation of bulk momentum transport
2. increase in u' in x-direction followed by increase in v' in negative y-direction
3. turbulence is anisotropic
4. turbulence is isotropic

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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.

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