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Let's say we have a fully developed turbulent flow on x axis (simple shear flow). Time-averaged components of velocity on y and z axis are 0. If a lump of particles is moving upwards, then the fluctuating part of y-velocity (u'_y) must be positive (u'_y>0). If the lump is going downwards, then u'_y<0. In the book of Dr. Schlichting, Boundary Layer Theory (page 560), it is also said that the lump (either it goes upwards or downwards) maintains its time averaged velocity, so it gives rise to the negative (or positive) component of u'_x.

I would like an explanation on why the mean velocity of the lump remains constant when it changes layer and what's the meaning of negative or positive component of u'_x. I know that the length that the lump travels without changing its mean velocity is called "mixing length", but why does it take it some time to change the velocity? Is it because of the vortexes in the turbulent flow?enter image description here

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