HI,

I am wondering if someone could tell me why it is that in Tennekes and Lumley's classic text that their in no time derivative involved in the rate of change of kinetic energy equation (p60-61). I cannot figure out why the term dissapears. Thanks.

Why don't you see your TA or professor?

On page 59, in the first sentence of section 3.1 it says "...the equations of motion for steady mean flow in an incompressible fluid are..".

Right there, the term STEADY should ring a bell! A flow that is steady does not change in time, thus the time derivatives are dropped.

All capital letters in T&L refer to steady terms. I know, it may be a bit confusing, especially since equation 3.1.3 includes the Reynolds stress, which stems from turbulent fluctuations. Turbulent fluctuations happen on a very small time scale, whereas the term STEADY refers to the large time scale of the flow.