Dear all,

I am now confusing about the fundamental concepts of turbulence.

What's fully developed turbulence? Surely we could see the Re is high enough, but we don't know the exact value for the word "high" for a given complex flow. There should exist some criteria to determine the flow state. I have found some one use turbulent energy spectrum to judge whether it is fully developed turbulence or not based on -5/3. I don't know whether this is a general method.

Any comment is welcome, if possible please give the references. thanks a lot!

regards, sincerely, sarah

Fully developed turbulence seems synonymous to "fully turbulent" as opposed to transitional or intermittent turbulent/laminar. The question is not, if the turbulence level is high or low, it's whether the flow at a given location is turbulent at all times or intermittent. Fully turbulent flow will typically show the -5/3 power in the energy spectrum, if there is a wide enough cascade of scales. I don't have a definite reference, but try any book on turbulence, e.g. "Turbulent Flows" by S. Pope.

in order to clear the question you can think at a flow on flat plate.

In the nearby of the leading edge the flow is laminar because the Rex (the Reynolds number based on the abscissa) is small. Proceding forward the REx increases and the flow become transitional when the Rex is approximately 500.000.

Going further the flow becomes more and more turbulent.

When the statistics of the turbulence don't vary at all and reach a defined decaying (energy transfer between eddies) the flow is fully turbulent.

The same things happen in time for a given location when there is a variable boundary condition.