hi all. i have a question: what is the definition of the random fluctuations of turbulence? the text book say it is the real velocity minus the mean velcity ,but how is the mean velocity got?in my opinion ,it should be time averaged,but the time average is based on some time scale,different time scale will creat different mean velocity and so the random fluctuation if different either. so is the mean velocity and the fluctuations definite? and also the turbulence kinematic energy is defined by these fluctuations ,is it definite or varying with the average time scale? thanks ben

That's a good question I guess all have when start studying CFD. =)

By mean quantities (can be velocity or any other variable), the original idea is to have an average based on the complete scale, from starting to infinity.

Please note that I didn't say time scale, because there are other ways of averaging. The most common approach in CFD codes, is time averaging. But you could have space averaging and even what they call ensemble averaging, where you average by a certain number of experiments. All of them have their applicability.

Let's concentrate now on time averaging. By definition, you assume a steady-state solution where the mean properties are based on an integral from zero time to *infinity*. This is the correct definition for the Reynolds-averaged Navier-Stokes, for instance. Any thing that fluctuates around this averaged value, would be your turbulence, in a rough manner. Thus, you can't have time-dependent solutions with the correct definition for RANS.

However, people realized that, for high Reynolds-number, turbulence fluctuations would be lower than time-dependent mean flow variations. The URANS (U for unsteady) has been invented to deal with such idea. In this definition, time integration does not go from zero to infinity, but rather to a time scale that is large enough to avoid turbulent fluctuations but still is able to capture the time-dependent mean-flow phenomena. This definition incurs in the problems you related by which chacteristic length scale one should get. This has large effects in the final solutions.

A great discussion on that subject is presented in the Wilcox's "Turbulence modeling for CFD" book. It's REALLY worthy a careful reading.

Best regards, Biga

dear Biga, I really appreciate your reply,I think the basic question is the definition of random fluctuation in a math language.I guess the so called random fluctuations in spectral space may have many scales which the non-random quantity also have ,so it is hard for methods based on averaging or filtering in time or space to distinguish between random and non-random. I sure will try to find and refer wilcox's book,I am kind of still confused on this problem.

best regards ben