Like if you were looking at vortex shedding off a cylinder, you'd get very different results depending on how your averaging window compares to the shedding frequency

So then, how would we interpret this ambiguity of defining our so called 'mean' which is used for stuff like time and lengthscale correlations

And more importantly, the "variation about the mean" as a measure of things

I get it there can't be an iron clad rule, but there ought to be some definable boundaries between the mean and the variation... Even if it is based off some ab initio description of phenomenon of interest. like here, would I average over a rans like period, or something shorter than the the shedding of largest vortices

What has been your approach until now?

In my case I've just been looking at an atmospheric boundary layer through an empty domain, so the mean is pretty well defined. I just start the averaging at a certain point in time after the simulation has had time to start up, and let it average over the rest of the run time

I tried a few sensitivity studies before losing track of it in the pandemic. I could see that obviously the mean saturates very quickly (as a function of window size), but I never got around to studying the variation about it.

no shedding or anything like that to deal with

So a cumulative average

Yep

Also in my consulting work I've often taken the approach of "If I was going to run this test in real life rather than CFD, what would the approach be"

So for instance when doing airport turbulence studies

If I was going to go out and measure it in real life, I'd never take an averaging window of like 10s or something - I'd set up an anemometer and leave it there for a few hours, and probably take a rolling 30 minute average or so. In the wind community it's generally accepted that you need at least 10 minutes to get a representative average

So I use that as a rough guideline in the absence of any published literature to the contrary, and make sure to do a couple of sensitivity studies to check the results don't change drastically

but that's a very 'engineering' approach and not an academic one

and pretty unsatisfying haha

I guess it gets back to the fundamentals, Reynolds decomposition and time averaging vs ensemble averaging

If you have a clear separation of scales (eg vortex shedding) the problem is simple, like you say you average over a rans like period and you can take the large shedded whirls as basically an unsteady mean

But if there's not a clear separation then things are murky and I'm not smart enough to even begin coming up with an answer 😕

Yeah it works but there's no aha! moment there 😄

Yep, this is part of the reason I've gone back to do a PhD, come across so many "that'll do" moments at my job, wanted more "aha" moments 😅

Thanks 🙂 good to know these are genuine questions

The rule of thumb is 20 eddy-turnover times for the averaging window

Hey there. I need to implement the reynolds-stress-transport equation in openfoam as a postprocessing function object would anybody be interested in a collaboration?

Is there a solution existing probably?

no-one? Is there really no Interest in the description of the transport of reynolds-stresses? 🙂

Why as a function object?

Also, the server has people from across timezones, so expect responses, if any, to take time. 🙂

i am not a patient person 😄

why not as a function object? this is a postprocessing step that needs to run while the LES is executing