But yeah I think it is because the dissipation is independant from the geometry or velocity unlike the larger eddy because on the left side is the production 😃

they must have some mathematical explanation I guess, cause all eddies are assumed isotropic when larger are definitely not. What can physically cause them to be not problem dependant?

maybe because the smaller eddys are more dominated by the dissipation ^^

When a large Eddy is produced by a geometry it is hard to say that it is isotropic where the smaller one are "driven" by the dissipation wich goes in every direction the same way

what do you mean driven by the dissipation?

isn't dissipation the process of being dissipated into heat?

yes

I mean that the dissipation is isotropic and thats the reason why the eddys are isotropic 😄

but Im not sure about this 😉

is just whats in my head 😄

Just checked my notes..trying to translate it: In every turbulent flow of big enough reynolds-numbers the smalscale movement takes on a statistically universal form, which depends on the kinematic viscosity and the massdepend dissipation rate.

So just as siegi already mentioned

We did not do any math about it, but I think it is comparable to the heat problem: the molecule move statistically.. how much they move is (simplified) a question of temperature and coeffiecients... the movement of the small scale eddies is somewhat similiar, it is a question of kinematic viscosity and massdepend dissipation rate

ok thanks!

I will ask on cfd online

just curiosity

😄

I didn't get his 2nd and 3rd point though

deleted a few things because i have to think a bit more about it first

Next try: 😃

You asked over there why they can't depend on geometry and I think there might be two ways to look at this First: One large eddy becomes two smaller ones, which although become two smaller ones and so on until they dissipate When looking at it this way then you have this giant room (the largest eddies have been in it) and all of it is full of small eddies... 99% of them are far away from any geometric boundary Second: Again one large eddy becomes two smaller ones. The geometric boundaries played a major role for the large eddie, and is a little less important for the two smaller ones.. however they will strongly effect each other. When they become two smaller ones this effect becomes bigger. At the end you have this ton of small eddies, statistically distributed that are only effected by each other and the geomtry of the beginning does not play a role anymore.

"Actually, we should come back to the character of turbulence that is hystorically illustrated in literature, that is the case of homogeneous isotropic turbulence. An energy equilibrium is assumed at small scales. As a matter of fact, just when considering wall bounded flows it appears no longer true that below a certain characteristic lenght scale you can consider a universal behaviour of the eddies. This is for example the case in which using LES you adopts a DNS-like grid resolution normal to a wall."

so the answer to "why is turbulence isotropic at small scales?", the answer is simple : it's not

😄

So its okay in the main flow but near the wall you need a fine grid because the eddys are not isotropic anymore?

as I get it yes. Then there is also the sub-question of which size are the eddies in the means flow. I would say that when LES gives exactly the same results as DNS

if you have a mesh with y+=x+=z+=1 everywhere for DNS

and resolve LES and find that with a cube of size x+ = 30 you got the exact same results