Re: Length scales in DNS
 

>This is because the peak of the dissipation spectrum is not at eta but at about 10* eta.

That's important to know. Not only that the peak is at 10*eta, but you also have to say that everything below that scale doesn't add up to anything significant. But one good answer always offers a bunch of new questions :)

To see this in relation to the discussion about continuum mechanics: How far is Kolmogorov's length scale actually away from the mean free path of a molecule (I imagine several orders of magnitude)? Then, how safe is it to say that even if we consider the complete range of dissipative scales down to the smallest, the assumptions of continuity and thermodynamic equilibrium still hold? Is dissipation a phenomenon (or concept) that is entirely (or at least most dominantly) described by continuum dynamics? Do smaller scales contribute anything to turbulent dynamics, even if not through dissipation? What is actually the precise mechanism that transforms directed kinetic energy into "random" motion, associated with heat? Does that mechanism have anything to do with molecular motion, not describable through the continuum assumption? I guess I should brush up on kinetic theory... :)

Re: Length scales in DNS
 

Lots of interesting stuff being said in this tread. Why don't you guys try to summarize a bit of this in the DNS section in the Wiki. The DNS section is very thin now, it just has a brief intro to what DNS it. You can find the DNS section is here:

Wiki DNS section

If you put it in the wiki others can learn from it and the next time someone raises a similar question here we can use the wiki as a reference.

Re: Length scales in DNS
 

>That's important to know. Not only that the peak is at >10*eta, but you also have to say that everything below that >scale doesn't add up to anything significant.

It is a bit more complicated. The dissipation spectrum has a quite long tail (see Pope). If you carry out a DNS and resolve just beyond the the peak, you will miss some of the details. Nevertheless, the behaviour of the large scales will quite realistic probably. They are able to drain their energy. If, however, you are interested in the small scales (dissipative scales, small-scale vortices) you also need to resolve the tail of the dissipation spectrum well and this puts a more severe constraint on the resolution. In that case dx < 3*eta.

In the atmosphere eta is of the order of 1 mm and in the ocean of the order of 1 cm I believe. This is far from the mean free path of molecules. The continuum assumption is thus quite accurate. The dissipation can thus be desribed by continuum dynamics.