Turbulence is originally a 3D phenomena, what are the main hypothesis and considerations when treating with turbulence in 2D?

Dear Arman,

Turbulence is always 3D as you say, 2D is just a statistical simplification of the same. For instance, if you have a flow in a channel wherein the velocity in one direction is essentially the same at all cross sections, you could consider the problem to be a 2D one, (taking any one slice). In a similar fashion, if the turbulence statistics in one direction are not varying largely in one direction compared to the others, the problem can be considered as statistically two-dimensional. This is the case with geophysical turbulence such as tornaodes. Soap film turbulence is yet another case, although there is no consensus on this being 2d turbulence. Nevertheless, it is clear that the mechanisms at work in 2d turbulence could be completely different from that in 3d. Also, from a numerical perspective people report steady 2d turbulent flow results, which should not be confused as turbulence is inherently unsteady. The term "steady" refers to the fact that the mean flow is invariant with time. Therefore, any simplification of a turbulent flow is to be seen from a purely statistical point of view, realising that the approximations are valid only under restricted conditions of flow.

You can have a look at Stephen Pope's book on turbulence for more information. You could also google for some nice reading material with regard to 2d turbulence although the theoretical development, though interesting is not widespread.

Hope this helps Regards,

Ganesh

An little point : The more important propretie of 2D turbulence is that, in order to conserve the enstrophie there are no dissipative energy.

I can invit you to read Marcel Lesieur'book for more detail about turbulence.