121. On interaction between coherent condensate and turbulent flow in two dimensions

It looks like I did not review new nice papers in ArXiv for so long time While I have no idea what is the reason for this particular fact, I tell you that the ultimate reason for similar facts was always my tremendous  laziness. What could a man do with such an evil? The only sane manly way seems to constantly try to overcome your disadvantages So, let me try.

The nice paper of the day I would like to review is the PRL paper by Xia, Punzmann, Falkovich and Shats. The paper is about developed turbulence or, more precisely, about interaction between the turbulent flow  and coherent condensate. The topic seems to be rather exotic, so why did it catch my eye, you may ask?

Well, the first reason is that Grigory Falkovich is among the authors. He is one of the best present-day experts in developed turbulence. You may know him as one of the authors of the famous textbook by Zakharov, L’vov and Falkovich – the book where weak turbulence (Zakharov himself is the author of the theory) is explained in understandable way.

The second reason is related to physics of atmospheric turbulence

There exists a well known controversy regarding the behavior of the energy flux in atmospheric turbulence. As we know, turbulence in atmosphere is driven by the gradients in solar heat, which lead to horizontal motion at scales from 1000 to 10000 km and vertical convection at scales of the order 10 km. If we measure the spectrum of turbulence in the upper troposhere (10-500 km), we will find

. (1)

This seems to be the usual Kolmogorov’s cascade. On the other hand, if we measure the spectrum at heights 500-3000 km (in stratosphere), we are going to find a faster power law behavior

. (2)

This fact is actually quite amusing, since spectra (1) and (2) appear naturally in the Kraichnan theory of 2D turbulence – the spectrum (1) corresponds to inverse energy cascade, and (2) – to direct vorticity cascade.  Why does the 2-”dimensionalization” happen in reality? The width of the atmosphere is comparable to scales involved in the problem, but the characteristic horizontal scale is comprable to the characteristic vertical scale.

And where does the separation of scales 10-500-3000 km come from? Another issue is that possibly at large scales the main energy is stored in the coherent flow, not in turbulent flow (3000 km is of the order of the radius of the Earth, so ratation of the Earth should be already important). Is it what realized in Nature or not? If the large scale coherent flow is present, how does it affect the spectra of turbulence?

The last question in this set is the one which the authors tried to address by an experiment (in the lab, not in the atmosphere ). In this experiment, turbulence was generated electromagnetically in the conducting liquid (more precisely, since they wanted a convection resembling the one in the atmosphere, they placed light conducting liquid on top of the heavy non-conducting one). The current flowing through the conducting liquid generated vortices, and the interaction of the latter has naturally led to turbulence.

I am not going to dive into technicalities of the experiment and will just tell you the answer. It turns out that formation of the coherent flow suppresses turbulence due to the stretching and subsequent breakdown of vortices. Strong large vortices (with vorticity higher than the condensate shear level) actually survive, so that the coherent flow only breaks down small vortices. Thus, if the coherent flow is present in upper atmosphere, this may in principle explain behavior in formula (2) – turbulent flow will be suppressed in the UV due to the breakdown of smaller scale vortices.

How does this have anything to do with inverse and direct cascades as well as effective 2D behavior is not clear at all (even if the condensate is present, why do the spectra resemble the ones in Kraichnan theory?). Also, the author’s experiment and the atmosheric turbulence at very large scales are two quite different physical realities. Rotation of the Earth is clearly important at extremely large scales, and it should strongly affect the spectra of turbulence.

But in overall, I think, the experiment is very interesting, and I would probably pay to see how vortices are getting broken by the coherent flow (the authors used a system of several laser to light up and visualize the flow – these laser things always make experimental physics seem beautiful and theoretical physics – ugly compared to experimental )