From 2D to 3D in fluid turbulence: unexpected critical transitions.

*(English)*Zbl 1460.76381Summary: How do the laws of physics change with changes in spatial dimension? Maybe not at all in some cases, but in important cases, the changes are dramatic. Fluid turbulence – the fluctuating, intermittent and many-degree-of-freedom state of a highly forced fluid – determines the transport of heat, mass and momentum and is ubiquitous in nature, where turbulence is found on spatial scales from microns to millions of kilometres (turbulence in stars) and beyond (galactic events such as supernovae). When the turbulent degrees of freedom are suppressed in one spatial dimension, the resulting turbulent state in two dimensions (2D) is remarkably changed compared with the turbulence in three dimensions (3D) – energy flows to small scales in 3D but towards large scales in 2D. Although this result has been known since the 1960s due to the pioneering work of Kraichnan, Batchelor and Leith, how one transitions between 3D and 2D turbulence has remained remarkably unexplored. For real physical systems, this is a highly significant question with important implications about transport in geophysical systems that determine weather on short time scales and climate on longer scales. Is the transition from 3D to 2D smooth or are there sharp transitions that signal a threshold of the dominance of one type of turbulence over another? Recent results by S. J. Benavides and A. Alexakis [ibid. 822, 364–385 (2017; Zbl 1387.86026)] suggest that the latter may be the case – a surprising and provocative discovery.

##### MSC:

76F06 | Transition to turbulence |

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##### References:

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