Two-dimensional Turbulence

Thin fluid layers mimic many aspects of atmospheric and oceanic flows, which are also essentially two-dimensional since the extent of these flows in horizontal direction (hundreds of kilometres) exceeds the depth of the atmosphere or the ocean (~5 km). Their properties are close to ideal two-dimensional flow. The behavior of 2D turbulence is fundamentally different from 3D: it is capable of self-organizing into large coherent flow (figure below).

We study generation of coherent flows by turbulence in thin fluid layers. Once the flow is formed, it starts controlling turbulence that feeds it.

Such systems, where turbulence and large-scale coherent flows coexist in dynamical equilibrium are common in nature: famous Jupiter’s zonal bands and the Great Red Spot (figure above), Earth’s Antarctic Circumpolar Current (Southern Ocean), zonal jets in the Earth atmosphere etc.

Our recent studies have revealed several striking similarities between plasma self-organization during low-to-high confinement transitions and spectral condensation in 2D bound turbulence. Spectral condensation is the process of the energy accumulation at the scale of the system size due to the inverse energy cascade. These results are published in:
Shats M.G., Xia H., Punzmann H., Spectral condensation of turbulence in plasmas and fluids and its role in low-to-high phase transitions in toroidal plasma, Physical Review E, 71, 046409 (2005) [PDF]

 

 

Shown above is the evolution of the 2D flow in the process of spectral condensation. An initial matrix of 10x10 vortices self-organizes into one large vortex whose size is determined by the size of the boundary.

Another study focuses on the effects of the large-scale flows on turbulence. In particular, we identify two mechanisms, namely shear decorrelation and sweeping of vortices, to be responsible for the turbulence suppression in 2D system.
M.G. Shats, H. Xia, H. Punzmann and G. Falkovich
Suppression of Turbulence by Self-Generated and Imposed Mean Flows
Physical Review Letters, 99, 164502 (2007) [PDF]