Two-dimensional Turbulence
Turbulence in thin fluid layers
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 kilometers) exceeds the depth of the atmosphere or the ocean (~5 km).
The behavior of 2D turbulence is fundamentally different from 3D: it is capable of self-organizing into large coherent flow. We study experimentally the 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.
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. Click here to see the movie [1 MB].
A recent paper on the interaction between turbulence and self-generated vortex:
H. Xia, H. Punzmann, G. Falkovich and M.G. Shats, Turbulence-Condensate Interaction in Two Dimensions, Physical Review Letters, 101, 194504 (2008) [PDF]
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]
We also found several interesting similarities between
plasma self-organization during low-to-high confinement transitions and spectral
condensation in 2D bound turbulence:
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]
