next up previous contents
Next: Vorticity equation in two Up: Introduction to turbulence Previous: Intermittency   Contents

Two-dimensional turbulence

The study of two-dimensional incompressible flows at high Reynolds numbers presents several reasons of interest. A principal reason is provided by its relevance for geophysics. Indeed, the intermediate-scale dynamics of oceans and atmosphere, because of the combined effects of their stratification and the earth's rotation, can be roughly described as a two-dimensional flow. An other reason comes from plasma physics, where the presence of a strong mean magnetic field can confine the turbulent motions of plasma in the plane perpendicular to the magnetic field, and again the dynamics can be described by two-dimensional magneto-hydrodynamics (2D MHD) [15].

The classical theory of two-dimensional turbulence originates from the works of Batchelor, Kraichnan and Leith [16,17,18], which showed that the conservation of vorticity along the streamlines which occurs in two dimensions, produces radical changes in the behavior of turbulence.

Far from being a simplified version of the three-dimensional problem, two-dimensional turbulence presents a rich panorama of new phenomena, like the formation of coherent vortices from an initially disordered ``sea'' of vorticity which have attracted a large interest.

Finally, Navier-Stokes equation in two dimensions has the appealing feature to be less demanding on a computational level than the three-dimensional case, allowing to reach relatively high $Re$ numbers in direct numerical simulation (DNS).



Subsections
next up previous contents
Next: Vorticity equation in two Up: Introduction to turbulence Previous: Intermittency   Contents
Stefano Musacchio 2004-01-09