Two-Dimensional Turbulence

In physical systems, a reduction in dimensionality often leads to exciting new phenomena. Here we discuss the novel effects arising from the consideration of fluid turbulence confined to two spatial dimensions. The additional conservation constraint on squared vorticity relative to three-dimensional (3D) turbulence leads to the dual-cascade scenario of Kraichnan and Batchelor with an inverse energy cascade to larger scales and a direct enstrophy cascade to smaller scales. Specific theoretical predictions of spectra, structure functions, probability distributions, and mechanisms are presented, and major experimental and numerical comparisons are reviewed. The introduction of 3D perturbations does not destroy the main features of the cascade picture, implying that 2D turbulence phenomenology establishes the general picture of turbulent fluid flows when one spatial direction is heavily constrained by geometry or by applied body forces. Such flows are common in geophysical and planetary contexts, are beautiful to observe, and reflect the impact of dimensionality on fluid turbulence.