An elucidation of the paradox of 3D fluid system susceptibility to quasi-2D turbulence

Fifty years ago, Robert Kraichnan predicted the interesting existence of two-dimensional (2D) turbulence in ideal ‘flatland.’ Since then, many experiments have followed the convention that 2D flows are best observed in thinner fluid layers (hence the term ‘flatland’). In Physics of Fluids, experimental physicists Hua Xia and Nicolas François at The Australian National University survey recent discoveries that show the paradoxical existence of 2D turbulence in seemingly unfavorable conditions in thick fluid layers and on the wave surface, a three-dimensional (3D) motion.

The authors describe how vertical fluid motion can be effectively suppressed by a large-scale horizontal flow in thick layers of fluid and how this flow generates 2D turbulence that reinforces the inverse energy cascade, or the transfer of spectral energy towards large scales. For example, they discuss their prior work demonstrating the silencing of vertical eddy viscosity, via vertical shear Ω_s = d(V_h)/dz, upon an imposed or self-generated flow that causes an inverse energy cascade in thick fluid layers.

The authors also review recent literature on surface wave-driven flows that seminally describes how 3D waves generate horizontal vortices that, in turn, fuel the inverse cascade. As an example, they also discuss their earlier work showing energy migration from vertical oscillations into horizontal flow and describe why this energy is injected into a narrow spectral range.

Corresponding author Hua Xia says that “2D turbulence, or more precisely, the inverse energy cascade, and the resulting self-organization, may even be more common in nature than Kraichnan initially thought.” The authors state, in their article, that this review lays the foundation for more discussion on how certain 3D fluid systems are conducive to quasi-2D turbulence.

Source: “Two-dimensional turbulence in three-dimensional flows,” by H. Xia and N. Francois, Physics of Fluids (2017). The article can be accessed at https://doi.org/10.1063/1.5000863 .