Quasi-two-dimensional Turbulence

TL;DR

This review explores quasi-two-dimensional turbulence, where flows exhibit mixed energy transfer behaviors, revealing complex phases and transitions as systems shift from three to two dimensions, with implications for various physical phenomena.

Contribution

It summarizes recent discoveries on the transition, phases, and cascade properties of quasi-two-dimensional turbulence, highlighting the coexistence of energy transfer directions.

Findings

Identification of different turbulence regimes

Observation of simultaneous energy transfer to large and small scales

Description of phase transitions in turbulence behavior

Abstract

Many fluid-dynamical systems met in nature are quasi-two-dimensional: they are constrained to evolve in approximately two dimensions with little or no variation along the third direction. This has a drastic effect in the flow evolution because the properties of three dimensional turbulence are fundamentally different from those of two dimensional turbulence. In three-dimensions energy is transferred on average towards small scales, while in two dimensions energy is transferred towards large scales. Quasi-two-dimensional flows thus stand in a crossroad, with two-dimensional motions attempting to self-organize and generate large scales while three dimensional perturbations cause disorder, disrupting any large scale organization. Where is energy transferred in such systems? It has been realized recently that in fact the two behaviors can coexist with a simultaneous transfer of energy both to large and to small scales. How the cascade properties change as the variations along the third direction are suppressed has lead to discovery of different regimes or phases of turbulence of unexpected richness in behavior. Here, recent discoveries on such systems are reviewed. It is described how the transition from three-dimensional to two-dimensional flows takes place, the different phases of turbulence met and the nature of the transitions from one phase to the other. Finally, the implications these new discoveries have on different physical systems are discussed.