Search for conformal invariance in compressible two-dimensional turbulence

Abstract

We present a search for conformal invariance in vorticity isolines of two-dimensional compressible turbulence. The vorticity is measured by tracking the motion of particles that float at the surface of a turbulent tank of water. The three-dimensional turbulence in the tank has a Taylor microscale Re λ ≃ 160. The conformal invariance theory being tested here is related to the behavior of equilibrium systems near a critical point. This theory is associated with the work of Löwner, Schramm and others and is usually referred to as Schramm-Löwner Evolution (SLE). The system was exposed to several tests of SLE. The results of these tests suggest that zero-vorticity isolines exhibit noticeable departures from this type of conformal invariance.

Conformal invariance of weakly compressible two-dimensional turbulence

“…This result, which suggests an intriguing connection between (non-equilibrium) turbulent flows and statistical models at the critical point, has been extended to other 2D incompressible flows, including surface quasi-geostrophic turbulence [11] and a class of active scalar turbulence [12]. Conformal invariance has also been investigated experimentally in Lagrangian reconstructed vorticity field of a turbulent surface flow [13] (two-dimensional section of a three-dimensional flow), where deviations from SLE predictions have been observed.…”