Extreme concentration fluctuations due to local reversibility of mixing in turbulent flows

Mixing of a passive scalar in a fluid (e.g. a radioactive spill in the ocean) is the irreversible process towards homogeneous distribution of a substance. In a moving fluid, due to the chaotic advection [H. Aref, T. Fluid Mech. 143 (1984) 1; J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989)] mixing is much faster than if driven by molecular diffusion only. Turbulence is known as the most efficient mixing flow [B. I. Shraiman and E. D. Siggia, Nature 405 (2000) 639]. We show that in contrast to spatially periodic flows, two-dimensional turbulence exhibits local reversibility in mixing, which leads to the generation of unpredictable strong fluctuations in the scalar concentration. These fluctuations can also be detected from the analysis of the fluid particle trajectories of the underlying flow.