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Andrew D Bragg : Lagrangian irreversibility and inversions in 3 and 2 dimensional turbulence

Studying how small inertial particles suspended in turbulent flows move relative to each other provides fundamental insights into their transport, mixing and collisions. These insights are crucial for tackling diverse problems ranging from droplet growth in warm clouds, to planetesimal formation through collisional aggregation in turbulent protoplanetary nebula. A deeper understanding of the relative motion of the particles can be obtained by investigating both their forward-in-time (FIT) and backward-in-time (BIT) dispersion. When FIT and BIT dispersion are different it signifies irreversibility, and since FIT and BIT dispersion are related to different problems, understanding the irreversibility is of fundamental and practical importance.
I will present new theoretical arguments and asymptotic predictions, along with results from Direct Numerical Simulations (DNS) of the governing equations, to show that inertial particle dispersion can be very strongly irreversible in turbulence, with BIT being much faster than FIT dispersion in 3-dimensional turbulence. The results also show that inertial particles can disperse much faster than fluid (interialess) particles. I will also present arguments, confirmed by DNS results, that in 2-dimensional turbulence the nature of the irreversibility and the direction of the particle energy fluxes can invert when the particle inertia exceeds a certain threshold. These results significantly advance our understanding of dispersion problems, and lead to new capabilities for predicting the effect of inertia on the rate at which particles spread out and mix together in turbulence, and the rate at which they collide.

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