Uncovering the multifractality of Lagrangian pair dispersion in shock-dominated turbulence

Abstract

Lagrangian pair dispersion provides insights into mixing in turbulent flows. By direct numerical simulations (DNS) we show that the statistics of pair dispersion in the randomly forced two-dimensional Burgers equation, which is a typical model of shock-dominated turbulence, is very different from its incompressible counterpart because Lagrangian particles get trapped in shocks. We develop a heuristic theoretical framework that accounts for this -- a generalization of the multifractal model -- whose prediction of the scaling of Lagrangian exit times agrees well with our DNS.