Intermittency and non-universality of pair dispersion in isothermal compressible turbulence
Statistical properties of the pair dispersion of Lagrangian particles (tracers) in incompressible turbulent flows provide insights into transport and mixing. We explore the same in transonic to supersonic compressible turbulence of an isothermal ideal gas in two dimensions, driven by large-scale solenoidal and irrotational stirring forces, via direct numerical simulations. We find that the scaling exponents of the order-$p$ negative moments of the distribution of exit times -- in particular, the doubling and halving times of pair separations -- are nonlinear functions of $p$. Furthermore, the doubling and halving time statistics are different. The halving-time exponents are universal -- they satisfy their multifractal model-based prediction, irrespective of the nature of the stirring. However, the doubling-time exponents are not. In the solenoidally-stirred flows, the doubling time exponents can be expressed solely in terms of the multifractal scaling exponents obtained from the structure functions of the solenoidal component of the velocity. Moreover, they depend strongly on the Mach number, Ma, as elongated patches of high vorticity emerge along shock fronts at high Ma. In contrast, in the irrotationally-stirred flows, the doubling-time exponents do not satisfy any known multifractal model-based relation, and are independent of Ma. Our findings are of potential relevance to astrophysical disks and molecular clouds wherein turbulent transport and mixing of gases often govern chemical kinetics and the rates of formation of stars and planetesimals.