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.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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