Intermittency and nonuniversality of pair dispersion in isothermal compressible turbulence

We study statistical properties of the pair dispersion of Lagrangian particles 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- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>p</a:mi> </a:math> negative moments of the doubling and halving times of pair separations are nonlinear functions of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>p</b:mi> </b:math> . 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. 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, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mtext>Ma</c:mtext> </c:math> . In contrast, in the irrotationally stirred flows, the doubling-time exponents do not satisfy any known multifractal model-based relation, and are independent of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mtext>Ma</d:mtext> </d:math> . Our work is a generalization of Richardson's law of pair dispersion to compressible turbulence.