Intermittency and non-universality of pair dispersion in isothermal compressible turbulence

Abstract

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.

References in corpus (24)

• Theory of Star Formation
• Control of star formation by supersonic turbulence
• Interstellar Turbulence I: Observations and Processes
• A high-bias, low-variance introduction to Machine Learning for physicists
• The Statistics of Supersonic Isothermal Turbulence
• Mach Number Dependence of Turbulent Magnetic Field Amplification: Solenoidal versus Compressive Flows
• Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
• Relative dispersion in fully developed turbulence: The Richardson's Law and Intermittency Corrections
• Is the Scaling of Supersonic Turbulence Universal?
• Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks
• Timescales of Turbulent Relative Dispersion
• Pair dispersion in synthetic fully developed turbulence
• The Varieties of Dynamic Multiscaling in Fluid Turbulence
• Geometry and violent events in turbulent pair dispersion
• Dynamics of Passive-Scalar Turbulence
• Dynamic Multiscaling in Two-dimensional Fluid Turbulence
• Dispersion of tracer particles in a compressible flow
• How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence
• Universal alignment in turbulent pair dispersion
• Non-local dispersion and the reassessment of Richardson's t3-scaling law
• Generalization of Turbulent Pair Dispersion to Large Initial Separations
• Dynamic Multiscaling in Turbulence
• Spectral characterisation of inertial particle clustering in turbulence
• Probing the nature of dissipation in compressible MHD turbulence