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Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks

Published online by Cambridge University Press:  19 December 2011

Lukas Konstandin ,
Christoph Federrath ,
Ralf S. Klessen  and
Wolfram Schmidt
Lukas Konstandin*
Affiliation:
Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg, Germany
Christoph Federrath
Affiliation:
Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg, Germany Ecole Normale Supérieure de Lyon, Centre de Recherche Astrophysique, 46 Allée d’Italie, F-69364 Lyon, France Centre for Stellar and Planetary Astrophysics, School of Mathematical Sciences, Monash University, Clayton VIC 3168, Australia
Ralf S. Klessen
Affiliation:
Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg, Germany
Wolfram Schmidt
Affiliation:
Institut für Astrophysik der Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
*
†Email address for correspondence: [email protected]
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Abstract

We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show significantly larger density contrast, more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. We show that the absolute values of Lagrangian and Eulerian structure functions of all orders in the integral range are only a function of the root mean square Mach number, but independent of the forcing. With the assumption of a Gaussian distribution for the probability density function of the velocity increments for large scales, we derive a model that describes this behaviour.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 692 , 10 February 2012 , pp. 183 - 206
Copyright
Copyright © Cambridge University Press 2011

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