The World’s Largest Turbulence Simulations

Principal Investigator:
Ralf Klessen(1), Christoph Federrath (2)

(1) Universität Heidelberg, Germany (2) Australian National University

Local Project ID:

HPC Platform used:
SuperMUC of LRZ

Date published:

Interstellar turbulence shapes the structure of the multi-phase interstellar medium (ISM) and is a key process in the formation of molecular clouds as well as the build-up of star clusters in their interior. The key ingredient for our theoretical understanding of ISM dynamics and stellar birth is the sonic scale in the turbulent cascade, which marks the transition from supersonic to subsonic turbulence and produces a break in the turbulence power spectrum. To measure this scale and study the sonic transition region in detail, scientists, for the first time, ran a simulation with the unprecedented resolution of 10,0483 grid cells.

Understanding turbulence is critical for a wide range of terrestrial and astrophysical applications. For example, turbulence on earth is responsible for the transport of pollutants in the atmosphere and determines the movement of weather patterns. But turbulence plays a central role in astrophysics as well. For instance, the turbulent motions of gas and dust particles in protostellar disks enables the formation of planets. Moreover, virtually all modern theories of star formation rest on the statistics of turbulence (Padoan et al., 2014). Especially the theoretical assumptions about turbulence behind star formation theories allow the prediction of star formation rates in the Milky Way and in distant galaxies (Federrath & Klessen, 2012). Interstellar turbulence shapes the structure of molecular clouds and is a key process in the formation of filaments which are the building blocks of star-forming clouds. The key ingredient for all these models is the so-called sonic scale. The sonic scale marks the transition from supersonic to subsonic turbulence and produces a break in the turbulence power spectrum from E ∝ k−2 to E ∝ k−5/3 . While the power-law slopes of -2 and -5/3 for the supersonic and subsonic parts of the spectrum have been measured independently, there is no simulation currently capable of bridging the gap between both regimes. This is because previous simulations did not have enough resolution to separate the injection scale, the sonic scale and the dissipation scale.

The aim of this project is to run the first simulation that is sufficiently resolved to measure the exact position of the sonic scale and the transition region from supersonic to subsonic turbulence. A simulation with the unprecedented resolution of 10,0003 grid cells will be needed for resolving the transition scale.


In the framework of a GCS Large Scale Project, an allocation exceeding 40 million core-h has been granted to this project on SuperMUC. The application used for this project is FLASH, a public, modular grid-based hydrodynamical code for the simulation of astrophysical flows (Fryxell et al., 2000). The parallelisation is based entirely on MPI. In the framework of the SuperMUC Phase 2 scale-out, the current code version (FLASH4) has been optimised to reduce the memory and MPI communication requirements. In particular, non-critical operations are now performed in single precision, without causing any significant impact on the accuracy of the results. In this way, the code runs with a factor of 4.1 less memory and 3.6 times faster than the version used for the previous large-scale project at LRZ (Federrath, 2013), and scales remarkably well up to the full machine on SuperMUC Phase 2 (see Figure 1).

Our current 10,0483 simulation has been nearly completed at the time of writing, and data processing is in progress. Some early impression of the forthcoming results can be seen from the highlights of the work of Federrath (2013), based on the previous large-scale project on turbulence simulations (up to 4,0963 grid cells), selected as the SAO/NASA ADS paper of the year 2013.

Highly-compressible supersonic turbulence is complex, if compared to the subsonic, incompressible regime, because the gas density can vary by several orders of magnitude. Using three-dimensional simulations, we have determined the power spectrum in this regime (see Figure 2), and found E ∝ k−2 , confirming earlier indications obtained with much lower resolution (Kritsuk et al., 2007). The resolution study in Figure 2 shows that we would not have been able to identify this scaling at any lower resolution than 4,0963 cells. Extremely high resolution and compute power are absolutely necessary for the science done here.

Figure 3 displays the unprecedented level of detail in density structure achieved with our current 10,0483 simulation. This visualization highlights the enormous complexity of the turbulent structures on all spatial scales covered in these simulations. A simulation video is provided below or is available at:


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Research Team:

Christoph Federrath1, Ralf S. Klessen2,3, Luigi Iapichino4, & Nicolay J. Hammer4

1 Research School of Astronomy and Astrophysics, Australian National University (
2 Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik (
3 Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen
4 Leibniz-Rechenzentrum der Bayerischen Akademie der Wissenschaften (,

References and Links:

Federrath, C. 2013, Monthly Notices of the Royal Astronomical Society, 436, 1245

Federrath, C., & Klessen, R. S. 2012, Astrophysical Journal, 761, 156

Fryxell, B., Olson, K., Ricker, P., et al. 2000, Astrophysical Journal Supplement Series, 131, 273

Kritsuk, A. G., Norman, M. L., Padoan, P., & Wagner, R. 2007, Astrophysical Journal, 665, 416

Padoan, P., Federrath, C., Chabrier, G., et al. 2014, Protostars and Planets VI, 77

Gauss Centre for Supercomputing:

Uni Heidelberg:˜chfeder/pubs/supersonic/supersonic.shtml

Scientific Contact:

Dr. Christoph Federrath 
Research School of Astronomy and Astrophysics
The Australian National University
Cotter Road, Canberra, ACT 2611, Australia
Email: christoph.federrath[at]

Tags: LRZ Astrophysics Heidelberg University