The Potsdam turbulence decay comparisons

This web site is set up for the coordination of the comparative study of turbulence decay simulations using different grid- and particle-codes. The following can be found in this page:

Participating scientists
Details on the setup of initial conditions
Download initial conditions
Instructions
Results

Initial Conditions

All participants have agreed to start their simulations of turbulence decay from the same initial conditions. Due to technical constraints the initial conditions were produced using GADGET, i.e. were based on the SPH particle distributions. For this we have followed the process described in detail by Mac Low et al. (1998) and Mac Low (1999).

A 10,000,000 stationary particle distribution was first created. The particles (initially at uniform density) were then accelerated using the driving routine described by Mac Low et al. (1998) and Mac Low (1999). A Gaussian velocity field for each of the 3 velocity components is produced (driven at wave-numbers k=1..2 only) on a 3D spatial grid and at predefined time intervals. At each of these intervals a velocity kick is imposed to each particle according to the cell it lies within. The magnitudes of the velocities used for the particle velocity kicks are given by the amount of kinetic energy input required at each time interval in order for a desired value of the 3D turbulence Mach number to be obtained/maintained. We have driven such a turbulent velocity field on the particle distribution for 2 free-fall times. A 3D Mach number of 3.2 was established. Details on the energy input rate used can be found in Jappsen et al. (2005).

The isothermal temperature is 11.4K (and the mean molecular weight used is 2.36). We refer to this state of the system as the initial state, corresponding to t=0, and in order to distinguish it from the second set of initial conditions (see below), we have named it as "non-driven" initial conditions. We have interpolated the density and velocity distribution of the SPH particles on 3D grids of 3 different cell sizes (64, 128, 256). The computational domain size is 0.29 pc.

We have continued driving the particle distribution for another 2 free-fall times using the turbulent velocity field described above. We refer to this state as "driven" initial conditions, corresponding to time t=2. We have also interpolated the density and velocity distributions of the SPH particles on grids of 3 different sizes.

Download Initial Conditions

The initial conditions can be downloaded from this site. They are in the form of zipped tar files containing a density (_dens.dat) and 3 velocity (_*vel.dat, *=x,y,z) grid values. The naming convention of the tar (and their included .dat) files is the following: type_state_grid_time, where type is "nd" for the non-driven and "dr" for the driven case; state is "ic" for initial conditions; grid is 064, 128, 256 according to the number of cells in the grid; and time is 000 and 020 (respectively, for the "nd" and "dr" types).

All data files contain the data in a single column ascii format. To read the data you need to construct 3 nested loops each of grid length (grid value according to the file name) with x, y and z being respectively the faster indices. They all refer to cell centred information. So please use (i-(1/2))*L_box/grid for the cell centres in each Cartesian direction, where L_box=0.29 pc and grid value according to the file name. In case of face centred velocity distribution (e.g. for ZEUS) please shift by -(1/2)*L_box/grid in each direction while keeping the other two directions as before and for the last (grid+1) face of the shifted directions please use again the first face (as periodic boundaries are used here).

The (code) units of the above data points are:
UnitLength (in cm) = 3.085678e18 (or 1 pc)
UnitMass (in g) = 1.989e33 (or 1 solar mass)
UnitVelocity (in cm/s) = 847500.89 (set so that UnitTime = 1 free fall time)
UnitDensity = UnitMass/UnitLength**3
In our code, constants like k, G etc, have their physical values translated to the above code unit system. The EOS is ideal gas and the polytropic exponent gamma=1.

Here you can find the following files:
CORRECTED DATA FILES WITH NEW VELOCITY NORMALISATION AND NEW SCHEME FOR THE INTERPOLATION INTO A GRID
dr_ic_256_020_data.tar.gz

Instructions

The above initial conditions are to be evolved isothermally, without any driving (i.e. turbulence decay) and without self-gravity, using periodic boundary conditions.

Please run the "dr" initial conditions only. We are interested in determining the time after which turbulence gets "established" using our SPH turbulence-driving scheme, this is why we have produced two sets of initial conditions. See below our conclusion on this.

Please run the 256 cubes first and you will be instructed later on the need of a resolution study, for which the smaller cubes could be used.

Please switch off AMR initially in your codes (where applicable). Use of AMR may be decided later.

For comments please email me at skitsionas@aip.de.

Results

We have evolved the above initial conditions for 10 free-fall times (t_ff~0.11 Myr, using the initial uniform (stationary) density of 3.31 x 10^-19 g/cm³), or equivalently 10 unit times (see unit definitions above). We are currently analysing our GADGET, FLASH, TVD, ZEUS, ENZO, PHANTOM & VINE results, in order to obtain the corresponding power spectra, density- and velocity-PDFs as well as structure functions.

We have decided that all participants should use the same analysis scripts.
Instructions on the use of the script calculating power spectra can be found here. The script itself lies here.
Instructions on the use of the script calculating PDFs can be found here. The script itself lies here.
The script for calculating structure functions can be found here.

A preview of our individual power spectra can be found here. Combined volume-weighted spectra can be found here. Combined density-weighted spectra can be found here.

The conclusion we have made so far is that the initial conditions generated after driving for only 2 t_ff (marked with "nd") do not represent fully established turbulence. See here how the two different sets of initial conditions compare. Therefore, the choice of the "dr" initial conditions (generated after driving for 4 t_ff) for our comparisons (see instructions above) is justified.

We have also shown that by using density-weighted velocities for the calculation of power-spectra we recover a Kolmogorov type of scaling, at least for the small inertial range that the resolution of these simulations allows, e.g. examine the density-weighted power spectra against the volume-weighted ones.

Examples of density, rate of strain, vorticity, and velocity PDFs can be found here.

Finally, examples of structure functions can be found here.

References

Jappsen, A.-K., Klessen, R. S., Larson, R. B., Li, Y., Mac Low, M.-M., 2005, A&A, 435, 611

Mac Low, M.-M., 1999, ApJ, 524, 169

Mac Low, M.-M., Klessen, R. S., Burkert, A., Smith, M. D., 1998, Phys. Rev. Lett., 80, 2754