Active Turbulence (active-turbulence)

One line description of the data: 760 generalized Navier–Stokes active-turbulence simulations on a $128\times 256128\; \backslash times\; 256$ latitude–longitude grid.

Longer description of the data: This dataset simulates actively driven incompressible flows on the sphere using the generalized Navier–Stokes model of Mickelin et al. A band-limited linear instability continuously injects vortices at a characteristic length scale, while nonlinear advection and dissipation determine their subsequent evolution. Depending on the parameters, the system exhibits anomalous turbulence with vortices organized into persistent chains (A phase) or more conventional two-dimensional turbulence (T phase). We vary the normalized sphere-to-vortex size $R\mathrm{/}\mathrm{\Lambda }R/\backslash Lambda$ and the normalized active bandwidth $\kappa \mathrm{\Lambda }\backslash kappa\backslash Lambda$, together with the random initial-condition seed. The burst-like B-phase configuration is excluded from the dataset.

Code or software used to generate the data: Dedalus v3, an MPI-parallel spectral framework for solving PDEs.

Visualization:

About the data

Dimension of discretized data: 225 snapshots per trajectory on a $128\times 256128\; \backslash times\; 256$ (lat × lon) grid.

Fields available in the data:

HDF5 path	Shape	Units	Description
t0_fields/vorticity	(1, 225, 128, 256)	$1\mathrm{/}\tau 1/\backslash tau$	Vorticity $\omega \backslash omega$
scalars/{r_over_lambda, kappa_lambda, seed, R, tau, Lambda, kappa}	()	—	Run parameters (stored as floats)
dimensions/{time, lat, lon}	(225,), (128,), (256,)	$\tau \backslash tau$, °, °	Coordinates

The stored field is float32; the time coordinate is float64. Velocity can be recovered from vorticity by solving the spherical Poisson equation $\mathrm{\Delta }\psi =-\omega \backslash Delta\backslash psi=-\backslash omega$ for the stream function and computing the corresponding divergence-free velocity field.

Number of trajectories: 760: 19 physical parameter combinations, each with 40 initial-condition seeds. The configuration $R\mathrm{/}\mathrm{\Lambda }=2R/\backslash Lambda=2$, $\kappa \mathrm{\Lambda }=0.4\backslash kappa\backslash Lambda=0.4$ is excluded because it lies in the burst-like B phase. 608/76/76 train/validation/test split in data/{train,valid,test}/, stratified so that every parameter combination contributes 32/4/4 seeds.

Estimated size of the ensemble of all simulations: Approximately 18 GB (gzip-compressed HDF5).

Storage format: One HDF5 file per run. Normalization statistics computed on the train split are in stats.yaml.

Grid type: $128\times 256128\; \backslash times\; 256$ regular equiangular latitude–longitude grid, excluding the poles. The simulations are performed on a Gauss–Legendre × equispaced-longitude spectral grid with $N_{\theta }=128N\_\backslash theta\; =\; 128$, $N_{\varphi }=256N\_\backslash phi\; =\; 256$ and dealiasing factor 3/2, and resampled to the regular grid using cubic-spline interpolation in latitude.

Initial conditions: A small-amplitude random vorticity field ${\omega }_0=\epsilon {\sum }_{\mathrm{\ell }=2}^{{\mathrm{\ell }}_{\text{init}}}{\sum }_{m=-\mathrm{\ell }}^{\mathrm{\ell }}{a}_{\mathrm{\ell }m}{Y}_{\mathrm{\ell }m}\backslash omega\_0\; =\; \backslash varepsilon\; \backslash sum\_\{\backslash ell=2\}^\{\backslash ell\_\backslash textup\{init\}\}\; \backslash sum\_\{m=-\backslash ell\}^\{\backslash ell\}\; a\_\{\backslash ell\; m\}\; Y\_\{\backslash ell\; m\}$ in the real spherical-harmonic basis, with independent coefficients $a_{\mathrm{\ell }m}\sim \mathcal{N}(0,1)a\_\{\backslash ell\; m\}\; \backslash sim\; \backslash mathcal\{N\}(0,\; 1)$ and amplitude $\epsilon ={10}^{-3}\backslash varepsilon\; =\; 10^\{-3\}$. The flat spectrum covers every mode from $\mathrm{\ell }=2\backslash ell\; =\; 2$ up to four modes beyond the upper edge of the unstable band, ${\mathrm{\ell }}_{\text{init}}=\lceil R(\pi \mathrm{/}\mathrm{\Lambda }+\kappa \mathrm{/}2)\rceil +4\backslash ell\_\backslash textup\{init\}\; =\; \backslash lceil\; R(\backslash pi/\backslash Lambda\; +\; \backslash kappa/2)\; \backslash rceil\; +\; 4$, so the seed overlaps the whole unstable band. Modes $\mathrm{\ell }=0,1\backslash ell\; =\; 0,\; 1$ are excluded.

Boundary conditions: Spherical.

Simulation time-step $(\mathrm{\Delta }t)(\backslash Delta\; t)$: CFL-adaptive (RK222), initialized at $0.005\tau 0.005\backslash ,\backslash tau$ and capped at $0.05\tau 0.05\backslash ,\backslash tau$. The $\mathrm{\ell }=1\backslash ell\; =\; 1$ (rigid-rotation) coefficients of vorticity and stream function are set to zero after every step. The exact dynamics keep this mode at zero, but it is undamped, so without the projection numerical error accumulates into a spurious solid-body rotation.

Data are stored separated by $(\delta t)(\backslash delta\; t)$: $0.2\tau 0.2\backslash ,\backslash tau$. Snapshots are written at adaptive solver steps, so each lies within $0.0012\tau 0.0012\backslash ,\backslash tau$ of its nominal time; use dimensions/time for exact values.

Total time range $(t_{\text{min}}(t\_\backslash textup\{min\}$ to $t_{\text{max}})t\_\backslash textup\{max\})$: $20\tau 20\backslash ,\backslash tau$ to $64.8\tau 64.8\backslash ,\backslash tau$. Each run is simulated from $t=0t\; =\; 0$ to $65\tau 65\backslash ,\backslash tau$; the first $20\tau 20\backslash ,\backslash tau$, which contain the linear growth of the seed perturbation and the subsequent overshoot, are discarded. dimensions/time counts $\tau \backslash tau$ from the start of the simulation, so the stored time axis starts at $2020$.

Set of coefficients or non-dimensional parameters evaluated:

• r_over_lambda $=R\mathrm{/}\mathrm{\Lambda }\in \{2,4,7,10\}=\; R/\backslash Lambda\; \backslash in\; \backslash \{2,\; 4,\; 7,\; 10\backslash \}$, the sphere radius relative to the characteristic vortex size
• kappa_lambda $=\kappa \mathrm{\Lambda }\in \{0.4,0.7,1.0,1.4,1.8\}=\; \backslash kappa\backslash Lambda\; \backslash in\; \backslash \{0.4,\; 0.7,\; 1.0,\; 1.4,\; 1.8\backslash \}$, the normalized width of the unstable band
• seed $\in \{0,\dots ,39\}\backslash in\; \backslash \{0,\; \backslash ldots,\; 39\backslash \}$, the initial-condition seed

The combination $(R\mathrm{/}\mathrm{\Lambda },\kappa \mathrm{\Lambda })=(2,0.4)(R/\backslash Lambda,\backslash kappa\backslash Lambda)=(2,0.4)$ is excluded. The sphere radius and inverse peak driving rate are fixed to $R=1R=1$ and $\tau =1\backslash tau=1$.

Approximate time to generate the data: Approximately 3–20 minutes of solver time per trajectory (median about 6.5 minutes).

Hardware used to generate the data: CPU generation on sciCORE compute nodes (AMD EPYC or Intel Xeon), using 16 MPI ranks per run.

Loading

Download a single run (≈22 MB) and read it with h5py:

import h5py
from huggingface_hub import hf_hub_download

path = hf_hub_download("sada-group/active-turbulence", "data/test/run_0041.h5", repo_type="dataset")
with h5py.File(path, "r") as f:
    w = f["t0_fields/vorticity"][0]                          # (225, 128, 256), in 1/tau
    t = f["dimensions/time"][:]                              # tau since simulation start (20.0 ... 64.8)
    params = {k: f["scalars"][k][()] for k in f["scalars"]}

To download a whole split (or the full 18 GB dataset), use snapshot_download with allow_patterns:

from huggingface_hub import snapshot_download

root = snapshot_download(
    "sada-group/active-turbulence",
    repo_type="dataset",
    allow_patterns=["data/test/*", "stats.yaml"],  # drop allow_patterns for everything
)

Please cite the associated paper if you use this data in your research:

@misc{muser2026dandelionsphericalflowerneural,
      title={Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics},
      author={Till Muser and Giovanni Abati and Ivan Dokmanić},
      year={2026},
      eprint={2608.27521},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2608.27521},
}

as well as the original active-turbulence paper and the solver:

@article{mickelin2018anomalous,
  title={Anomalous chained turbulence in actively driven flows on spheres},
  author={Mickelin, Oscar and S{\l}omka, Jonasz and Burns, Keaton J. and Lecoanet, Daniel and Le Bars, Michael and Fauve, Stephan and Dunkel, J{\"o}rn},
  journal={Physical Review Letters},
  volume={120},
  number={16},
  pages={164503},
  year={2018},
  doi={10.1103/PhysRevLett.120.164503}
}

@article{burns2020dedalus,
  title={Dedalus: A flexible framework for numerical simulations with spectral methods},
  author={Burns, Keaton J. and Vasil, Geoffrey M. and Oishi, Jeffrey S. and Lecoanet, Daniel and Brown, Benjamin P.},
  journal={Physical Review Research},
  volume={2},
  number={2},
  pages={023068},
  year={2020},
  doi={10.1103/PhysRevResearch.2.023068}
}