---
license: mit
task_categories:
- image-to-3d
tags:
- mathematics
- partial-differential-equations
- computational fluid dynamics
- physics
- neural operator
size_categories:
- 1K<n<10K
---
# Navier Stokes Dataset of Isotropic Turbulence in a periodic box

<!-- Provide a quick summary of the dataset. -->

The dataset for tensor-to-tensor or trajectory-to-trajectory neural operators, generated from Navier-Stokes equations 
to model the isotropic turbulence [1] such that the spectra satisfy the inverse cascade discovered by A.N. Kolmogorov [2].

[1]: McWilliams, J. C. (1984). The emergence of isolated coherent vortices in turbulent flow. *Journal of Fluid Mechanics*, 146, 21-43.
[2]: Kolmogorov, A. N. (1941). The local structure of turbulence in incompressible viscous fluid for very large Reynolds Numbers. *Dokl. Akad. Nauk SSSR*, 30, 301.

## Dataset Details

### Dataset Description

<!-- Provide a longer summary of what this dataset is. -->

The dataset contains several cases of isotropic turbulence modeled by Navier-Stokes equations. The data are generated either 
by a pseudo-spectral solver with 4th-order Runge-Kutta for the convection term, or a higher order Finite Volume IMEX methods. 
The different initial conditions have different peak wavenumbers of O(1), and eventually their spectra all converge to the Kolmogorov
inverse cascade.

- **Curated by:** S. Cao
- **Funded by National Science Foundation:** NSF award DMS-2309778
- **License:** MIT license

### Dataset Sources [optional]

<!-- Provide the basic links for the dataset. -->

- **Repository:** [https://github.com/scaomath/torch-cfd](https://github.com/scaomath/torch-cfd)
- **Paper:** [More Information Needed]
- **Demo:**
  - [The classical Kolmogorov inverse cascade with a solenoidal forcing and small drag.](https://github.com/scaomath/torch-cfd/blob/main/examples/Kolmogrov2d_rk4_cn_forced_turbulence.ipynb)
  - [The fast training using the data with a small number of vortices.](https://github.com/scaomath/torch-cfd/blob/main/examples/ex2_SFNO_train_fnodata.ipynb)
  - [The fast converging to the inverse cascade.](https://github.com/scaomath/torch-cfd/blob/main/examples/ex2_SFNO_5ep_spectra.ipynb)

## Dataset Structure

<!-- This section provides a description of the dataset fields, and additional information about the dataset structure such as criteria used to create the splits, relationships between data points, etc. -->

Each individual chunk of data is pickled in single-file format.

## Dataset Creation

### TO-DO

## Citation

<!-- If there is a paper or blog post introducing the dataset, the APA and Bibtex information for that should go in this section. -->

```bibtex
@article{2024SpectralRefiner,
  title={Spectral-Refiner: Fine-Tuning of Accurate Spatiotemporal Neural Operator for Turbulent Flows},
  author={Shuhao Cao and Francesco Brarda and Ruipeng Li and Yuanzhe Xi},
  journal={arXiv preprint arXiv:2405.17211},
  year={2024},
  primaryClass={cs.LG}
}
```