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💨🌏🌊 Geophysical fluid dynamics pseudospectral solvers with Julia and FourierFlows.jl.

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This package leverages the FourierFlows.jl framework to provide modules for solving problems in Geophysical Fluid Dynamics on periodic domains using Fourier-based pseudospectral methods.


To install, use Julia's built-in package manager (accessed by pressing ] in the Julia REPL command prompt) to add the package and also to instantiate/build all the required dependencies

(v1.6) pkg> add GeophysicalFlows
(v1.6) pkg> instantiate

The most recent version of GeophysicalFlows.jl requires Julia v1.6 (the current long-term-release) or later. We strongly urge you to use this version.

The latest version that is compatible with Julia v1.5 is GeophysicalFlows.jl v0.13.1.


See examples/ for example scripts. These examples are best viewed by browsing them within the package's documentation.

Some animations created with GeophysicalFlows.jl are online @ youtube.


  • TwoDNavierStokes: the two-dimensional vorticity equation.
  • SingleLayerQG: the barotropic or equivalent-barotropic quasi-geostrophic equation, which generalizes TwoDNavierStokes to cases with topography, Coriolis parameters of the form f = f₀ + βy, and finite Rossby radius of deformation.
  • MultiLayerQG: a multi-layer quasi-geostrophic model over topography and with the ability to impose a zonal flow U_n(y) in each layer.
  • SurfaceQG: a surface quasi-geostrophic model.
  • BarotropicQGQL: the quasi-linear barotropic quasi-geostrophic equation.


For now, GeophysicalFlows.jl is restricted to run on either a single CPU or single GPU. These restrictions come from FourierFlows.jl. Multi-threading can enhance performance for the Fourier transforms. By default, FourierFlows.jl will use the maximum number of threads available on your machine. You can set the number of threads used by FourierFlows.jl by setting the environment variable, e.g.,


For more information on multi-threading users are directed to the Julia Documentation.

If your machine has more than one GPU available, then functionality within CUDA.jl package enables the user to choose the GPU device that FourierFlows.jl should use. The user is referred to the CUDA.jl Documentation; in particular, CUDA.devices and CUDA.CuDevice. The user is also referred to the GPU section in the FourierFlows.jl documentation.

Getting help

Interested in GeophysicalFlows.jl or trying to figure out how to use it? Please feel free to ask us questions and get in touch! Check out the examples and open an issue or start a discussion if you have any questions, comments, suggestions, etc.


If you use GeophysicalFlows.jl in research, teaching, or other activities, we would be grateful if you could mention GeophysicalFlows.jl and cite our paper in JOSS:

Constantinou et al., (2021). GeophysicalFlows.jl: Solvers for geophysical fluid dynamics problems in periodic domains on CPUs & GPUs. Journal of Open Source Software, 6(60), 3053, doi:10.21105/joss.03053.

The bibtex entry for the paper is:

  doi = {10.21105/joss.03053},
  url = {},
  year = {2021},
  publisher = {The Open Journal},
  volume = {6},
  number = {60},
  pages = {3053},
  author = {Navid C. Constantinou and Gregory LeClaire Wagner and Lia Siegelman and Brodie C. Pearson and André Palóczy},
  title = {GeophysicalFlows.jl: Solvers for geophysical fluid dynamics problems in periodic domains on CPUs \& GPUs},
  journal = {Journal of Open Source Software}


If you're interested in contributing to the development of GeophysicalFlows.jl we are excited to get your help, no matter how big or small a contribution you make! It's always great to have new people look at the code with fresh eyes: you will see errors that other developers have missed.

Let us know by open an issue or start a discussion if you'd like to work on a new feature or implement a new module, if you're new to open-source and want to find a cool little project or issue to work on that fits your interests! We're more than happy to help along the way.

For more information, check out our contributor's guide.