Raschii

Raschii is a Python library for constructing non-linear regular waves. Supported wave models are:

• Stream function waves (M. M. Rienecker and J. D. Fenton, 1981)
• Stokes second- through fifth-order waves (based on J. D. Fenton, 1985)
• Airy waves, the standard linear wave theory

Raschii directly computes the series expansion coefficients (for Stokes waves), or solves a minimization problem for the coefficients (for stream function waves). Once the expansion coefficients of the wave has been found you can

1. Compute the free-surface elevation
2. Compute the particle velocities at any point in the wave field (and in the air phase by use of the potential-flow solution above the free-surface).
3. Export the wave field to a file in the SWD file format (Spectral Wave Data, see more below). The SWD library can then be used to compute many other properties such as the velocity potential, the particle accelerations, the stream function, the Bernoulli pressure, and several other properties.

A comparison of fifth-order Stokes waves and fifth-order Fenton stream function waves. Deep water, wave height 12 m, wave length 100 m.

Using the Raschii waves

Raschii can output waves in the SWD (spectral wave data) standard file format for use as the incoming incident waves in flow analysis programs such as potential-flow or CFD (Euler and Navier-Stokes equations etc). The SWD file format is used by other linear and non-linear wave-generation tools, such as the non-linear irregular-wave HOSM solver DNV WAMOD. By supporting the SWD file format you avoid having to implement your own wave models for all types of waves, and you can instead use a uniform wave API for all types of linear and non-linear waves and let the SWD library handle the details of the wave kinematics.

Raschii also includes a command line program to plot regular waves from the supported wave models and C++ code generation for using the results in other programs, such as in FEniCS expressions for initial and boundary conditions in a FEM solver (if you do not want to link to the SWD library for some reason).

Installation and running

Raschii can be installed using pip, uv, or any other Python package manager that supports the Python Package Index (PyPI). Example:

pip install raschii

You can also run Raschii in your web browser using PyScript/Pyodide, see the online demo!

Using Raschii from Python

An example of using Raschii from Python:

import raschii

fwave = raschii.FentonWave(height=0.25, depth=0.5, length=2.0, N=20)

print(fwave.surface_elevation(x=0))
print(fwave.surface_elevation(x=[0, 0.1, 0.2, 0.3]))
print(fwave.velocity(x=0, z=0.2))

This will output:

[0.67352456]
[0.67352456 0.61795882 0.57230232 0.53352878]
[[0.27263788 0.        ]]

See the documentation for more information on the available parameters, methods and attributes of the wave classes.

Using Raschii from the command line

You can also use Raschii from the command line. You can plot the wave elevation and particle velocities, and also write SWD files. See the help for the command line programs to get detailed usage info.

python -m raschii.cmd.plot -h
python -m raschii.cmd.swd -h

Substitute python with python3 or uv run as appropriate to your installation. You must install the matplotlib Python package to be able to use the plot command.

An example of using Raschii from the command line:

# Plot a 0.2 m high wave that is 2 meters long in 1.5 meters water depth
# Some information about the wave is also shown
python -m raschii.cmd.plot -N 5 Fenton 0.2 1.5 2

# Save the same stream function wave to a SWD file
python -m raschii.cmd.swd -N 5 fenton.swd Fenton 0.2 1.5 2

The plot tool allows comparing multiple waves, the SWD file writer only supports a single wave at a time and does currently not support Airy waves.

Documentation

The documentation can be found on Raschii's Read-the-Docs pages.

Development

Raschii is developed in Python on GitHub using the Git version control system.

Raschii is automatically tested using pytest and GitHub Actions and the current CI build status is .

Releases

Version 1.1.1 - Unreleased

• Use PyScript to run Raschii in the browser (instead of the incomplete Dart port).
• Increase the speed of the SWD file writer

Version 1.1.0 - Jun 18. 2025

• Support for giving the wave period instead of the wave length
• Support for infinite depth waves. This is not fully complete, but should be sufficient to export proper SWD files for infinite depth waves. Set depth=-1 to use infinite depth waves.
• Better testing of the SWD file exporter when the SpectralWaveData package is not installed by including a simplified SWD file reader for the tests.
• Move repository and CI to GitHub. Tested on Python 3.10 (Ubuntu 22.04), and Python 3.12 (uv).

Version 1.0.7 - Sep 30. 2024

• Support for numpy 2.1
• Drop support for Python 3.9 and older (following numpy)
• Added testing with latest Python available via uv (currently CPython 3.12)

Version 1.0.6 - Jun 28. 2024

• Support for numpy 2.0
• Add type annotations
• Add API docs for public API functions

Version 1.0.5 - Jan 25. 2024

• Update the documentation
• Unbreak the read-the-docs builder
• Switch to pyproject.toml from setup.py (replace setuptools with hatchling)
• No new code or functionality added or removed, just housekeeping

Version 1.0.4 - Aug 28. 2020

• Add the raschii.cmd.plot and raschii.cmd.swd command line programs

Version 1.0.3 - Aug 28. 2020

• Fix missing time dependency in Stokes surface elevation
• Ensure all wave models implement T and omega attributes
• Test that the surface elevation has the correct period for all wave models
• Include SWD file format support for writing generated waves to files for interchange with other tools.

Version 1.0.2 - Jun 4. 2018

Some more work on air-phase / water phase velocity blending

• Change the air blending zone to be horizontal at the top (still follows the wave profile at the bottom). The air phase blending still has no influence on the wave profile or water-phase velocities, but the transition from blended to pure air-phase velocities is now a bit smoother for steep waves and the divergence of the resulting field is lower when projected into a FEM function space (analytically the divergence is always zero).

Version 1.0.1 - May 31. 2018

Small bugfix release

• Fix bug related to sign of x component of FentonAir C++ velocity
• Improve unit testing suite
• Improve FEM interpolation demo

Version 1.0.0 - May 29. 2018

The initial release of Raschii

• Support for Fenton stream functions (Rienecker and Fenton, 1981)
• Support for Stokes 1st - 5th order waves (Fenton, 1985)
• Support for Airy waves
• Support for C++ code generation (for FEniCS expressions etc)
• Command line program for plotting waves
• Command line demo for converting fields to FEniCS
• Unit tests for most things
• Documentation and (currently non-complete online demo)
• Support for computing a combined wave and air velocity field which is continuous across the free surface and divergence free (currently only works with the Fenton stream function wave model).

Copyright and license

Raschii is copyright Tormod Landet (2018--).

Raschii is licensed under the Apache 2.0 license, a permissive free software license compatible with version 3 of the GNU GPL. See the file LICENSE for the details.