Raschii is a Python library for constructing non-linear regular waves and is named after Thysanoessa raschii, the Arctic Krill.

Supported wave models are currently:

  • 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, standard linar waves cosine waves

Raschii includes a command line program to plot regular waves from the suported 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. There is also a limited Dart port which is used in the online demo.

A comparison of Stokes and Fenton waves of fifth order

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

Installation and running

Raschii can be installed by running:

python3 -m pip install raschii

This will also install dependencies like numpy.

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

This will output:

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


Raschii is developed in Python on Bitbucket by use of the Git version control system. If you are reading this on github, please be aware that you are seeing a mirror that could potentially be months out of date. All pull requests and issues should go to the Bitbucket repository.

Raschii is automatically tested on CircleCI and the current CI build status is circleci_status.


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 blanding still has no influenece 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).