Overview

py2Periodic provides a framework for solving PDEs with a pseudospectral method on doubly-periodic domains. In short, the framework defines a base-class, sub-class relationship between the numerical and physical aspects of the problems it solves, respectively. The intention is to provide the user with the ability to rapidly implement and customize new physical models. Moreover, because all the physical models implemented with py2Periodic, code that sets up, runs, and analyzes different physical problems can be reused or easily adapated.

Installation

At the moment the only way to use py2Periodic is to clone the git repository and use the examples as is. The project is not a proper package, but hopefully will become one in the future. The current requirements of py2Periodic are:

• numpy
• matplotlib
• pyFFTW
• h5py

Documentation

Documentation is currently sparse. Incomplete pdfs that describe some of the physical problems currently implemented can be found in /docs/.

The base class: doublyPeriodic.py

The base class code is contained in doublyPeriodic.py in the main directory /py2Periodic/. The base-class definition defines the physical and numerical grids, the Fourier transform, various helper functions for introducing scalar diagnostics to be calculated, routines that run the model, create plots, and save model output.

Time-steppers for the model, which are implemented as attributes instantiated and assigned to the model class at model instantiation, are defined in timeSteppers.py in /py2Periodic/.

Physical problem sub-classes

Physical problems are classes that inherit their numerics from the base class doublyPeriodic.model. The code for each physical problem is contained in /py2Periodic/physics/. The physical problems currently implemented are

• Two-dimensional turbulence (twoDimTurbulence.py)
• Linearized, hydrostatic, single-mode Boussinesq equations in xy (linearizedBoussinesq_xy.py)
• Two-layer quasi-geostrophic flow with optional bathymetry (twoLayerQG.py)
• Two-layer quasi-geostrophic flow with tracers in each layer and optional bathymetry with (twoLayerTracers.py)
• The 'YBJ' model for a single near-inertial wave mode in two-dimensional turbulence (nearInertialWaves_xy.py)
• The single-mode hydrostatic wave equation modeling hydrostatic internal waves in two-dimensional turbulence (hydrostaticWaveEqn_xy.py)

Tests and examples

Tests exist for all of the models. In addition, there is a single, somewhat underdeveloped example in /examples/waveIsotropization that first generates and saves a two-dimensional turbulent vorticity field, and then introduces a wave field into the vorticity field in both the hydrostatic wave equation model and the linearized Boussinesq model. The wave field subsequently is scrambled and isotropized and, crucially, the two models generally agree.