Diffusive Behavior of Transport Noise on S2

This directory contains the code used to generate the data for the research paper *Diffusive Behavior of Transport Noise on S2*.
The paper can be found here.

The aim of the paper is to study the diffusive properties of transport noise of the sphere.
This is accompanied by numerical tests carried out using the code presented here.
The code requires the `quflow` package (see its GitHub Page) for simulating 2D Euler dynamics on the sphere, using the Zeitlin discretization.

To run the simulations used in the study, use `run_RegularizedTransportNoise.py`.
This script is used for simulations for various fluid dynamics equations (Euler, Navier-Stokes, SALT-Euler, Double Bracket Euler) in the Zeitlin model.
It handles ensemble runs, stochastic forcing, and final result visualization.
Alternatively, there's `parallel_RegularizedTransportNoise.py`, which uses `multiprocessing` to speed things up, but the underlying maths is the same.

The remaining files are:

 - `auxiliary.py`: Contains auxiliary functions used in simulations and post-processing.
 - `BasicTransportNoise.py`: the 'vanilla' script for running 2D Euler with transport noise. 
Serves as an example of how to set up transport noise within quflow.
 - `SLP_plot.py`: provides a visualization example.
 - `visualization.py`: contains all visualization scripts.