READ ME File For 'Dataset in support of the Southampton doctoral thesis "Resolvent-based models for nonlinear solutions of wall-bounded flows and statistical estimation of chaotic systems"'

Dataset DOI: https://doi.org/10.5258/SOTON/D3555

ReadMe Author: Thomas P. Burton, University of Southampton, https://orcid.org/0000-0001-7998-2278

This dataset supports the thesis entitled: Resolvent-Based Models for Nonlinear Solutions of Wall-Bounded Flows and Statistical Estimation of Chaotic Systems
AWARDED BY: Univeristy of Southampton
DATE OF AWARD: 2025

DESCRIPTION OF THE DATA
There are three main components to this dataset:
  1. DNS flow data for Rotating-Plane Couette Flow (RPCF) stored in binary files that can be directly read (see: https://github.com/The-ReSolver/rpcf for details on how the data is stored);
  2. Chaotic simulation and optimisation data for the Lorenz system, stored in a HDF5 file format;
  3. Optimisation data for equilibrium and periodic solutions for RPCF displayed in the thesis, stored in a JLD2 file format (see: https://github.com/JuliaIO/JLD2.jl)

DNS Data:
 Snapshots are provided for RPCF at various Reynolds numbers (25, 50, 400, 450, 1000, 5000) that feature priminantly in the results presented in the thesis. Each Reynolds number has their
 own directory, containing snapshots used to generated the results presented in the thesis. Each snapshot is stored as a directory containing files for the velocity, vorticity, and streamfunction
 fields of the flow at the given time snapshot, as well as a metadata file that contains the snapshot time, kinetic energy, and rate of change of the kinetic energy. Each file containing the
 field data are stored as binary files that can be directly read as standard double precision floats. The processes used to read and write the fields are available in the source code used to
 simulate the flow, available freely at: https://github.com/The-ReSolver/rpcf/.

Lorenz Data:
 The data provided for the Lorenz system are focused on two main parts: chaotic data, and optimisation data. The chaotic data is the result of state evolution of a long simulation of the ODE
 system using SciPy along with the times of the snapshots. Also provided are computed histograms and power spectra computed for plots displayed in chapter 5 of the thesis. The optimisation data
 contains generated UPO, quasi-trajectory optimisations, and the convergence of observables over quasi-trajectories at various periods. All data is stored in a HDF5 file format and can be unpacked
 using any package that is compliant to the HDF5 standard. The data was generated using the code available at https://github.com/tb6g16/pyReSolver, and the h5py package was used for the data
 storage.

RPCF Optimisation:
 The equilibrium solutions obtained from the optimisations discussed in the thesis. Also provided is the full optimisation data for the periodic solution at Re=450. The data is all provided in
 the JLD2 file format (available at https://github.com/JuliaIO/JLD2.jl). This file format is quite similar to the HDF5 file format, and requires a version of Julia (1.0 or later) to read. The code
 used to generate the solutions shown is available in the GitHub organisation https://github.com/The-ReSolver, primarily the Fields.jl, OptimWrapper.jl, and ResolventAnalysis.jl packages.

Date of data collection: 2022-2025

Licence:
CC By

Related publication:
Resolvent-based optimization for approximating the statistics of a chaotic Lorenz system, 2025


Date that the file was created: June, 2025