1. ABOUT THE DATASET -------------------- Title: Dataset accompanying "Data-driven derivation of the properties of turbulent convection" Creator(s): Chris Wareing[1], Alasdair Roy[1], Matthew Golden[2], Roman Grigoriev[2], Steven Tobias[1] Organisation(s): [1] Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK [2] School of Physics, Georgia Institute of Technology, North Avenue, Atlanta, GA 30332, USA Rights-holder(s): Copyright 2024 University of Leeds Publication Year: 2024 Paper abstract: We present the DNS of turbulent convective flows coupled with machine learning techniques in order to recover governing equations, constraints and boundary conditions from the simulated data. We use the Dedalus framework for spectrally solving differential equations to generate an extended time-series of twoand three-dimensional DNS data modelling Rayleigh-B´enard convection and convective plane Couette flow. To this data, we apply the data-driven Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and the Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) method. Using SINDy, necessarily starting from the state variables and hence a wide range of library terms in order to include appropriate products and derivatives, we are able to recover the governing equations at Rayleigh numbers from laminar, through transitional to turbulent flow conditions, albeit with increasing difficulty with larger Reynolds number, especially in recovery of the diffusive terms (with coefficient magnitude proportional to p 1/R). Using SPIDER and starting from a much smaller library of terms defined by physical possibilities, we are able to more easily recover the governing equations for all R and go on to recover constraints (the continuity equation) and boundary conditions, demonstrating the benefits and capabilities of SPIDER to go beyond SINDy for these fluid problems governed by second-order PDEs. Data Description: This repository presents the means to reproduce all the data and analyses in this paper. Specifically, that includes Dedalus v3.0 scripts, SINDy scripts (and the SINDy implementation used) and SPIDER scripts (and the SPIDER library used) Cite as: Wareing, Roy, Golden, Grigoriev and Tobias (2024) Dataset for "Data-driven derivation of the properties of turbulent convection", https://doi.org/10.5518/1577 Related publication: To be confirmed. Contact: Dr Chris Wareing, University of Leeds, C.J.Wareing@leeds.ac.uk Prof Steve Tobias, University of Leeds, S.M.Tobias@leeds.ac.uk 2. TERMS OF USE --------------- Unless otherwise stated, this dataset is licensed under a Creative Commons Attribution 4.0 International Licence: https://creativecommons.org/licenses/by/4.0/ 3. PROJECT AND FUNDING INFORMATION ---------------------------------- This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. D5S-DLV-786780). 4. CONTENTS ----------- README_Wareingetal2024.tst - this file Figure1-README.txt - details of how to recreate Figure 1 Figure2-README.txt - details of how to recreate Figure 2 Figure3-README.txt - details of how to recreate Figure 3 Figure4-README.txt - details of how to recreate Figure 4 Figure5-README.txt - details of how to recreate Figure 5 Figure6-README.txt - details of how to recreate Figure 6 Figure7-README.txt - details of how to recreate Figure 7 DedalusScripts.zip - The Dedalus v3.0 scripts used in this work SINDyScripts.zip - The SINDy scripts and library used in this work SPIDERScripts.zip - The SPIDER scripts and library files used in this work. 5. METHODS ---------- For the exact details of the Dedalus, SINDy and SPIDER methods used, please read the paper that this dataset accompanies. The details are too long to repeat here.