Exploring unresolved inquiries regarding the meaning of Reynolds averaging and decomposition: A review Kowalski, Andrew S. Abril Gago, Jesús Density effects Eddy covariance Extensive variables In the late 19th century, Osborne Reynolds published two papers whose impact on atmospheric turbulence studies can hardly be overstated. The first, Reynolds (1883) established both his eponymous, dimensionless number and his reputation as the father of turbulence science, which is beyond doubt. However, his second famous paper (Reynolds, 1895) sowed seeds of confusion regarding the mathematical separation of average (mean) and fluctuating (turbulent) components of a fluid flow. Here, we revisit both the prehistory and aftereffects of Reynolds’s second famous article, which seems to have been published largely thanks to his already entrenched reputation. We show that successions of authors have misrepresented Reynolds’s innovations – now known as Reynolds averaging and decomposition (RAAD) –, putting his name to methodologies that he never intended. We attribute this, in part, to Reynolds’s predilection for long, inscrutable sentences, as well as his self-contradiction regarding the methodology for averaging the normal stress (or pressure). We examine two additional issues that are intimately related to using RAAD to define turbulent fluxes, namely its application to intensive versus extensive variables and the appearance of “Leonard terms” in the averaged equation of motion, neither of which is completely resolved. Throughout the manuscript, we identify a set of unanswered questions concerning RAAD and conclude that a complete mathematical description of turbulence is unlikely to emerge without addressing these issues, including the original inconsistency that was introduced by Osborne Reynolds himself. 2025-02-27T12:02:09Z 2025-02-27T12:02:09Z 2024-12-16 journal article Andrew S. Kowalski, Jesús Abril-Gago, Exploring unresolved inquiries regarding the meaning of Reynolds averaging and decomposition: A review, Agricultural and Forest Meteorology, Volume 362, 2025, 110364, ISSN 0168-1923, https://doi.org/10.1016/j.agrformet.2024.110364 https://hdl.handle.net/10481/102771 10.1016/j.agrformet.2024.110364 eng http://creativecommons.org/licenses/by/4.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Atribución 4.0 Internacional Elsevier