Brian Launder is Professor of Mechanical Engineering at The University of Manchester. For the special issue of Philosophical Transactions A celebrating the 350th anniversary of the journal, he has written a commentary on one of the highlights from our archive, Osborne Reynolds’ 1895 paper ‘On the dynamical theory of incompressible viscous fluids and the determination of the criterion’. Here he tells us a bit more about this paper.

Water drop by Koshy Koshy/Flickr CC-BY 2.0.

Why was this a landmark paper?
The averaged form of the Navier-Stokes equations that Reynolds provided formed the basis for computing turbulent flows for the subsequent century. Indeed, it is still the most popular route for computing turbulent flows. There were at least three other ground-breaking features: (i) his obtaining a differential equation for the turbulent kinetic energy budget and identifying the physical processes that were represented therein; (ii) his initial use of mass-weighted averaging 50 years before the paper generally cited for this ‘innovation’; and (iii) the strategy Reynolds adopted for determining the stability limit of a flow, an approach discarded in the early 20th Century but then re-discovered in improved form in publications in the 1950s.


You mention that the paper initially received very little interest. Why was this, and how did it come to be accepted as such an important paper?

The paper, even following revision, was found difficult to follow. Moreover, although (as noted above) the equations that formed the basis for computing turbulent flow were presented, these equations themselves contained unknown terms (the Reynolds stresses) for which no path for their determination was provided. Only with the work of G.I. Taylor FRS shortly before World War I (and numerous other contributions over the subsequent eighty years) was that problem addressed.


Did you discover anything surprising when researching this paper?

When I first read the paper in the early 1990s I was astonished to find that Reynolds had contributed items (i) and (ii) noted above (contributions for which he is not widely credited in the literature). Only when I was preparing the present Phil Trans paper did a referee point out Reynolds’ contribution noted at (iii). Finally, the written exchanges between the editor and referees and Reynolds’ rebuttal (viewed from the Royal Society archive whilst preparing this commentary) provide a rich insight to all those individuals.

More information about the anniversary issue can be found here. All commentaries, archive papers and supplementary files can be accessed for free. Check back at this blog for more Q&As, videos and blog posts over the coming months.


Leave a Reply

  • (will not be published)