Brian E. Launder

This paper examines the evolution of closing the Reynolds-averaged Navier–Stokes equations by approximating the Reynolds stresses via the second-moment transport equations themselves. This strategy first proposed by Rotta is markedly in contrast to the more usual approach of computing an effective “turbulent viscosity” to deduce the turbulent stresses as in a Newtonian fluid in laminar motion. This paper covers the main elements in the development of this approach and shows examples of applications in complex shear flows that collectively include the effects of three-dimensional straining, force fields, and time dependence that affect the flow evolution in ways that cannot be readily mimicked with an eddy viscosity model.

The paper examines aspects of the career of Professor Sir Horace Lamb, FRS, a highly regarded classical fluid mechanicist, who, over a period of some thirty-five years at Manchester, made notable contributions in research, in education and in wise administration at both national and university levels. The article reveals the unusual sequence of events that led to his removing from Adelaide, South Australia, where he had served for nine years as the Elder Professor of Mathematics, to Manchester where he frequently interacted (sometimes rather coolly) with Manchester's other outstanding fluid mechanicist of the period, Osborne Reynolds.

Reynolds' paper sought to explain the change in character of flow through a pipe from laminar to turbulent that his earlier experiments had shown to occur when the dimensionless group that today bears his name exceeded approximately 2000. This he did by decomposing the velocity into mean and fluctuating components and noting how the average kinetic energy generation and dissipation rates changed with Reynolds number. The paper was only grudgingly accepted by two very distinguished referees and initially raised little external interest. As years went by, however, the averaged form of the equations of motion, known as the Reynolds equations (which were an intermediate stage in Reynolds' analysis) became the acknowledged starting point for computing turbulent flows. Moreover, some 50 years after his paper, a refinement of his strategy for predicting transition was also successfully taken up. For some engineering problems, the continual rapid growth of computing resources has meant that more detailed approaches for computing turbulent flow phenomena can nowadays be employed. However, this growth of computing power likewise makes possible a Reynolds-averaging strategy for complex flow systems in industry or the environment which formerly had to adopt less comprehensive analyses. Thus, Reynolds' approach may well remain in use throughout the present century. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society .