Organised Eddies in Turbulent Shear Flows

Abstract

The subject of the conference might provoke a bystander to wonder why so much brain power and material resources are being applied to extracting recurrent patterns from chaotic turbulent flows and what we hope to do with the information if and when we have it. If we regard the scientific study of turbulent flow as beginning with the work of Osborne Reynolds and his mean value equations for mean velocity and mean turbulent kinetic energy, most work over the first fifty years took place in the absence of information about the mechanisms of turbulent transport of momentum and heat. Nevertheless, the early workers made important and enduring advances in basic understanding, in particular, by recognising that, although the transfer of mechanical energy to heat must be by working against viscous stresses, the magnitude of the transfer is nearly independent of the magnitude of the fluid viscosity. It was concluded that the transfer from motions on scales comparable with flow widths to the motions of very small scale that dissipate the energy depends on successive, quasi-independent transfers between “eddies” of increasingly smaller sizes. Today, that is expressed in the Kolmogorov theory of local isotropy which leads to the well-established k ^−5/3 spectrum. Another was the deduction of the logarithmic distribution of velocity close to a solid boundary. These achievements depended mostly on consideration of equilibrium flows in which it was plausible to suppose that the motion was determined by simple boundary conditions and the use of dimensional analysis.