Homogeneous Turbulence Dynamics (2nd edition) [Book Review]

Abstract

In his 1932 address to the British Society for the Advancement of Science the famed mathematician Sir Horace Lamb was said to have made the following seemingly prescient statement: 'I am an old man now, and when I die and go to heaven, there are two matters on which I hope for enlightenment. One is quantum electrodynamics and the other is the turbulent motion of fluids. About the former, I am really rather optimistic'. Turbulent flow is a ubiquitous aspect of nature and its understanding has important implications for a wide variety of applications including weather prediction, industrial flows and aeronautics. Increasingly detailed and precise experiments combined with highly resolved numerical simulations have led to some insights, but despite over 100 years of research a full understanding of the detailed mechanics of turbulence and its implications for quantities of applied interest such as drag, lift and mixture fraction remains incomplete. For example, as understood by G. I. Taylor, an important goal is to predict the statistics of a turbulent flow. Even under simplifying assumptions that the statistics are homogeneous (i.e. invariant under translation) and isotropic, we still do not have satisfactory theories for the formation and maintenance under large scale forcing of the so-called inertial range Kolmogorov energy spectrum. We have a lot of what Philip Saffman termed 'postdictions' but very few real predictions. Homogeneous isotropic turbulence is an idealization and in real flows one must contend also with sources of anisotropy such as rotation, stratification or shear, as well as inhomogeneity arising from geometry as occurs for example in boundary layers. Nevertheless, there has been important progress in all areas.

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