Turbulence, its community, and our approach

Even if you have not studied turbulence, you already know a lot about it. You have seen the chaotic, ever-changing, three-dimensional nature of chimney plumes and flowing streams. You know that turbulence is a good mixer. You might have come across an article that described the intrigue it holds for mathematicians and physicists.

Unless a fluid flow has a low Reynolds number or very stable stratification (less dense fluid over more dense fluid), it is turbulent. Most flows in engineering, in the lower atmosphere, and in the upper ocean are turbulent. Because of its “mathematical intractability” – turbulence does not yield exact mathematical solutions – its study has always involved observations. But over the past three decades numerical approaches have proliferated; today they are a dominant means of studying turbulent flows.

Turbulence has long been studied in both engineering and geophysics. G. I. Taylor's contributions spanned both (Batchelor, 1996). The Lumley and Panofsky (1964) work was my introduction to that breadth, but as Lumley later commented, their parts of that text “just…touch.” Today the turbulence field seems more coherent than it was in 1964, although it still has subcommunities and dialects (Lumley and Yaglom, 2001).

In Part I of this book we focus on the physical understanding of turbulence, surveying its key properties. We'll use its governing equations to guide our discussions and inferences. We shall also discuss the main types of numerical approaches to turbulence.