Geoscience Reference
In-Depth Information
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Introduction
1.1 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 “mathe-
matical 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 topic we focus on the physical understanding of turbulence, sur-
veying 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. You might be concerned by our use of little mathematical “tricks” -
not because they're complicated or difficult, but because you've never seen them
before and might not have thought of them yourself. Don't worry: we pass them
on because they are some of the useful tools developed over the many years that
scholars have pondered turbulence. You can pass them on too.
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