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The Nature of High Reynolds Number Turbulence

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26th August 2008 to 19th December 2008
Peter Bartello McGill University
Peter Davidson University of Cambridge
David Dritschel University of St Andrews
Yukio Kaneda Nagoya University
Rich Kerswell University of Bristol


Programme Theme

Turbulence is a notoriously difficult subject. Our attempts to understand it tend to consist of an uneasy mix of plausible but uncertain hypotheses, deterministic but highly simplified cartoons, and vast, complex data sets.

For the small scales in turbulence this mixture of hypothesis, theory and experiment is given some unity by the phenomenological picture established by Richardson, Taylor and Kolmogorov. This phenomenology paints a picture of cascades of energy and information from large-scale eddies down to small, and of universal features of these cascades, provided the Reynolds numbers is large enough. In some sense this vision has worked well, providing a convenient conceptual framework within which many empirical observations can be rationalised. However, it was clear from the outset that this was too simplistic a point of view and half a century later there remain many fundamental unanswered questions. For example, exactly what do we mean by an eddy or a cascade, and how should we interpret cascade-like arguments in terms of the evolving morphology of the vorticity field? Indeed, what is the spatial structure of the vorticity field and how does this relate to the observed energy spectra?

Our understanding of turbulent boundary-layers, and of turbulence in rotating-stratified fluids, is equally uncertain. For example, the log-law of the wall represents an early milestone in turbulence theory. It is based on the hypothesis that the near-wall eddies are immune from the remote eddies in the core flow. However, we have always known that the near-wall eddies cannot be independent of the larger far-field vortices, so why does the log-law work so well? There are many other controversies in shear flows. For example, it has been known for over thirty years that turbulence near a wall is dominated by streaks of low-speed fluid and by long, stream-wise vortices. It is now generally agreed that these streaks and vortices interact in some kind of quasi-periodic cycle, yet the nature of this cycle, and its possible relationship to the structures seen in transition studies, is still a matter of debate. The situation is little better in rotating-stratified turbulence, where there is a subtle interaction between waves and turbulence. While all agree that, in such flows, the large vortices acquire a distinctive shape, reminiscent of cigars or pancakes, few can agree on the mechanisms by which these structures form. Evidently, there is much to debate.

The goal of this programme is to bring together leading experts from across the world to debate these fundamental questions. The discussion will be wide ranging, from the initiation of turbulence through to its asymptotic state at high Reynolds number, including the effects of rotation and stratification, and the addition of different phases, such as bubbles, particles and polymers.

Final Scientific Report: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons