Developments in turbulence research: a review based on the 1999 Programme of the Isaac Newton Institute , Cambridge

Recent research is making progress in framing more precisely the basic dyna mical and statistical questions about turbulence and in answering them. It is helping both to define the likely limits to current methods for modellin g industrial and environmental turbulent flows, and to suggest new approach es to overcome these limitations. Our selective review is based on the them es and new results that emerged from more than 300 presentations during the Programme held in 1999 at the Isaac Newton Institute, Cambridge, UK, and o n research reported elsewhere. A general conclusion is that, although turbu lence is not a universal state of nature, there are certain statistical mea sures and kinematic features of the small-scale flow field that occur in mo st turbulent flows, while the large-scale eddy motions have qualitative sim ilarities within particular types of turbulence defined by the mean flow, i nitial or boundary conditions, and in some cases, the range of Reynolds num bers involved. The forced transition to turbulence of laminar flows caused by strong external disturbances was shown to be highly dependent on their a mplitude, location, and the type of flow. Global and elliptical instabiliti es explain much of the three-dimensional and sudden nature of the transitio n phenomena. A review of experimental results shows how the structure of tu rbulence, especially in shear flows, continues to change as the Reynolds nu mber of the turbulence increases well above about 10(4) in ways that curren t numerical simulations cannot reproduce. Studies of the dynamics of small eddy structures and their mutual interactions indicate that there is a set of characteristic mechanisms in which vortices develop (vortex stretching, roll-up of instability sheets, formation of vortex tubes) and another set i n which they break up (through instabilities and self-destructive interacti ons). Numerical simulations and theoretical arguments suggest that these of ten occur sequentially in randomly occurring cycles. The factors that deter mine the overall spectrum of turbulence were reviewed. For a narrow distrib ution of eddy scales, the form of the spectrum can be defined by characteri stic forms of individual eddies. However, if the distribution covers a wide range of scales (as in elongated eddies in the 'wall' layer of turbulent b oundary layers), they collectively determine the spectra (as assumed in cla ssical theory). Mathematical analyses of the Navier-Stokes and Euler equati ons applied to eddy structures lead to certain Limits being defined regardi ng the tendencies of the vorticity field to become infinitely large locally Approximate solutions for eigen modes and Fourier components reveal striki ng features of the temporal, near-wall structure such as bursting, and of t he very elongated, spatial spectra of sheared inhomogeneous turbulence; but other kinds of eddy concepts are needed in less structured parts of the tu rbulence. Renormalized perturbation methods can now calculate consistently, and in good agreement with experiment, the evolution of second- and third- order spectra of homogeneous and isotropic turbulence. The fact that these calculations do not explicitly include high-order moments and extreme event s, suggests that they may play a minor role in the basic dynamics. New methods of approximate numerical simulations of the larger scales of tu rbulence or 'very large eddy simulation' (VLES) based on using statistical models for the smaller scales (as is common in meteorological modelling) en able some turbulent flows with a non-local and non-equilibrium structure, s uch as impinging or convective flows, to be calculated more efficiently tha n by using large eddy simulation (LES), and more accurately than by using ' engineering' models for statistics at a single point. Generally it is shown that where the turbulence in a fluid volume is changing rapidly and is ver y inhomogeneous there are flows where even the most complex 'engineering' R eynolds stress transport models are only satisfactory with some special ada ptation, this may entail the use of transport equations for the third momen ts or non-universal modelling methods designed explicitly for particular ty pes of flow. LES methods may also need flow-specific corrections for accura te modelling of different types of very high Reynolds number turbulent flow including those near rigid surfaces. This paper is dedicated to the memory of George Batchelor who was the inspi ration of so much research in turbulence and who died on 30th March 2000. T hese results were presented at the last fluid mechanics seminar in DAMTP Ca mbridge that he attended in November 1999.