This international scientific workshop was organized in Lyon, France, from 10 to 12 May 2000. Its focus was ‘Two-point closures and their applications’, with the understanding that the analysis and design of such models requires expert knowledge coming from a wide range of areas in turbulence research, e.g. experiments, numerical simulations, asymptotic models, etc.

In the global challenge of turbulence modelling, two-point closures prove useful in many ways. Two-point correlations and spectra are useful measures of the distortion of the eddy structure of turbulence by stratification, large-scale strains, rotation, etc. In some cases, e.g. near boundaries, spectra can be drastically changed. In addition to the accurate characterization of turbulence, the explicit computation of two-point correlations or spectra shows how the internal dynamics of the various scales of motion are affected by such distortion, especially the cascade process on which the production/dissipation relationship depends. Distortion can be the cause of large departures from isotropic homogeneous turbulence, pulling turbulent flows far away from the local equilibrium that is often assumed. A rather weak departure can allow the use of linearized theories such as rapid distortion theory, for the applicability of which rational bounds may be estimated by comparisons with weakly nonlinear calculations. A different approach is necessary when dealing with larger departures, for instance due to growth of instabilities. In that case new physical or similarity arguments have to be employed to obtain a satisfactory description of the modification to the cascade process, which can even undergo reversal in the limit when three-dimensional turbulence becomes two-dimensional. Of course, significant changes in spectra have direct implications for one-point measures of turbulence – which can be explicitly derived by integration of two-point correlations – used in most industrial closure schemes. Such one-point models consequently need to be adapted when turbulence is strongly affected by distortion.