An international group of outstanding scientists presents a balanced discussion of various controversies in current turbulence theory. Six topics from the present-day approach to turbulence are each introduced by a survey, followed by three commentaries and a panel discussion. This analysis evaluates future developments of theories presently used for understanding and modelling turbulent flows.

Opening remarks.- Achilles and the tortoise (and the Hare) discuss CFD and turbulent flow.- The utility and drawbacks of traditional approaches.- The utility and drawbacks of traditional approaches Comment 1.- The utility and drawbacks of traditional approaches Comment 2.- The utility and drawbacks of traditional approaches Comment 3.- Discussion of "utility and drawbacks of traditional approaches".- Future directions in turbulence research and the role of organized motion.- Whither coherent structures? Comment 1.- The role of coherent structures - Comment no. 2.- The role of coherent structures Comment 3.- Discussion of "The Role of Coherent Structures".- Can dynamical systems approach turbulence?.- Fixed points of turbulent dynamical systems and suppression of nonlinearity Comment 1.- Chaotic fluid dynamics and turbulent flow Comment 2.- The utility of dynamical systems approaches Comment 3.- Discussion on the utility of dynamical systems approach.- On Moffatt's paradox or can empirical projections approach turbulence?.- The potential and limitations of direct and large eddy simulations.- On large eddy simulation using subgrid turbulence models Comment 1.- The potential and limitations of direct and large-eddy simulations Comment 2.- The potential and limitations of direct and large-eddy simulations Comment 3.- Discussion of "the potential and limitations of direct and large Eddy simulations.- What can we hope for from cellular automata?.- Prospects for a lattice gas computer.- Cellular automata and massively parallel physics Comment 2.- A new strategy for hydrodynamics - lattice gases Comment 3.- Discussion of "What can we hope for from cellular automata".- Phenomenological modelling : Present .... and future?.- Phenomenological modeling: Presentand future Comment 1.- Turbulence modeling: Present and future Comment 2.- Simplex discussion regarding "modeling: Present and future" with emphasis upon high speeds Comment 3.- Discussion on "phenomenological modeling: Present and future".