The onset of turbulent flow at moderate Reynolds numbers are predicted by a direct 2-D numerical simulation and by an unsteady turbulence model, respectively. The global dynamic characteristics of the flow (mean drag, Strouhal number, oscillating lift coefficient) are accurately predicted, in agreement with the physical experiment. An original type of large-eddy simulation is developed for the unsteady turbulence modelling of flows with coherent structures and modified closure assumptions for the calculation of the unsteady eddy-viscosity are suggested. The results show a good agreement with physical experiments (Re=40,000) for the wake flow past a rectangular body. Especially, under the present unsteady turbulence modelling, it is shown that the dynamic characteristics of the organised, alternating eddies are predicted satisfactorily.
The problem of predicting turbulent wake flows with unsteady coherent structures is a high priority research topic in the state of the art of turbulence modelling, because of its importance in Off-shore Mechanics (off-shore structures). Especially, the prediction of the unsteady quasi-periodic efforts on the above solid structures, as well as the frequencies of inherent vibrations appearing at high Reynolds numbers, are not predicted. In fact, the majority of turbulence modelling studies concern the steady flow past bodi"es at high Reynolds numbers, and there are not yet, to our knowledge, successful methods for prediction of an unsteady wake flow with coherent structures. The difficulty comes from the fact that the assumptions on which the classic turbulence models have been developed, concern fully developed turbulent flows, being in spectral equilibrium in the sense of Kolmogorov. However, the development of the alternating eddies in the wake and of other classes of organised eddies (Braza, Chassaing & Ha Minh [1990]) provide a spectrum with predominant frequencies among continuous frequency windows, which is a situation of spectral non-equilibrium.
