Dynamics and low-dimensionality of a turbulent near wake

We investigate the dynamics of the near wake in turbulent flow past a circular cylinder up to ten cylinder diameters downstream. The very near wake (up to three diameters) is dominated by the shear layer dynamics and is very sensitive to disturbances and cylinder aspect ratio. We perform systematic spectral direct (DNS) and large-eddy simulations (LES) at Reynolds number (Re) between 500 and 5000 with resolution ranging from 200 000 to 100 000 000 degrees of freedom. In this paper, we analyse in detail results at Re = 3900 and compare them to several sets of experiments. Two converged states emerge that correspond to a U-shape and a V-shape mean velocity profile at about one diameter behind the cylinder. This finding is consistent with the experimental data and other published LES. Farther downstream, the flow is dominated by the vortex shedding dynamics and is not as sensitive to the aforementioned factors. We also examine the development of a turbulent state and the inertial subrange of the corresponding energy spectrum in the near wake. We find that an inertial range exists that spans more than half a decade of wavenumber, in agreement with the experimental results. In contrast, very low-resolution spectral simulation as well as other dissipative LES do not describe accurately the inertial range although they predict low-order statistics relatively accurately. This finding is analysed in the context of coherent structures using a phase averaging technique and a procedure to extract the most energetic (on the average) eigenmodes of the flow. The results suggest that a dynamical model would require of the order of twenty modes to describe the vortex shedding dynamics with reasonable accuracy.