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.