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We conduct direct numerical simulations with 300 million degrees of freedom of turbulent flows past a stationary and a forced oscillating rigid cylinder at the Reynolds number Re=10,000. This one-order of magnitude increase in Reynolds number (compared to previous DNS) is accomplished by employing a multilevel-type parallel algorithm within the spectral element framework. Comparisons with the available experimental data show that the simulation has captured the flow quantities, mean, and rms statistics of the cylinder wake correctly. We also examine the effect of the randomness in the inflow on the vortex formation at a lower Reynolds number. We demonstrate that noisy inflows cause a vortex shedding-mode switching in the cylinder wake.