Chaotic transport in two‐ and three‐dimensional flow past a cylinder

The response of transport measures (Nusselt number, drag and lift force) for two‐ and three‐dimensional flow past a heated cylinder reaching a chaotic state is investigated numerically using a spectral element discretization at a Reynolds number Re=500. The undisturbed two‐dimensional flow remains periodic at this Reynolds number, unless a suitable forcing is applied on the naturally produced system. Three‐dimensional simulations establish that three‐dimensionality sets in at Re≊200. Successive supercritical states are established through a series of period‐doublings, before a chaotic state is reached at a Re≊500. For the two‐dimensional forced flow, all transport measures oscillate aperiodically in time and undergo a ‘‘crisis,’’ i.e., a sudden and dramatic increase in their amplitude. The corresponding three‐dimensional, naturally produced chaotic state corresponds to a less drastic change of the transport quantities with both rms and mean values lower than their two‐dimensional counterparts.