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Direct numerical simulations at Re = 200 have been conducted of the flow past rows of tandem cylinders. Local stability analysis shows that the wakes of two tandem cylinders are characterised by the formation of a region where the mean flow is locally absolutely unstable immediately behind the second cylinder, followed by a long region that is convectively unstable. The location where the flow changes from absolutely to convectively unstable provides a prediction of where the placement of a third body could trigger a global change, which is confirmed with simulations of the flow past three cylinders, and the flow past two cylinders followed by a short flat plate. A third body placed downstream of the absolute/convective instability transition location is effectively cloaked, its presence having virtually no impact on the flow both upstream and downstream. However, when a body is placed upstream of this location it triggers a global change in the flow, its presence being broadcast throughout the flow domain. However, a third cylinder placed well upstream of this location does not trigger the global change. Sensitivity analysis of the mean flow is conducted, and it is shown that the third cylinder does not simply act as a small perturbation that can excite sensitive regions, but when it is very close to the second cylinder it induces a mean flow correction that eliminates the sensitive regions which may explain why it does not trigger the global change.