Control of wake structure may lead to a reduction in the unsteady forces and vibrations in the marine structures. In this paper, the finite-volume method (FVM) is used to simulate the flow around two-dimensional obstacles with different cross-sections. Maxwell equations are used to provide the coupling between the flow field and the magnetic field. The range of Stuart (Su) and Reynolds (Re) numbers are 0–10 and 1–200, respectively. The effects of the magnetic field on the control of the wake structure and vortex shedding behind the obstacles are investigated in details. Moreover, an analogy has been performed between different configurations. Finally, several empirical equations for steadiness and disappearance Stuart numbers are presented for each obstacle. It was found that the diamond and circular configurations have the largest and smallest effects on steadiness and disappearance Stuart numbers among all the configurations. Additionally, it was observed that the drag coefficient slowly reduces by exerting the magnetic field at low Stuart numbers.

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