This thesis presents the results from a series of numerical experiments, designed to study the fundamental wake vortex dynamics that cause the suppression of the Karman shedding and lead to a drag reduction of the flow past a bluff body with a wavy stagnation face. The simulations have been performed using the spectral/hp element method over a range of Reynolds numbers from 10 to 500 past wavy square and circular cross-section cylinders. Starting from fully developed shedding past a straight cylinder at a Reynolds number of 100, a sufficiently high waviness is impulsively introduced resulting in the stabilisation of the near wake to a time-independent state. It is shown that the spanwise waviness sets up a cross-flow within the growing boundary layer on the leading edge surface thereby generating streamwise and vertical components of vorticity. This redistribution of vorticity and the subsequent development of the three-dimensional shear layers lead to the breakdown of the unsteady and staggered Karman vortex wake into a steady and symmetric near wake structure. The steady nature of the near wake is associated with a reduction in total drag of about 16% compared with the straight, non-wavy cylinder. Further increases in the amplitude of the waviness lead to the emergence of hairpin vortices from the near wake region. This wake topology has similarities to the wake of a sphere at low Reynolds numbers. It is found that wavy circular cylinders need to be deformed more than wavy square-section cylinders in order to suppress the Kârmân vortex shedding. At higher Reynolds numbers, the drag reduction is substantially increased. For example, at Re = 200 and 500, the drag reduction is 20% and 34%, respectively. Two methods based on three-dimensional forms of surface bleed for suppressing the Kârmân shedding past straight, non-wavy cylinders are also investigated.