WKBJ analysis in the periodic wake of a cylinder

The nature of the three-dimensional transition arising in the flow past a cylinder is investigated by applying the Lifschitz–Hameiri theory along special Lagrangian trajectories existing in its wake. Results show that the von Kármán street is unstable with regard to short-wavelength perturbations. The asymptotic analysis predicts the possible existence of both synchronous (as modes A and B) and asynchronous (as mode C) instabilities, each associated to specific Lagrangian orbits. The proposed study provides useful qualitative information on the origin of the different modes but no quantitative agreement between the growth rates predicted by the asymptotic analysis and by a global stability analysis is observed. The reasons for such mismatch are briefly discussed and possible improvements to the present analysis are suggested.