Three-dimensional instabilities in oscillatory flow past elliptic cylinders

We investigate the early development of instabilities in the oscillatory viscous flow past cylinders with elliptic cross-sections using three-dimensional direct numerical simulations. fhis is a classical hydrodynamic problem for circular cylinders, but other configurations have received only marginal attention. Computed results for some different aspect ratios A from 1 :1 to 1 : 3, all with the major axis of the ellipse aligned in the main flow direction, show good qualitative agreement with Hall's stability theory (J, Fluid Mech., vol. 146,1984, pp, 347-367), which predicts a cusp-shaped curve for the onset of the primary instability. The three-dimensional flow structures for aspect ratios larger than 2 :3 resemble those of a circular cylinder, whereas the elliptical cross-section with the lowest aspect ratio of 1 : 3 exhibits oblate rather than tubular three-dimensional flow structures as well as a pair of counter-rotating spanwise vortices which emerges near the tips of the ellipse. Contrary to a circular cylinder, instabilities for an elliptic cylinder with sufficiently high eccentricity emerge from four rather than two different locations in accordance with the Hall theory.