A MODEL OF WAVE DYNAMICS IN THE FAR WAKE OF A CYLINDER

Interesting interactions in the far wake behind cylinder, leading in p articular to the appearance of a strong secondary oblique wave, have r ecently been discovered experimentally by Williamson and Prasad [J. Fl uid Mech. 256, 269, 315 (1993)]. They are induced from a very small am ount of noise, added to the decaying primary wave. The problem is inve stigated theoretically with simple amplitude equations, based on tempo ral instability of the small amplitude waves. The symmetry of the wake flow requires that quadratic interactions arise only among triads of wave numbers involving one varicose and two sinuous waves, or three va ricose waves. As the primary wave, corresponding to vortex shedding, i s sinuous, the interacting secondary waves must be of opposite paritie s. In this case, it is found that the sinuous wave will always prevail downstream. The preferential appearance of the secondary oblique wave in the far wake can be reproduced by letting an initially very small varicose parallel wave interact with the primary wave. The secondary o blique wave results from a classical three-wave, quadratic nonlinear i nteraction between the waves. In addition, our model reproduces the ob servation that upon increasing the noise amplitude the oblique wave ap pears sooner (further upstream) in the wake. The occurrence of paralle l waves very far downstream which depends on the frequency relationshi p between the waves, can be understood by considering the interactions between parallel and oblique secondary waves of both parities. We pro pose a reasonable scenario explaining the experimental observations of Williamson and Prasad. (C) 1997 American Institute of Physics.