ON CHAOS IN WAKES

We distinguish between "separable" flows around bodies, which can approximately be described by finite-dimensional autonomous systems (ASs) of ordinary differential equations and "non-separable" wakes which do not have this property. For the separable wakes, a systematic method for the construction of the AS from the Navier-Stokes equations is presented and applied to the two-dimensional flow around a circular cylinder. With the concept of separability, the possibility of bifurcations and chaotic behaviour for the wake of a body in uniform flow is discussed. It is shown that the Hopf and pitchfork bifurcations are the generic instabilities of the steady flow around a body of finite size and of the two-dimensional flow around an arbitrarily shaped cylinder. With increasing Reynolds number the corresponding periodic flows are likely to become unstable by an intermittency scenario, a period-doubling cascade, or a Hopf bifurcation. In addition, typical three-dimensional perturbations of the two-dimensional steady and periodic cylinder wake are considered. Theoretical arguments indicate that the dynamics of turbulent wakes are very unlikely to be characterized by a low-dimensional, strange attractor.