NUMERICAL-SIMULATION OF THE MECHANISMS GOVERNING THE ONSET OF THE BENARD-VON-KARMAN INSTABILITY

The onset of the Benard-von Karman instability consisting of the selec tive amplification of the linear unstable mode and yielding finally th e well-known saturated state has been described many times on the basi s of both numerical and experimental results in various configurations . However, neither the role of the harmonics and their coupling has be en examined quantitatively, nor has the spatial structure of the insta bility been studied in detail. A recently developed numerical method o f simulation of quasi-periodic flows makes it possible to integrate th e investigation of linear and non-linear characteristics within a sing le numerical method, The simulation of the 2D afterbody wake presented in this paper allows us to follow the amplification of the instabilit y over many orders of magnitude. It is shown that at all stages of its development the instability is characterized by a series of harmonics , each of them amplified with a multiple of the fundamental amplificat ion rate during the linear regime. The amplification of harmonics resu lts from an energy transfer from the mean flow to harmonics of increas ingly higher order. Ultimately the energy losses compensate this trans fer and an equilibrium, commonly called saturation of the instability, is reached. It is shown that the coupling between the fundamental har monic and the mean flow is mainly responsible for the saturation. The convergence rate of the development of the instability into harmonics is investigated. A full description of the spatial structure of all si gnificant harmonics both in the linear regime and at saturation is obt ained. The results show that time and space characteristics of the ins tability can be investigated simultaneously in an efficient way. Such an approach might be particularly important in 3D wakes where the geom etry has a strong influence on the behaviour of unstable flows.