ISSN:
0271-2091
Keywords:
numerical simulation
;
spectral time discretization
;
Navier-Stokes equations
;
laminar flow
;
shear flow
;
unsteady flow
;
periodic flow
;
instability
;
Hopf bifurcation
;
non-linearity
;
non-linear theory
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
The onset of the Bénard-von Kármán instability consisting of the selective amplification of the linear unstable mode and yielding finally the well-known saturated state has been described many times on the basis of both numerical and experimental results in various configurations. However, neither the role of the harmonics and their coupling has been examined quantitatively, nor has the spatial structure of the instability been studied in detail. A recently developed numerical method of simulation of quasi-periodic flows makes it possible to integrate the investigation of linear and non-linear characteristics within a single numerical method. The simulation of the 2D afterbody wake presented in this paper allows us to follow the amplification of the instability 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 amplification rate during the linear regime. The amplification of harmonics results from an energy transfer from the mean flow to harmonics of increasingly higher order. Ultimately the energy losses compensate this transfer and an equilibrium, commonly called saturation of the instability, is reached. It is shown that the coupling between the fundamental harmonic 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 significant harmonics both in the linear regime and at saturation is obtained. The results show that time and space characteristics of the instability can be investigated simultaneously in an efficient way. Such an approach might be particularly important in 3D wakes where the geometry has a strong influence on the behaviour of unstable flows.
Additional Material:
27 Ill.
Type of Medium:
Electronic Resource
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