SPATIAL STRUCTURE OF THE VONKARMAN,BENARD INSTABILITY

A complete description of both the temporal and spatial characteristic s is essential for the understanding of the mechanisms generating and sustaining the instability in the infinite cylinder wake. Experimental methods have been able to provide accurate measures of the temporal c haracteristics but present serious limitations for the study of the sp atial structure of the instability. Numerical simulations give access to a full space-time picture of the instability, however the amount of numerical data makes it impossible to use them in their raw form even in 2D. After relaxation of transients the instability reaches a limit cycle described in a natural way by a set of Fourier harmonics. In th is paper we present the results obtained by an on-line processing of a direct simulation of an infinite cylinder wake at saturation for Re = 48 and Re = 100. As few as 5 harmonics are found to account For the c omplete space-time behavior of the instability within a 2% accuracy fo r the whole range of Reynolds number between the threshold (45.9) and 100. The spatial structure of individual harmonics up to 5 is analyzed . The characteristics of the envelopes of the harmonics and of the pha ses (wave length, phase velocity) are visualized and studied over the whole flow field. Special care is taken to separate the unperturbed fl ow (the unstable steady and symmetric solution of the Navier-Stokes eq uations obtained for the same supercritical Reynolds number) from the mean flow to study its non linear modification due to the instability. The theoretical question of symmetry breaking is raised on the basis of the spatial symmetry properties of the Fourier harmonics of the ins tability.