ABSTRACT
Figure 10 Vorticity field at t = 317.30T/2lr, liw = 0.5U0/R,- clockwise vorticity, ........... counter clockwise vorticity: 5/R = 0.2, Kc = 4.0
from a predictable time development to chaos has been investigated. The "quasi-periodicity phase locking" scenario has been found. The presence of clearly recognizable vortex structures in the chaotic regime (see figure 10) seems to suggest that, at least in the range of the parameters presently investigated, only few degrees of freedom are excited and a small number of first order differential equations should be sufficient to capture the qualitative and quantitative features of the oscillatory flow around a circular cylinder. This idea is supported by a comparison between present findings and those of Blondeaux, Corana & Vittori (6). The above authors studied the attractor characteristics of the chaotic flow produced by an oscillating pressure gradient near a wavy wall and found that the correlation dimension of the flow attractor is smaller than 10 when the ratio of the viscous length 5 and the wavelength 1 of the waviness is 0.03 and U0T /211'1 is smaller than 1.5, which are values of the parameters similar to those presently investigated. However, even though similarities exist between the present flow and that studied in Blondeaux, Corana & Vittori (6), as both papers deal with oscillatory flows, it should be pointed out that the geometry of the fluid domain has a large influence on the route to chaos. Indeed, Blondeaux & Vittori (7), [8) found that the chaotic behaviour in the oscillatory flow over a wavy wall is reached through a sequence of pitchfork bifurcations, i.e. following the Feingebaum scenario. Differences should thus be expected also in attractor characteristics, which will be determined in a forthcoming paper.
