The transition process which leads the oscillatory flow over a wavy wall from a periodic behavior to chaos is studied by means of the numerical algorithm described by Blondeaux and Vittori [J. Fluid Mech. 226, 257 (1991)]. By increasing the Reynolds number, it has been found that the flow experiences an infinite sequence of period doublings (pitchfork bifurcations) which take place at successive critical values. These critical values of the Reynolds number accumulate to a finite limit with the Feigenbaum rate of convergence. For Reynolds numbers larger than the above limit a chaotic flow is detected.

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