Strange attractor characteristics of the chaotic flow induced by an oscillating pressure gradient over a rippled bed

The oscillatory flow over a wavy wall is computed by means of the numerical algorithm described in Blondeaux & Vittori (1991), and the attractor of the system is studied for different values of the parameters. In particular, the correlation dimension and the largest Lyapunov exponent are determined. It is found that for a fixed geometrical configuration and by increasing the Reynolds number, the flow experiences a sequence of period doublings and then becomes chaotic. Similarly, a chaotic behaviour is reached for fixed characteristics of the oscillatory flow by increasing the steepness of the waviness. Within the range of the parameters presently studied, the chaotic status is characterized by a low dimension. This fact suggests that in principle the flow time development could be described by means of a small number of first order ordinary differential equations.