The intermaterial area density generated by time- and spatially periodic 2D chaotic flows

This paper explores in some detail the spatial structure and the statistica l properties of partially mixed structures evolving under the effects of a time-periodic chaotic flow. Numerical simulations are used to examine the e volution of the interface between two fluids, which grows exponentially wit h a rate equal to the topological entropy of the flow. Such growth is much faster than predicted by the Lyapunov exponent of the flow. As time increas es, the partially mixed system develops into a self-similar structure. Freq uency distributions of interface density corresponding to different times c ollapse onto an invariant curve by a simple homogeneous scaling. This scali ng behavior is a direct consequence of the generic asymptotic directionalit y property characteristic of 2D time-periodic flows. Striation thickness di stributions (STDs) also acquire a time-invariant shape after a few (similar to 5-10) periods of the flow and are collapsed onto a single curve by stan dardization. It is also shown that STDs can be accurately predicted from di stributions of stretching values, thus providing an effective method for ca lculation of STDs in complex flows. (C) 1999 Elsevier Science Ltd. All righ ts reserved.