Finite-size Lyapunov exponents: a new tool for lake dynamics

Chaotic motion of particles in fluid flows was recognised decades ago but this phenomenon has only been acknowledged recently in civil engineering. Herein it is shown that chaotic advection has a wide range of important hydraulic and environmental applications. The most important characteristics of chaotic particle transport, such as the filamentary (fractal) distribution of advected particle ensembles and their importance for active chemical or biological processes, which has far-reaching ecological or environmental consequences, are reviewed. An important tool to discover and describe the filamentary distribution is the finite-size Lyapunov exponent. As a particular example, its application to an idealised shallow, wind-driven lake is presented. It is shown that the finite-size Lyapunov exponent provides a useful tool to investigate, for example, the spatial distribution of pollution in the lake - it can help to determine the most exposed shore segments and identify effectively mixed or stagnant regions in the lake.