Lagrangian Coherent Structures

Mounting evidence suggests that fluid advection can effectively be studied by considering special material surfaces, which are referred to here as Lagrangian coherent structures (LCSs). What makes these material surfaces special is their distinguished attracting or repelling nature. Notably, LCS are often locally the most strongly attracting or repellingmaterial surfaces in theflow, and as such have a strong influence on the flow topology. In fact, by understanding their evolution, one can often reveal mechanisms that underly complex laminar, and even turbulent, fluid transport in conspicuous detail. Conceptually, LCS can be approached from the dynamical systems perspective, or from amore physically based fluidmechanics perspective. Starting from the former, we note that fluid advection is described by the equation