ABSTRACT
A remarkable feature of two-dimensional (2D) flows is the spontaneous emergence of large-scale coherent structures. If energy is injected at a constant rate at some intermediate scale, the energy transfer in 2D flows is characterized by an inverse cascade toward large scales, leading to the development of coherent structures [18,25]. These structures have a direct impact on the dynamics of particles advected by the flow, which covers a vast range of applications. For instance, in plankton blooms in the ocean [9,29], filamentary flow patterns are known to trap the advected particles for long periods of time, increasing the access to nutrients for different plankton species, and inducing changes to their traditional population dynamics. Likewise, in References 52–54, it was shown that particles carried by the blood flow in 2D models of blood vessels can behave chaotically. Such process also leads to particle trapping, a mechanism that boosts blood coagulation and accelerates the development of diseases as stenosis and aneurysms. The movement of oil spill ashore is also influenced by such structures. Mezić et al. [37] developed a diagnostic tool, based on the theory of 2D chaotic advection in fluids, which is able to estimate the location of oil spreading. Another important application is in the process of ozone depletion [28], where it is known that the filamentary structure of the polar vortex affects the dispersion of chemically active particles in the stratosphere, with similar behavior also observed in the atmospheres of Venus [42] and Saturn [12]. Several other examples can also be found in microfluids [57], combustion [62], and even in the theory of the evolution of life [55] (for a review, see Reference 60).
