Inertial Particle Dynamics in Traveling Wave Flow

The dynamics of inertial particles in fluid flows have been the focus of extensive research due to their relevance in a wide range of industrial and environmental processes. Earlier studies have examined the dynamics of aerosols and bubbles using the Maxey-Riley equation in some standard systems but their dynamics within the traveling wave flow remain unexplored. In this paper, we study the Lagrangian dynamics of inertial particles in the traveling wave flow which shows mixing, and segregation in phase space as well as the formation of Lagrangian Coherent Structures (LCS). We first obtain the finite-time Lyapunov exponent (FTLEs) for the base fluid flow defined by the traveling wave flow using the Cauchy-Green deformation tensor. Further, we extend our calculations to the inertial particles to get the inertial finite-time Lyapunov exponent (iFTLEs). Our findings reveal that heavier inertial particles tend to be attracted to the ridges of the FTLE fields, while lighter particles are repelled. By understanding how material elements in a flow separate and stretch, one can predict pollutant dispersion, optimize the mixing process, and improve navigation and tracking in fluid environments. This provides insights into the complex and non-intuitive behavior of inertial particles in chaotic fluid flows, and may have implications for pollutant transport in wide-ranging fields such as atmospheric and oceanic sciences.