Nonlinear dynamics of inertial particles in the ocean: from drifters and floats to marine debris and Sargassum

Buoyant, finite-size, or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small, or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey-Riley equation. Derived from first principles-a result of over a century of research since the pioneering work by Sir George Stokes-the Maxey-Riley equation is a Newton-type law with several forces including (mainly) flow, added mass, shear-induced lift, and drag forces. In this paper, we present an overview of recent efforts to transfer the Maxey-Riley framework to oceanography. These involved: (1) including the Coriolis force, which was found to explain behavior of submerged floats near mesoscale eddies; (2) accounting for the combined effects of ocean current and wind drag on inertial particles floating at the air-sea interface, which helped understand the formation of great garbage patches and the role of anticyclonic eddies as plastic debris traps; and (3) incorporating elastic forces, which are needed to simulate the drift of pelagic Sargassum. Insight into the nonlinear dynamics of inertial particles in every case was possible to be achieved by investigating long-time asymptotic behavior in the various Maxey-Riley equation forms, which represent singular perturbation problems involving slow and fast variables.