# Building a Maxey--Riley framework for surface ocean inertial particle dynamics

## TL;DR

This paper develops a Maxey--Riley based framework for modeling surface ocean inertial particle dynamics, accounting for Earth's rotation, wind, and ocean currents, and introduces a shape correction heuristic for nonspherical particles.

## Contribution

It presents a novel vertically averaged Maxey--Riley set adapted for Earth's rotation and surface conditions, improving upon previous models by including wind drag effects.

## Key findings

- Velocity decays exponentially to a weighted average of seawater and air velocities.
- The weighted average velocity explains phenomena like debris trapping in mesoscale eddies.
- The new set outperforms previous models that ignored wind drag effects.

## Abstract

A framework for the study of surface ocean inertial particle motion is built from the Maxey--Riley set. A new set is obtained by vertically averaging each term of the original set, adapted to account for Earth's rotation effects, across the extent of a sufficiently small spherical particle that floats at an assumed unperturbed air--sea interface with unsteady nonuniform winds and ocean currents above and below, respectively. The inertial particle velocity is shown to exponentially decay in time to a velocity that lies close to an average of seawater and air velocities, weighted by a function of the seawater-to-particle density ratio. Such a weighted average velocity turns out to fortuitously be of the type commonly discussed in the search-and-rescue literature, which alone cannot explain the observed role of anticyclonic mesoscale eddies as traps for marine debris or the formation of great garbage patches in the subtropical gyres, phenomena dominated by finite-size effects. A heuristic extension of the theory is proposed to describe the motion of nonspherical particles by means of a simple shape factor correction, and recommendations are made for incorporating wave-induced Stokes drift, and allowing for inhomogeneities of the carrying fluid density. The new Maxey--Riley set outperforms an ocean adaptation that ignored wind drag effects and the first reported adaption that attempted to incorporate them.