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We present a theory that predicts the presence of such attractors and sets down criteria for their existence in swirling, 3D vortex flows that serve as idealizations of ocean eddies. The three-dimensional fluid circulation in the eddy consists of a horizontal azimuthal flow along with an overturning component, and when this circulation is steady and axially symmetric, the fluid trajectories are confined to a set of nested tori that foliate the container. In this \u201cbackground\u201d state, a single attractor for slightly buoyant rigid spheres may exist close to the center of the nested tori. When the axisymmetric background flow is perturbed by a non-symmetric, and possibly time-dependent, disturbance, additional attractors can arise within new Kolmogorov\u2013Arnold\u2013Moser tori that appear in the resonant structures created by the disturbance. The tori appear as \u201cislands\u201d in the stroboscopic sections for fluid parcels. Under conditions laid out in the theory, an attracting orbit for slightly buoyant rigid spheres can form near the center of an island. The criteria are tested against numerical simulations of rigid particle trajectories using the Maxey\u2013Riley equations.<\/jats:p>","DOI":"10.1063\/5.0288722","type":"journal-article","created":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T15:45:58Z","timestamp":1765295158000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["A theory for attractors of microplastic particles in the resonant structures of a 3D eddy"],"prefix":"10.1063","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2183-3020","authenticated-orcid":false,"given":"Larry J.","family":"Pratt","sequence":"first","affiliation":[{"name":"Woods Hole Oceanographic Institution , Woods Hole, Massachusetts 02540,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2115-4522","authenticated-orcid":false,"given":"Irina I.","family":"Rypina","sequence":"additional","affiliation":[{"name":"Woods Hole Oceanographic Institution , Woods Hole, Massachusetts 02540,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,12,9]]},"reference":[{"key":"2025120910455050300_c2","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1017\/S0022112067001053","article-title":"A unified theory of homogeneous and stratified rotating fluids","volume":"29","year":"1967","journal-title":"J. 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