{"paper":{"title":"Magnetohydrodynamic drag on an oscillating sphere in a rotating spherical cavity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A unified boundary-layer theory gives the magnetohydrodynamic drag on an oscillating sphere in a rotating cavity.","cross_cats":["physics.geo-ph"],"primary_cat":"physics.flu-dyn","authors_text":"David C\\'ebron, Paolo Personnettaz","submitted_at":"2026-04-12T12:03:23Z","abstract_excerpt":"The drag on an oscillating sphere is a classical fluid-mechanics problem, yet no existing theory simultaneously accounts for confinement, rotation, viscosity and magnetic fields. We consider a conducting sphere undergoing translational oscillations inside a rotating spherical cavity, modelling confined magnetohydrodynamic flows relevant to planetary interiors and liquid metal experiments. In planetary settings, these motions correspond to the polar and equatorial Slichter modes of Earth's inner core. Existing theories are restricted to separate asymptotic regimes, including viscous drag in bou"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive boundary layers and obtain the magnetohydrodynamic drag from Alfvén-wave radiation, viscous effects and Ohmic dissipation (accounting for pressure effects). The theory is extended to non-axisymmetric equatorial modes and to rotation perturbations of the polar mode... Our magnetohydrodynamic simulations validate our theory, providing a quantitative framework for planetary interiors.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes small-amplitude translational oscillations so that linearised boundary-layer approximations remain valid, and that electromagnetic contrasts between the solid sphere and fluid (or outer boundary) can be treated through standard matching conditions without additional surface effects.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A boundary-layer model unifies viscous, Alfvén-wave, and Ohmic contributions to the drag on an oscillating sphere in a rotating MHD cavity, extended to equatorial modes and validated by simulations for planetary applications.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A unified boundary-layer theory gives the magnetohydrodynamic drag on an oscillating sphere in a rotating cavity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"adb89fe4ab3c0e8dbd124c5cad4e1539fe72341fd086e20c82e4f710976937c2"},"source":{"id":"2604.10594","kind":"arxiv","version":2},"verdict":{"id":"53cf30b3-9325-4f3a-a7aa-508a53fa7790","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:48:06.149191Z","strongest_claim":"We derive boundary layers and obtain the magnetohydrodynamic drag from Alfvén-wave radiation, viscous effects and Ohmic dissipation (accounting for pressure effects). The theory is extended to non-axisymmetric equatorial modes and to rotation perturbations of the polar mode... Our magnetohydrodynamic simulations validate our theory, providing a quantitative framework for planetary interiors.","one_line_summary":"A boundary-layer model unifies viscous, Alfvén-wave, and Ohmic contributions to the drag on an oscillating sphere in a rotating MHD cavity, extended to equatorial modes and validated by simulations for planetary applications.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes small-amplitude translational oscillations so that linearised boundary-layer approximations remain valid, and that electromagnetic contrasts between the solid sphere and fluid (or outer boundary) can be treated through standard matching conditions without additional surface effects.","pith_extraction_headline":"A unified boundary-layer theory gives the magnetohydrodynamic drag on an oscillating sphere in a rotating cavity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.10594/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}