{"paper":{"title":"Stochastic modeling of Fourier modes in two-dimensional turbulence via filtered white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A stochastic model of Fourier modes driven by filtered white noise reproduces the effective diffusion of passive tracers in two-dimensional turbulence.","cross_cats":["cs.NA","math.MP","math.NA","math.PR","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"Andrea Zanoni, Franco Flandoli, Paolo Cifani","submitted_at":"2026-05-13T15:30:19Z","abstract_excerpt":"Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of two-dimensional turbulent flows forced at intermediate scales and identify significant statistical structures. In particular, we find the existence of a typical time correlation length, and propose a stochastic model for the Fourier components. Finally, we compute the transport of a passive tracer under purely convective dynamics by means of direct numerical simulation of"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The stochastic model for the Fourier components produces an effective diffusion for the passive tracer that matches the one obtained from direct numerical simulation of the turbulent flow.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Fourier modes can be modeled as independent processes driven by filtered white noise whose single correlation length is sufficient to capture the transport statistics, without needing cross-mode correlations or higher-order statistics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Filtered white noise stochastic model for Fourier modes in 2D turbulence reproduces effective diffusion of passive tracers seen in DNS.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A stochastic model of Fourier modes driven by filtered white noise reproduces the effective diffusion of passive tracers in two-dimensional turbulence.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0ae42d2f0184e679b044f8b5f7d30018da5e0cf863089473f6fa66e96778c49a"},"source":{"id":"2605.13671","kind":"arxiv","version":1},"verdict":{"id":"3383a4ec-c03c-4e64-9de5-ce96a552af04","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:47:15.530688Z","strongest_claim":"The stochastic model for the Fourier components produces an effective diffusion for the passive tracer that matches the one obtained from direct numerical simulation of the turbulent flow.","one_line_summary":"Filtered white noise stochastic model for Fourier modes in 2D turbulence reproduces effective diffusion of passive tracers seen in DNS.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Fourier modes can be modeled as independent processes driven by filtered white noise whose single correlation length is sufficient to capture the transport statistics, without needing cross-mode correlations or higher-order statistics.","pith_extraction_headline":"A stochastic model of Fourier modes driven by filtered white noise reproduces the effective diffusion of passive tracers in two-dimensional turbulence."},"references":{"count":37,"sample":[{"doi":"","year":2043,"title":"Apolin´ ario, Geoffrey Beck, Laurent Chevillard, Isabelle Gal- lagher, and Ricardo Grande","work_id":"9bfb9366-6b66-4189-8b4c-88a0e1d6d319","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Apolin´ ario, Laurent Chevillard, and Jean-Christophe Mourrat","work_id":"fb0b68e5-3229-4142-999f-2f02bbd8a799","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Stochastic model reduction: convergence and applications to climate equations.J","work_id":"add680af-c87b-4ac4-96dd-5055c771e0c5","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"G. Boffetta and S. Musacchio. Evidence for the double cascade scenario in two-dimensional turbulence.Phys. Rev. E, 82:016307, Jul 2010","work_id":"906275f0-9adf-4f8f-8cdc-468c4319f1f1","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Guido Boffetta and Robert E. Ecke. Two-dimensional turbulence. InAn- nual review of fluid mechanics. Volume 44, 2012, volume 44 ofAnnu. Rev. Fluid Mech., pages 427–451. Annual Reviews, Palo Alto, CA, ","work_id":"cc3981d8-ce56-43ac-9149-8fb91a6be470","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":37,"snapshot_sha256":"4e6fccd36f207758c0363d43e2fe2fc03b7cb14c236dc9fcb34cd39e51f505a9","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"}