{"paper":{"title":"On the Clark-alpha model of turbulence: global regularity and long--time dynamics","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"C. Cao, D.D. Holm, E.S. Titi","submitted_at":"2004-12-01T16:04:49Z","abstract_excerpt":"In this paper we study a well-known three--dimensional turbulence model, the filtered Clark model, or Clark-alpha model. This is Large Eddy Simulation (LES) tensor-diffusivity model of turbulent flows with an additional spatial filter of width alpha ($\\alpha$). We show the global well-posedness of this model with constant Navier-Stokes (eddy) viscosity. Moreover, we establish the existence of a finite dimensional global attractor for this dissipative evolution system, and we provide an anaytical estimate for its fractal and Hausdorff dimensions. Our estimate is proportional to $(L/l_d)^3$, whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0412007","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}