{"paper":{"title":"Effective degrees of nonlinearity in a family of generalized models of two-dimensional turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Chuong V. Tran, David G. Dritschel, Richard K. Scott","submitted_at":"2009-12-10T14:26:27Z","abstract_excerpt":"We study the small-scale behavior of generalized two-dimensional turbulence governed by a family of model equations, in which the active scalar $\\theta=(-\\Delta)^{\\alpha/2}\\psi$ is advected by the incompressible flow $\\u=(-\\psi_y,\\psi_x)$. The dynamics of this family are characterized by the material conservation of $\\theta$, whose variance $<\\theta^2>$ is preferentially transferred to high wave numbers. As this transfer proceeds to ever-smaller scales, the gradient $\\nabla\\theta$ grows without bound. This growth is due to the stretching term $(\\nabla\\theta\\cdot\\nabla)\\u$ whose ``effective deg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2003","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"}