{"paper":{"title":"Analysis and approximation of a fractional Laplacian-based closure model for turbulent flows and its connection to Richardson pair dispersion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Feifei Xu, Max Gunzburger, Nan Jiang","submitted_at":"2016-11-15T23:34:20Z","abstract_excerpt":"We study a turbulence closure model in which the fractional Laplacian $(-\\Delta)^\\alpha$ of the velocity field represents the turbulence diffusivity. We investigate the energy spectrum of the model by applying Pao's energy transfer theory. For the case $\\alpha=1/3$, the corresponding power law of the energy spectrum in the inertial range has a correction exponent on the regular Kolmogorov -5/3 scaling exponent. For this case, this model represents Richardson's particle pair-distance superdiffusion of a fully developed homogeneous turbulent flow as well as L\\'evy jumps that lead to the superdif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05096","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"}