{"paper":{"title":"Turbulence in cascading: Origin of the variance and skewness of density function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Xunchuan Liu","submitted_at":"2025-02-27T19:01:58Z","abstract_excerpt":"Turbulent systems typically exhibit log-normal volume density probability density functions (PDFs) on the $s = \\ln\\rho$ scale, with their variance ($\\sigma^2$) and skewness ($\\tau$) empirically regulated by the Mach number ($M$). In this work, we explain both the $\\sigma^2$--$M$ and $\\tau$--$M$ relationships from a thermodynamic and cascade perspective. Entropy conservation within the compressive modes yields the fiducial relation $\\sigma^2 = \\ln\\left(1 + M^2\\right)$, while deviations from a monotonic energy cascade modify this law into a dilogarithm function. Although skewness exerts a neglig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.20458","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.20458/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"}