{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5f1b5e174ac18bebd5131961fc5273456eb827e5e5d9b945408235956cecb2bf","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["9bfc012853bb12dfa5f87eb03ccaa039d02c980c195e57bba5f7af20893d3fea","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"cd03eed4ef2c760985b8c22a33180890b46d5362eebbf2f55e8eb6f7bdce6ad4","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"fluid.strat-rot.rotating-cascade","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"Rapid rotation makes turbulence nearly two-dimensional and can reverse the direction of energy flow, sending energy to large scales. The rotation rate at which this switch happens, and whether it is sharp like a phase transition, are unsettled.","posed_since":"","precise":"In forced rotating turbulence with rotation rate $\\Omega$, forcing scale $\\ell_f$ and Rossby number $\\mathrm{Ro} = u_f/(2\\Omega \\ell_f)$, an upscale energy flux appears below a critical $\\mathrm{Ro}_c$. Determine $\\mathrm{Ro}_{c}$ in the limits $\\mathrm{Re} \\to \\infty$ and $\\text{domain size} \\to \\infty$, the scaling of the upscale flux fraction near $\\mathrm{Ro}_c$, and whether the transition is continuous with critical exponents or discontinuous with hysteresis.","problem_ref":"9bfc012853bb12dfa5f87eb03ccaa039d02c980c195e57bba5f7af20893d3fea","references":"","settled_by":"DNS at increasing Re and domain size showing convergence of $\\mathrm{Ro}_{c}$ and of the exponent of the upscale flux near $\\mathrm{Ro}_{c}$.","status_note":"Simulations find a transition with hysteresis and metastable flux-loop states (Clark di Leoni, Alexakis, Biferale, Buzzicotti 2020); the large-Re, large-domain limit is not settled.","title":"Critical Rossby number for the inverse cascade in rotating turbulence","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b887b058cd2367c6441745b5be9ba281f3ccb282c6eb665306cbfe916fe28f12","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"ed7528bc212e913e1c1994f454e71ab25103baf5be2cb18c7ba33a45feacb7c0","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"B2qK5-g4dmyBQiIxjCu0WBZsluZbhTYtxJYcchGBtroQmPqpn0HwoZ_YbmmskFIDE0KAjLOPGKr6UIVbs-yjAQ"},"schema":"pubphys.envelope/1"},"record_hash":"b887b058cd2367c6441745b5be9ba281f3ccb282c6eb665306cbfe916fe28f12","leaf_index":3282}