{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"c4d81e479de5f4f2db738b54281d4b893828c42e1677f805aeb61c50c3a5c08a","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"4333916c4f1c466e42d6f910a8f976fd720bc4806e2a90a4623fa66a152b6545","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.strat-rot.rotating-cascade","kind":"well-posed","literature_status":"partially-resolved","n":"1","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 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":null,"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":"10bf729b197d5ee7bbcb1c2f468901326f7231ccc5c3ae2967db2e962f472a39"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9bfc012853bb12dfa5f87eb03ccaa039d02c980c195e57bba5f7af20893d3fea","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"191fcbb999e8bb839930898d40fc18dd32e4b6aa19a65eebbf2ccac0f735fc41","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"hJNMmeJz5hlAZDw9h_rzUjxEfQToJcJtBhBxNe9Ec9N87sX_MUuD636s4MsKg8aaTOFt8aFrSWzVydtkIEMhAw"},"schema":"pubphys.envelope/1"},"record_hash":"9bfc012853bb12dfa5f87eb03ccaa039d02c980c195e57bba5f7af20893d3fea","leaf_index":1444}