{"schema":"pubphys.bundle/1","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},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b887b058cd2367c6441745b5be9ba281f3ccb282c6eb665306cbfe916fe28f12","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"ed7528bc212e913e1c1994f454e71ab25103baf5be2cb18c7ba33a45feacb7c0","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"B2qK5-g4dmyBQiIxjCu0WBZsluZbhTYtxJYcchGBtroQmPqpn0HwoZ_YbmmskFIDE0KAjLOPGKr6UIVbs-yjAQ"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEI7XUovCEukT4cGZT0VOcaslEDuvW-LLGMe6M6Rf6st8DxIO1pE2jVAo2JFaSjZuyG9palGpO-dkro6AsRR0FUZ-eECPEgnKZxjYEh8845bZ3uJkRAaGzI5ylYNlE3sRty0ruIlZgI8CBRcgh42aYrlqhyXlWaB75FSD_sjQi9jxF3wH8ROEvPPAjwILVVxY-E-yEbunZ5HYRekv9CqmTuvmnx17GcAYvHmDWnCPEgpvctMuOG0vi_RUSine2LaKRo1ILLs6woM89dH9lE658I8CCCDXmUkeZqehiMAWCcQvv2JoH5u99QWPiBX1MRN-pP3QjwIMH_9aFK1xnp4BXFZuvdPeSXUB5AoGY62wnaRIKCKFSbCPAgdC7SAy2fK-S3eSva7tx7owCrlOOu0_v14gC5EshI7qAI8SBFZ7nkuh-5IaK75jNF2I3u9gWIJeTINL1f_rXWP5TwxwjxIK8CKI34eu_sgR6N3zB1SKGijO7ko6-mgEUnS-DdScYBCP_wCOf1iajMfCj1CPAQnjpoz1kO_dN22pXdltGw2AjxIE4XykgsZ_WSh2vkwqZCzoJ33eOitoafeDpQ-3_6R7A_CPAg4b6CYztt395HgCIMw1-W5LfG-vu-JwtH6wIGvmq0bZwI8CCtU0WsKh5BwLGGWacTQHMeBHwdClkCV-rMMMXN9ZvwZQjxBGrRZZPwCNknZwX9zuTwAIPf4w0u-QyOLCtodHRwczovL2JvYi5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn8Aj1kxLXPF3sgQjwEN3TRaAlnRGdywLUXJqL_hoI8SC_EwWue7sXTkhbkg2KtpDc5URgyM3Hol8HHDVDiM8uLgjxBGrRZZLwCDbPE8C0jkmw_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPEgcCe_goUV_i6JgQUm8vGIzFLLPxWjAk_iuhN8MP2HtsgI8CCPm2C9s0XubFI_iMYYTrp7NQVEucjiDVVOS-5XhW0I8AjwILGVzUe4o5G4eCfsNghhwOFziij306RNYES910HKmhrsCPAgVyONoXyQM0NgJkZo0hKVGO9f4juKf5A3CyvglhBsUm8I8CCeXSTiCzsu5jmLW6aIc74nszLe4FOEslRZChj0t1VKtAjxIDr4W3XX8r8aow1ZiGRWxWoIW9dJhunhLwmguwsGdTO-CPEgELz-YATskE_flI3EMFwbuOgsnBRGkzF1Xa9I7rj-MQ4I8SB7TgKiPXFKLsITxTCqIEY2E_JnlB0P9hnCf6F5J05tTgjxIGB0NKCvdVTHWPyb-krv47MzDAWBd4vLje6N98K_6F_kCPAgyX4-cC3jGOgERVTj6eTI3Q0pFr0C9fiQQx-WUXIglL0I8VkBAAAAAfPitX67BAWDTZtWcQxQWCkh0YqMzi1a4gPWRNWeuOKwAAAAAAD-____AlREAgAAAAAAFgAUEXKzahzT5T5tisLdW6UYvM0Pl9sAAAAAAAAAACJqIPAEctMOAAgI8SAwkgFiLjrE4i4UPDMn2c7HXieBbkduCVR_rk5GmSghhwgI8CAeAZYQYIMdaCxzBP3Y06gnuz57Ns-TKJavZGdhkML93AgI8CC198zLIu74yxwmwNzR3PAaynBKuua9UCcw2CyBaEcKWAgI8CAxSXU58ENTCGnlVmMfBUDSe7PUXkdlNQkIcCczUvUXcwgI8CBK0rtRametS55XkRoTu4TTLoEsynoQA2atuGtOoQFm7wgI8CDktVbsge1QvmY068_HWE5N8syaqVDu30QVb4oO2shIhAgI8CAAGBdnq6kVTyqINAoW1AWmqSMrCXQ-zEzglSNUuUMpuQgI8CATBv3oWI6GOVvAjwYVlDhrkZfDGzhtR2pU4wqu0FZXfQgI8SCoGD7CnRzwIA9X2TonvAhr38a1B-laaGkTXOoVnKLalAgI8CDalktNU8YluuKLPRSEzK1gNVgBc6BCdYNysw57Ar07xwgI8SDGbdDDNu9PiyInO5tAadJPrtta_57FjBI8_UoOLsJpTAgI8SCbq51S51-NRozSBQVPKUoYMzKmPum0xMbTObF39PnJNwgI8CAyk4ieSMUJWnWk5mF9mfI8CXyF1YaYfNBysYuAvBIouAgIAAWIlg1z1xkBA_OmOw"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEI9skBbhI0_ZnF-hgH_wOkcYcya7E_p1wOVCl2mS9ttRbxIPa3mU-GdxNTiQ6hJckeacIoKchruEOF-wt7U8CVumiwCPEgy_DrljauOvtYMYEudRcxM7X-bdghpTG_-JFjY7vzPnUI8SCxLNat8piJgpTIdUatITPBybvyHWLt6C93ost6wF05PQjxIDqTEmQOpqQEiogaqAeftMP-fvTLslXOnYEuXICLsnn5CPEga_Om-S11dVSur4H9GGH37epxYs98W7Nybn3ZIeZSTBII8SBT7Q-kliZbjcj0B93Wfmm0R72vVQSLHykUWw8pcZ577gjxIMMrFRsL2yt6eaedRrGpL3F7JOgq7Ux325nt-rbwOH2yCPAgdC7SAy2fK-S3eSva7tx7owCrlOOu0_v14gC5EshI7qAI8SBFZ7nkuh-5IaK75jNF2I3u9gWIJeTINL1f_rXWP5TwxwjxIK8CKI34eu_sgR6N3zB1SKGijO7ko6-mgEUnS-DdScYBCP_wCOf1iajMfCj1CPAQnjpoz1kO_dN22pXdltGw2AjxIE4XykgsZ_WSh2vkwqZCzoJ33eOitoafeDpQ-3_6R7A_CPAg4b6CYztt395HgCIMw1-W5LfG-vu-JwtH6wIGvmq0bZwI8CCtU0WsKh5BwLGGWacTQHMeBHwdClkCV-rMMMXN9ZvwZQjxBGrRZZPwCNknZwX9zuTwAIPf4w0u-QyOLCtodHRwczovL2JvYi5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn8Aj1kxLXPF3sgQjwEN3TRaAlnRGdywLUXJqL_hoI8SC_EwWue7sXTkhbkg2KtpDc5URgyM3Hol8HHDVDiM8uLgjxBGrRZZLwCDbPE8C0jkmw_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPEgcCe_goUV_i6JgQUm8vGIzFLLPxWjAk_iuhN8MP2HtsgI8CCPm2C9s0XubFI_iMYYTrp7NQVEucjiDVVOS-5XhW0I8AjwILGVzUe4o5G4eCfsNghhwOFziij306RNYES910HKmhrsCPAgVyONoXyQM0NgJkZo0hKVGO9f4juKf5A3CyvglhBsUm8I8CCeXSTiCzsu5jmLW6aIc74nszLe4FOEslRZChj0t1VKtAjxIDr4W3XX8r8aow1ZiGRWxWoIW9dJhunhLwmguwsGdTO-CPEgELz-YATskE_flI3EMFwbuOgsnBRGkzF1Xa9I7rj-MQ4I8SB7TgKiPXFKLsITxTCqIEY2E_JnlB0P9hnCf6F5J05tTgjxIGB0NKCvdVTHWPyb-krv47MzDAWBd4vLje6N98K_6F_kCPAgyX4-cC3jGOgERVTj6eTI3Q0pFr0C9fiQQx-WUXIglL0I8VkBAAAAAfPitX67BAWDTZtWcQxQWCkh0YqMzi1a4gPWRNWeuOKwAAAAAAD-____AlREAgAAAAAAFgAUEXKzahzT5T5tisLdW6UYvM0Pl9sAAAAAAAAAACJqIPAEctMOAAgI8SAwkgFiLjrE4i4UPDMn2c7HXieBbkduCVR_rk5GmSghhwgI8CAeAZYQYIMdaCxzBP3Y06gnuz57Ns-TKJavZGdhkML93AgI8CC198zLIu74yxwmwNzR3PAaynBKuua9UCcw2CyBaEcKWAgI8CAxSXU58ENTCGnlVmMfBUDSe7PUXkdlNQkIcCczUvUXcwgI8CBK0rtRametS55XkRoTu4TTLoEsynoQA2atuGtOoQFm7wgI8CDktVbsge1QvmY068_HWE5N8syaqVDu30QVb4oO2shIhAgI8CAAGBdnq6kVTyqINAoW1AWmqSMrCXQ-zEzglSNUuUMpuQgI8CATBv3oWI6GOVvAjwYVlDhrkZfDGzhtR2pU4wqu0FZXfQgI8SCoGD7CnRzwIA9X2TonvAhr38a1B-laaGkTXOoVnKLalAgI8CDalktNU8YluuKLPRSEzK1gNVgBc6BCdYNysw57Ar07xwgI8SDGbdDDNu9PiyInO5tAadJPrtta_57FjBI8_UoOLsJpTAgI8SCbq51S51-NRozSBQVPKUoYMzKmPum0xMbTObF39PnJNwgI8CAyk4ieSMUJWnWk5mF9mfI8CXyF1YaYfNBysYuAvBIouAgIAAWIlg1z1xkBA_OmOw"]},"log":{"leaf_index":"3282","tree_size":"3804","proof":["321fa3cfe97603fcad29823835b8f09709f40c0592cbbd63fb3fa0eeaea93d07","e59cd566b7284e856ebd9fd94daa817cf34dd88052dcabee130311ce44ef5143","6133400f0fc715eadbd09ee211903a27b4ea8bc8a1a52c14f7b349544efd88a2","73b77a216b0b76fdbdd962634950d39eea059726c37b676e117494560e58cf4d","6fbf8cad74743afe221b033c878d7b141ca146d1721d09e8f01fe9f91c8502a0","962851e91c289a87c3e6ceaf456eaeaa6b1a48011626c428b07d1e104ccf85cf","3fef28ac1d8101210e18ad35b80e9e8d05f05f4a3262630e4d567d864dd85611","1ed62395399131ae4d5b365e81f741fbe796392ae81801387a716b09dc35a694","48906313613fdfddd2bd907650210a7f3e59ccb380a2b862e892089f41bcdced","98b5a14b42b3a202b6ef825f66833fa505601404c4c0f14575f3ec922607a858","af34d80d0065c0ab502282775e865492e2cb49c9493f4594d63ba5577922854a","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n3804\nAK6t4qgu96+M9wScTrIlsJ10d/zhKVEtYguyM3aeJvo=\n\n— pubphys.com/log/v1 JFPwIPP8EtoxgcsQg7V7CwIdL4UKPqJtpv+eB8sFNJjyQHIdyA1VabmBsPyLqq2bLxJPn57rA6fQi8y0QDDjRXHvlQg=\n","promise":"pubphys.com/log/v1 promise\nb2d3031de6197f3c26be1a0c0064f9e20ac945c86d4e603121aed1f186a41b28\n3282\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwIHFqnAL4ov9Gw4JnQ8Gy0EFRXwWwHi8fxq051t9CEenqB4F4xT1KswB1wT6jfw2N+JDuLvw9/TbxDtxrAYGGBA8=\n"},"orcid_key_evidence":[],"attesting":null}