{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"42e16a267c01054e58fdc05603698b9f01b8010e6e36d32abd1e96b272d207dd","created":"2026-10-03T07:18:03Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"bbfcfdbb2f7f3c00f15f664063deb5aaaa0af315faba08840e348b1eb8db07b1","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.2d-turbulence.vortex-decay-exponent","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"In freely decaying flat turbulence, small vortices merge into fewer, larger ones. The rate at which the number of vortices falls with time has been measured, and a scaling theory exists, but whether the exponent is universal is not settled.","posed_since":"1991","precise":"In freely decaying 2D Navier-Stokes turbulence at large Re, the number density of coherent vortices decays as $n(t) \\sim t^{-\\xi}$. Early simulations gave $\\xi \\sim 0.7\\text{ to }0.75$, approximately (Carnevale et al. 1991); a scaling theory for inviscid decay predicts a vortex number density per unit vortex area $n(A,t) \\sim t^{-2/3}/A$ (Dritschel et al. 2008). Determine $\\xi$ in the limit $\\mathrm{Re} \\to \\infty$, and whether it is universal or depends on initial conditions and Re.","problem_ref":null,"references":"","settled_by":"A derivation of $\\xi$ verified by ensembles of high-resolution decaying DNS with varied initial spectra and Re.","status_note":"The 2008 scaling theory (Dritschel, Scott, Macaskill, Gottwald, Tran, PRL 2008) is supported by high-resolution inviscid simulations; its agreement with finite-Re values near 0.75 and its universality across initial conditions are not established.","title":"Decay exponent of vortex number in freely decaying 2D turbulence","topic_ref":"0182f1f595a8d4484a77534cfdcf00e164a201f0557ef3e8a7e29298531a113e"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"31b3c4d7c375e7952f4e9cdfda2e7824be45e283ad33868e18bb37f7cba1a034","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"fb9896d8945825e797a257c50235aef5a9055055d312d7f7bc83825e961a27e8","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Ja9RIK7a5KGP214n7QzBmSLOw8XWG5xLIBTEW2JFBMlA_q67mlZz8WRSBjRdtA6JEWePFgdLJNbtBxCHtQ6BBw"},"schema":"pubphys.envelope/1"},"record_hash":"31b3c4d7c375e7952f4e9cdfda2e7824be45e283ad33868e18bb37f7cba1a034","leaf_index":1393}