{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"f150ff833690d1b6dc4541a3f2690e0147370acfa9029ba26d64e4461f0eb0f7","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","b12e60e0ea7a246782220372db7a9a8e9980326b8ace8380e7a2da222a95ecb3"],"salt":"f07b848d96520a3d58d889cdb2b5f4629a61710240b7fee2a8532bc17d40b517","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.shear-transition.pipe-dp-exponents","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[{"note":"Pipe flow is one of the transitional shear-flow candidates for observing DP","parent_revision":"b12e60e0ea7a246782220372db7a9a8e9980326b8ace8380e7a2da222a95ecb3","relation":"special_case"}],"plain":"Near the onset of turbulence in a pipe, turbulent patches called puffs either decay or split, much like sick individuals recovering or infecting others. Pipe flow has now been placed in the class of this epidemic-type transition (directed percolation), but its critical exponents have not been measured directly in a pipe.","posed_since":"1986","precise":"Hagen-Poiseuille flow with $\\mathrm{Re} = U D / \\nu$ (U bulk velocity, D diameter) has its critical point $\\mathrm{Re}_c \\sim 2040$, where puff splitting balances decay. Measure directly the turbulent-fraction exponent $\\beta$ in $F_t \\sim \\varepsilon^{\\beta}$, $\\varepsilon = (\\mathrm{Re} - \\mathrm{Re}_c)/\\mathrm{Re}_c$, and the correlation exponents $\\nu_{\\mathrm{perp}}$ and $\\nu_{\\mathrm{par}}$, to test the ($1+1$)-dimensional directed-percolation values $\\beta \\sim 0.276, \\nu_{\\mathrm{perp}} \\sim 1.097, \\nu_{\\mathrm{par}} \\sim 1.734$, and determine the range of $\\varepsilon$ over which this scaling holds before puff jamming sets in. Answer: measured exponents with error bars and the width of the critical range.","problem_ref":null,"references":"","settled_by":"Turbulent-fraction and correlation measurements in pipes many thousands of diameters long, over times long compared with puff splitting and decay times, close enough to $\\mathrm{Re}_c$ to fit exponents.","status_note":"Experiments on pairwise puff interactions combined with simulations place the pipe transition in the directed-percolation class and reveal a jammed puff phase above $\\mathrm{Re}_c$ (Lemoult et al., Nature Physics 2024); direct fits of $\\beta$, $\\nu_{\\mathrm{perp}}$ and $\\nu_{\\mathrm{par}}$ in a pipe are still lacking.","title":"Direct measurement of directed-percolation exponents in pipe flow","topic_ref":"2aa8cdcaa55f798dfb19771ba7be3d165d6aebb316dba50bbe9ddce450fd9038"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ba1597187265b79787d75420d9a70a7748bb11eba7c59c6733135e8ceab03e47","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c22ddf03a54fd1318e1ab192b58233bc27e9013be8d0525fdb001131c426b4a1","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"x28zd3I81BRlMCB5WCTAcncloBtRy_4-oBpvmN5bfwBK_1pkZ7ElC9TVmQF84K4L7zqHvck2dBK8WBaZv1J4CQ"},"schema":"pubphys.envelope/1"},"record_hash":"ba1597187265b79787d75420d9a70a7748bb11eba7c59c6733135e8ceab03e47","leaf_index":2068}