{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T13:04:32Z","timestamp":1785416672049,"version":"3.56.0"},"reference-count":29,"publisher":"Optica Publishing Group","issue":"7","license":[{"start":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:00:00Z","timestamp":1776124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:00:00Z","timestamp":1776124800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N00014-20-102558"],"award-info":[{"award-number":["N00014-20-102558"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/00rk2pe57","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009918","name":"U.S. Army Space and Missile Defense Command","doi-asserted-by":"crossref","award":["AMTC-22-01-080"],"award-info":[{"award-number":["AMTC-22-01-080"]}],"id":[{"id":"10.13039\/100009918","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/03agkn750","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["J. Opt. Soc. Am. A"],"published-print":{"date-parts":[[2026,7,1]]},"abstract":"<jats:p>\n                    Optical turbulence caused by refractive index fluctuations poses a major challenge for imaging, free-space communication, and directed-energy systems. Rayleigh\u2013B\u00e9nard (RB) convection offers a controlled laboratory analog for studying buoyancy-driven turbulence and its optical effects. Building on theoretical predictions that link turbulence strength to heat flux, we experimentally determine the scaling constant\n                    <jats:italic>\u03b3<\/jats:italic>\n                    by simultaneously measuring the refractive index structure constant (\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    <jats:sup>2<\/jats:sup>\n                    ) and heat flux in an RB environment. Using a variable turbulence generator (VTG), we validate RB conditions through Nusselt\u2013Rayleigh scaling and direct numerical simulations (DNS). Three independent optical diagnostics were employed to estimate\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    <jats:sup>2<\/jats:sup>\n                    (scintillation, beam wander, and long-term beam spot size), while embedded sensors captured heat flux. This scaling constant validation is confined to the experimental conditions described. Results confirm the predicted\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    <jats:sup>2<\/jats:sup>\n                    \u221dQ\n                    <jats:sup>4\/3<\/jats:sup>\n                    relationship, with\n                    <jats:italic>\u03b3<\/jats:italic>\n                    =8.79\u00b10.61 closely matching simulations (8.65). This strong agreement demonstrates the robustness of the heat-flux-based scaling relationship and establishes RB systems as effective testbeds for turbulence characterization. These findings provide a practical framework for predicting optical performance in complex environments and advancing turbulence mitigation strategies.\n                  <\/jats:p>","DOI":"10.1364\/josaa.590033","type":"journal-article","created":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T19:00:10Z","timestamp":1774897210000},"page":"C20","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Heat flux as a key to predicting optical turbulence: experimental validation of a scaling constant in Rayleigh\u2013B\u00e9nard turbulence"],"prefix":"10.1364","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7156-0070","authenticated-orcid":true,"given":"David","family":"McLeod","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/037s24f05","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert A.","family":"Handler","sequence":"additional","affiliation":[{"name":"George Mason University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard J.","family":"Watkins","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/037s24f05","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,4,14]]},"reference":[{"key":"josaa-43-7-C20-R1","series-title":"","doi-asserted-by":"crossref","DOI":"10.1117\/3.626196","volume-title":"Laser Beam Propagation Through Random Media","volume":"PM152","author":"Andrews","year":"2005"},{"key":"josaa-43-7-C20-R2","volume-title":"The Effects of the Turbulent Atmosphere on Wave Propagation","author":"Tatarskii","year":"1971"},{"key":"josaa-43-7-C20-R3","doi-asserted-by":"publisher","first-page":"2678","DOI":"10.1364\/AO.51.002678","type":"journal-article","volume":"51","author":"Hou","year":"2012","journal-title":"Appl. Opt."},{"key":"josaa-43-7-C20-R4","doi-asserted-by":"publisher","first-page":"892","DOI":"10.1364\/JOSA.68.000892","type":"journal-article","volume":"68","author":"Hill","year":"1978","journal-title":"J. Opt. Soc. Am."},{"key":"josaa-43-7-C20-R5","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1146\/annurev.fluid.010908.165152","type":"journal-article","volume":"42","author":"Lohse","year":"2010","journal-title":"Annu. Rev. Fluid Mech."},{"key":"josaa-43-7-C20-R6","doi-asserted-by":"publisher","first-page":"054605","DOI":"10.1103\/PhysRevFluids.9.054605","type":"journal-article","volume":"9","author":"Handler","year":"2024","journal-title":"Phys. Rev. Fluids"},{"key":"josaa-43-7-C20-R7","doi-asserted-by":"publisher","first-page":"B85","DOI":"10.1364\/JOSAA.520909","type":"journal-article","volume":"41","author":"Ferlic","year":"2024","journal-title":"J. Opt. Soc. Am. A"},{"key":"josaa-43-7-C20-R8","doi-asserted-by":"crossref","DOI":"10.1142\/3097","volume-title":"Rayleigh-B\u00e9nard Convection: Structures and Dynamics, Advanced Series in Nonlinear Dynamics","volume":"11","author":"Getling","year":"1998"},{"key":"josaa-43-7-C20-R9","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/BF00280263","type":"journal-article","volume":"4","author":"Adrian","year":"1986","journal-title":"Exp. Fluids"},{"key":"josaa-43-7-C20-R10","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1088\/1367-2630\/6\/1\/072","type":"journal-article","volume":"6","author":"Celani","year":"2004","journal-title":"New J. Phys."},{"key":"josaa-43-7-C20-R11","doi-asserted-by":"publisher","first-page":"144001","DOI":"10.1103\/PhysRevLett.133.144001","type":"journal-article","volume":"133","author":"Shishkina","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"josaa-43-7-C20-R12","doi-asserted-by":"publisher","author":"Bershadskii","year":"2020","DOI":"10.48550\/arXiv.2003.04836","type":"preprint"},{"key":"josaa-43-7-C20-R13","doi-asserted-by":"publisher","first-page":"A8","DOI":"10.1017\/jfm.2024.164","type":"journal-article","volume":"984","author":"Xu","year":"2024","journal-title":"J. Fluid Mech."},{"key":"josaa-43-7-C20-R14","doi-asserted-by":"publisher","first-page":"6065","DOI":"10.1364\/AO.56.006065","type":"journal-article","volume":"56","author":"Nootz","year":"2017","journal-title":"Appl. Opt."},{"key":"josaa-43-7-C20-R15","doi-asserted-by":"publisher","first-page":"1662","DOI":"10.1364\/JOSAA.492749","type":"journal-article","volume":"40","author":"Ferlic","year":"2023","journal-title":"J. Opt. Soc. Am. A"},{"key":"josaa-43-7-C20-R16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/OCEANS-TAIPEI.2014.6964293","article-title":"EO signal propagation in a simulated underwater turbulence environment","volume-title":"OCEANS. 2014\u2014TAIPEI","author":"Hou","year":"2014"},{"key":"josaa-43-7-C20-R17","doi-asserted-by":"crossref","first-page":"PTh4C.3","DOI":"10.1364\/PCAOP.2019.PTh4C.3","article-title":"Measurements of temperature and image motion structure functions in a Rayleigh-B\u00e9nard water tank","volume-title":"Imaging and Applied Optics 2019 (COSI, IS, MATH, pcAOP)","author":"Montoya","year":"2019"},{"key":"josaa-43-7-C20-R18","doi-asserted-by":"publisher","first-page":"8505","DOI":"10.1364\/AO.51.008505","type":"journal-article","volume":"51","author":"Kulikov","year":"2012","journal-title":"Appl. Opt."},{"key":"josaa-43-7-C20-R19","doi-asserted-by":"publisher","first-page":"1725","DOI":"10.1364\/OL.36.001725","type":"journal-article","volume":"36","author":"Anguita","year":"2011","journal-title":"Opt. Lett."},{"key":"josaa-43-7-C20-R20","doi-asserted-by":"publisher","first-page":"31839","DOI":"10.1364\/OE.499467","type":"journal-article","volume":"31","author":"Wiley","year":"2023","journal-title":"Opt. Express"},{"key":"josaa-43-7-C20-R21","doi-asserted-by":"publisher","first-page":"17869","DOI":"10.1364\/OE.561320","type":"journal-article","volume":"33","author":"Wiley","year":"2025","journal-title":"Opt. Express"},{"key":"josaa-43-7-C20-R22","doi-asserted-by":"publisher","first-page":"1691","DOI":"10.1109\/LPT.2011.2166113","type":"journal-article","volume":"23","author":"Kaushal","year":"2011","journal-title":"IEEE Photon. Technol. Lett."},{"key":"josaa-43-7-C20-R24","doi-asserted-by":"publisher","first-page":"924","DOI":"10.1364\/OE.380405","type":"journal-article","volume":"28","author":"Watkins","year":"2020","journal-title":"Opt. Express"},{"key":"josaa-43-7-C20-R25","first-page":"JTu1A.57","article-title":"Experimental results on the effect of OAM state on the scintillation index for an asymmetric perfect vortex beam","volume-title":"Frontiers in Optics + Laser Science","author":"Cox","year":"2021"},{"key":"josaa-43-7-C20-R26","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0030-4018(02)02294-0","type":"journal-article","volume":"216","author":"Consortini","year":"2003","journal-title":"Opt. Commun."},{"key":"josaa-43-7-C20-R27","volume-title":"Hydrodynamic and Hydromagnetic Stability","author":"Chandrasekhar","year":"1961"},{"key":"josaa-43-7-C20-R29","doi-asserted-by":"publisher","first-page":"035001","DOI":"10.1103\/RevModPhys.96.035001","type":"journal-article","volume":"96","author":"Lohse","year":"2024","journal-title":"Rev. Mod. Phys."},{"key":"josaa-43-7-C20-R30","doi-asserted-by":"publisher","first-page":"025140","DOI":"10.1063\/5.0194967","type":"journal-article","volume":"36","author":"He","year":"2024","journal-title":"Phys. Fluids"},{"key":"josaa-43-7-C20-R31","doi-asserted-by":"publisher","first-page":"A58","DOI":"10.1017\/jfm.2024.996","type":"journal-article","volume":"1000","author":"Stevens","year":"2024","journal-title":"J. Fluid Mech."}],"container-title":["Journal of the Optical Society of America A"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=josaa-43-7-C20","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=josaa-43-7-C20&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T14:55:28Z","timestamp":1778684128000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=josaa-43-7-C20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,14]]},"references-count":29,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/josaa.590033","relation":{},"ISSN":["1084-7529","1520-8532"],"issn-type":[{"value":"1084-7529","type":"print"},{"value":"1520-8532","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,14]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/JOSAA.590033","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"13 January 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"27 March 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"14 April 2026","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9\n\t\t\t\t\t2026 Optica Publishing Group under the terms of the Optica Open Access\n\t\t\t\t\t\tPublishing Agreement","name":"copyright","label":"Copyright"}]}}