{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T05:11:31Z","timestamp":1774847491959,"version":"3.50.1"},"reference-count":37,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T00:00:00Z","timestamp":1770681600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Fluid Mech."],"published-print":{"date-parts":[[2026,2,10]]},"abstract":"<jats:p>\n                    Exact mathematical expressions are derived to predict the exponent\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline1.png\"\/>\n                        <jats:tex-math>$p$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    observed in non-equilibrium turbulence, where the classical dissipation law is replaced by a new dissipation scaling law\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline2.png\"\/>\n                        <jats:tex-math>$C_{\\varepsilon } \\sim \\textit{Re}_{\\lambda }^p$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . Here,\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline3.png\"\/>\n                        <jats:tex-math>$ \\textit{Re}_{\\lambda }$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is the Taylor-based Reynolds number and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline4.png\"\/>\n                        <jats:tex-math>$C_{\\varepsilon } = \\varepsilon L_{11} \/ u^{\\prime 3}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is the non-dimensional dissipation rate, defined by the viscous dissipation rate,\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline5.png\"\/>\n                        <jats:tex-math>$\\varepsilon$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , longitudinal integral scale,\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline6.png\"\/>\n                        <jats:tex-math>$L_{11}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , and root-mean-square of the velocity fluctuations\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline7.png\"\/>\n                        <jats:tex-math>$u^{\\prime} = \\sqrt {\\overline {u^{\\prime 2}}}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    (Vassilicos,\n                    <jats:italic>Annu. Rev. Fluid Mech.<\/jats:italic>\n                    , vol. 47, 2015, pp. 95\u2013114). Assuming homogeneous and isotropic turbulence, it is shown that the exact value of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline8.png\"\/>\n                        <jats:tex-math>$p$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    involves only first-order derivatives of these variables; however, at very high Reynolds numbers, and under particularly strong changes in the power input of the external forcing (without changing the shape of the forcing spectrum), the exact expression simplifies to\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline9.png\"\/>\n                        <jats:tex-math>$p = 3\\pi \/ 4\\alpha L_{110} - 5 \/ 2$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline10.png\"\/>\n                        <jats:tex-math>$L_{110}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is the initial value of the longitudinal integral scale and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112026111252_inline11.png\"\/>\n                        <jats:tex-math>$\\alpha$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    represents an effective forcing wavenumber. Thus, the main finding is that only large-scale effects are involved in the imposition of the non-equilibrium dissipation scaling law. The results are compared with direct numerical simulation (DNS) results of isotropic turbulence under abruptly changing forcing conditions and with experimental data of non-equilibrium decaying isotropic turbulence, showing consistent results.\n                  <\/jats:p>","DOI":"10.1017\/jfm.2026.11125","type":"journal-article","created":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T11:40:09Z","timestamp":1770723609000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Non-dimensional dissipation at strong unsteady transitions in isotropic turbulence"],"prefix":"10.1017","volume":"1028","author":[{"given":"Afonso Avelar","family":"Ghira","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03db2by73","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Lisboa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6717-5284","authenticated-orcid":false,"given":"Gerrit E.","family":"Elsinga","sequence":"additional","affiliation":[{"name":"Delft University of Technology"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6866-5469","authenticated-orcid":false,"given":"Carlos Bettencourt","family":"da Silva","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03db2by73","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Lisboa"}]}],"member":"56","published-online":{"date-parts":[[2026,2,10]]},"reference":[{"key":"S0022112026111252_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139170666"},{"key":"S0022112026111252_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2025.316"},{"key":"S0022112026111252_ref2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevFluids.10.044603"},{"key":"S0022112026111252_ref26","doi-asserted-by":"publisher","DOI":"10.1063\/1.864731"},{"key":"S0022112026111252_ref19","first-page":"538","article-title":"On degeneration of isotropic turbulence in an incompressible viscous liquid","volume":"31","author":"Kolmogorov","year":"1941","journal-title":"Dokl. 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Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}],"article-number":"A46"}}