Stability of a temporally evolving natural convection boundary layer on an isothermal wall

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dc.contributor.author Ke, J en
dc.contributor.author Williamson, N en
dc.contributor.author Armfield, S en
dc.contributor.author McBain, GD en
dc.contributor.author Norris, Stuart en
dc.date.accessioned 2019-09-19T01:38:27Z en
dc.date.available 2019-07-31 en
dc.date.issued 2019-10-25 en
dc.identifier.citation Journal of Fluid Mechanics 877:1163-1185 25 Oct 2019 en
dc.identifier.issn 0022-1120 en
dc.identifier.uri http://hdl.handle.net/2292/47756 en
dc.description.abstract The stability properties of a natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall with Prandtl number 0.71 are numerically investigated in the configuration of a temporally evolving parallel flow. The instantaneous linear stability of the flow is first invesitgated by solving the eigenvalue problem with a ‘frozen’ base flow. The critical point is found to be Grδ = 454.2 with the most unstable wavenumber of k = 0.0544, where Grδ is the Grashof number based on the velocity integral boundary layer thickness δ. Temporal responses of the discrete perturbation modes are numerically obtained by solving the two-dimensional linearised disturbance equations using a ‘frozen’ base flow as an initial-value problem at various Grδ. The resultant amplification rates of the discrete modes are compared with the quasi-steady eigenvalue analysis, and both two-dimensional and three dimensional full direct numerical simulations of the temporally evolving flow. The selective amplification that is commonly found in the spatially developing NCBL is also observed in the temporally evolving case. The amplification rate predicted by the linear theory compares well with the direct stability analysis from Grδ ∼ 8500 to a transition point of Grδ ∼ 1.3×104, confirming the temporally evolving NCBL shares very similar instantaneous stability properties to the ‘frozen’ steady base flow in this range. The transition Grashof number also coincides with the sudden change in the base flow and the mean flow statistics. The direct simulations show the value of the transition Grashof number depends on the initial perturbation amplitude. After the transition point, the direct stability results diverge from the linear stability predictions as the non-linear mechanisms become important. en
dc.description.uri https://catalogue.library.auckland.ac.nz/permalink/f/t37c0t/uoa_alma21156273970002091 en
dc.publisher Cambridge University Press (CUP) en
dc.relation.ispartofseries Journal of Fluid Mechanics en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.rights.uri https://www.cambridge.org/core/services/open-access-policies/open-access-journals/green-open-access-policy-for-journals en
dc.title Stability of a temporally evolving natural convection boundary layer on an isothermal wall en
dc.type Journal Article en
dc.identifier.doi 10.1017/jfm.2019.639 en
pubs.begin-page 1163 en
pubs.volume 877 en
dc.rights.holder Copyright: Cambridge University Press 2019 en
pubs.author-url https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/stability-of-a-temporally-evolving-natural-convection-boundary-layer-on-an-isothermal-wall/E0749385CF908E4557FF2B2DD2900C88 en
pubs.end-page 1185 en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.subtype Article en
pubs.elements-id 777433 en
pubs.org-id Engineering en
pubs.org-id Mechanical Engineering en
dc.identifier.eissn 1469-7645 en
pubs.record-created-at-source-date 2019-07-31 en
pubs.online-publication-date 2019-09-02 en


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