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Validation of symmetry-induced high moment velocity and temperature scaling laws in a turbulent channel flow
KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain.;KTH Royal Inst Technol, FLOW, Engn Mech, S-11428 Stockholm, Sweden..
Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..ORCID iD: 0000-0002-8458-7288
Tech Univ Darmstadt, Chair Fluid Dynam, Otto Bernd Str 2, D-64287 Darmstadt, Germany.;Tech Univ Darmstadt, Ctr Computat Engn, Dolivostr 15, D-64293 Darmstadt, Germany..
2024 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 109, no 2, article id 025104Article in journal (Refereed) Published
Abstract [en]

The symmetry -based turbulence theory has been used to derive new scaling laws for the streamwise velocity and temperature moments of arbitrary order. For this, it has been applied to an incompressible turbulent channel flow driven by a pressure gradient with a passive scalar equation coupled in. To derive the scaling laws, symmetries of the classical Navier-Stokes and the thermal energy equations have been used together with statistical symmetries, i.e., the statistical scaling and translation symmetries of the multipoint moment equations. Specifically, the multipoint moments are built on the instantaneous velocity and temperature fields other than in the classical approach, where moments are based on the fluctuations of these fields. With this instantaneous approach, a linear system of multipoint correlation equations has been obtained, which greatly simplifies the symmetry analysis. The scaling laws have been derived in the limit of zero viscosity and heat conduction, i.e., Ret -> infinity and Pr > 1, and they apply in the center of the channel, i.e., they represent a generalization of the deficit law, thus extending the work of Oberlack et al. [Phys. Rev. Lett. 128, 024502 (2022)]. The scaling laws are all power laws, with the exponent of the high moments all depending exclusively on those of the first and second moments. To validate the new scaling laws, the data from a large number of direct numerical simulations (DNS) for different Reynolds and Prandtl numbers have been used. The results show a very high accuracy of the scaling laws to represent the DNS data. The statistical scaling symmetry of the multipoint moment equations, which characterizes intermittency, has been the key to the new results since it generates a constant in the exponent of the final scaling law. Most important, since this constant is independent of the order of the moments, it clearly indicates anomalous scaling.

Place, publisher, year, edition, pages
American Physical Society (APS) , 2024. Vol. 109, no 2, article id 025104
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-345064DOI: 10.1103/PhysRevE.109.025104ISI: 001171289100003PubMedID: 38491667Scopus ID: 2-s2.0-85185395013OAI: oai:DiVA.org:kth-345064DiVA, id: diva2:1849224
Note

QC 20240405

Available from: 2024-04-05 Created: 2024-04-05 Last updated: 2024-04-05Bibliographically approved

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Alcantara-Avila, Francisco

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