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On the global nonlinear instability of the rotating-disk flow over a finite domain
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-1146-3241
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. University of London, United Kingdom.
2016 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 803, 332-355 p.Article in journal (Refereed) Published
Abstract [en]

Direct numerical simulations based on the incompressible nonlinear Navier-Stokes equations of the flow over the surface of a rotating disk have been conducted. An impulsive disturbance was introduced and its development as it travelled radially outwards and ultimately transitioned to turbulence has been analysed. Of particular interest was whether the nonlinear stability is related to the linear stability properties. Specifically three disk-edge conditions were considered; (i) a sponge region forcing the flow back to laminar flow, (ii) a disk edge, where the disk was assumed to be infinitely thin and (iii) a physically realistic disk edge of finite thickness. This work expands on the linear simulations presented by Appelquist el al. (J. Fluid. Mech., vol. 765, 2015, pp. 612-631), where, for case (i), this configuration was shown to be globally linearly unstable when the sponge region effectively models the influence of the turbulence on the flow field. In contrast, case (ii) was mentioned there to he linearly globally stable, and here, where nonlinearity is included, it is shown that both cases (ii) and (iii) are nonlinearly globally unstable. The simulations show that the flow can he globally linearly stable if the linear wavepacket has a positive front velocity. However, in the same flow field, a nonlinear global instability can emerge, which is shown to depend on the outer turbulent region generating a linear inward-travelling mode that sustains a transition front within the domain. The results show that the front position does not approach the critical Reynolds number for the local absolute instability, R = 507. Instead, the front approaches R = 583 and both the temporal frequency and spatial growth rate correspond to a global mode originating at this position.

Place, publisher, year, edition, pages
Cambridge University Press, 2016. Vol. 803, 332-355 p.
Keyword [en]
absolute/convective instability, boundary layer stability, rotating flows
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-193985DOI: 10.1017/jfm.2016.506ISI: 000382894700015ScopusID: 2-s2.0-84983391118OAI: oai:DiVA.org:kth-193985DiVA: diva2:1038379
Funder
Swedish Research Council, 621-2011-4526Swedish e‐Science Research Center
Note

QC 20161018

Available from: 2016-10-18 Created: 2016-10-14 Last updated: 2017-02-03Bibliographically approved
In thesis
1. The rotating-disk boundary-layer flow studied through numerical simulations
Open this publication in new window or tab >>The rotating-disk boundary-layer flow studied through numerical simulations
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with the instabilities of the incompressible boundary-layer flow thatis induced by a disk rotating in otherwise still fluid. The results presented include bothwork in the linear and nonlinear regime and are derived from direct numerical sim-ulations (DNS). Comparisons are made both to theoretical and experimental resultsproviding new insights into the transition route to turbulence. The simulation codeNek5000 has been chosen for the DNS using a spectral-element method (SEM) witha high-order discretization, and the results were obtained through large-scale paral-lel simulations. The known similarity solution of the Navier–Stokes equations for therotating-disk flow, also called the von K ́arm ́an rotating-disk flow, is reproduced by theDNS. With the addition of modelled small simulated roughnesses on the disk surface,convective instabilities appear and data from the linear region in the DNS are anal-ysed and compared with experimental and theoretical data, all corresponding verywell. A theoretical analysis is also presented using a local linear-stability approach,where two stability solvers have been developed based on earlier work. Furthermore,the impulse response of the rotating-disk boundary layer is investigated using DNS.The local response is known to be absolutely unstable and the global response, onthe contrary, is stable if the edge of the disk is assumed to be at radius infinity. Herecomparisons with a finite domain using various boundary conditions give a globalbehaviour that can be both linearly stable and unstable, however always nonlinearlyunstable. The global frequency of the flow is found to be determined by the Rey-nolds number at the confinement of the domain, either by the edge (linear case) or bythe turbulence appearance (nonlinear case). Moreover, secondary instabilities on topof the convective instabilities induced by roughness elements were investigated andfound to be globally unstable. This behaviour agrees well with the experimental flowand acts at a smaller radial distance than the primary global instability. The sharpline corresponding to transition to turbulence seen in experiments of the rotating diskcan thus be explained by the secondary global instability. Finally, turbulence datawere compared with experiments and investigated thoroughly.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. 47 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2017:01
Keyword
laminar-turbulent transition, convective instability, absolute instability, crossflow instability, direct numerical simulations
National Category
Engineering and Technology Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-200827 (URN)978-91-7729-269-2 (ISBN)
Public defence
2017-02-24, F3, Lindstedtsvägen 26, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20170203

Available from: 2017-02-03 Created: 2017-02-03 Last updated: 2017-02-03Bibliographically approved

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Appelquist, EllinorSchlatter, PhilipAlfredsson, P. HenrikLingwood, Rebecca J.
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