On the global nonlinear instability of the rotating-disk flow over a finite domain
2016 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 803, 332-355 p.Article in journal (Refereed) Published
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.
absolute/convective instability, boundary layer stability, rotating flows
Fluid Mechanics and Acoustics
IdentifiersURN: urn:nbn:se:kth:diva-193985DOI: 10.1017/jfm.2016.506ISI: 000382894700015ScopusID: 2-s2.0-84983391118OAI: oai:DiVA.org:kth-193985DiVA: diva2:1038379
FunderSwedish Research Council, 621-2011-4526Swedish e‐Science Research Center
QC 201610182016-10-182016-10-142016-10-18Bibliographically approved