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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Hussain, Z. Garrett, S. J. and Stephen, S. O. 2011. The instability of the boundary layer over a disk rotating in an enforced axial flow. Physics of Fluids, Vol. 23, Issue. 11, p. 114108.


    Appelquist, E. Schlatter, P. Alfredsson, P.H. and Lingwood, R.J. 2015. Investigation of the Global Instability of the Rotating-disk Boundary Layer. Procedia IUTAM, Vol. 14, p. 321.


    Alfredsson, P. Henrik and Lingwood, Rebecca J. 2014. Modeling Atmospheric and Oceanic Flows.


    Imayama, Shintaro Alfredsson, P. Henrik and Lingwood, R. J. 2014. On the laminar–turbulent transition of the rotating-disk flow: the role of absolute instability. Journal of Fluid Mechanics, Vol. 745, p. 132.


    Siddiqui, M. E. Mukund, V. Scott, J. and Pier, B. 2013. Experimental characterization of transition region in rotating-disk boundary layer. Physics of Fluids, Vol. 25, Issue. 3, p. 034102.


    Barrow, A. Garrett, S.J. and Peake, N. 2015. Global linear stability of the boundary-layer flow over a rotating sphere. European Journal of Mechanics - B/Fluids, Vol. 49, p. 301.


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  • Journal of Fluid Mechanics, Volume 663
  • November 2010, pp. 148-159

Model for unstable global modes in the rotating-disk boundary layer

  • J. J. HEALEY (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112010003836
  • Published online: 28 September 2010
Abstract

Recent simulations and experiments appear to show that the rotating-disk boundary layer is linearly globally stable despite the existence of local absolute instability. However, we argue that linear global instability can be created by local absolute instability at the edge of the disk. This argument is based on investigations of the linearized complex Ginzburg–Landau equation with weakly spatially varying coefficients to model the propagation of a wavepacket through a weakly inhomogeneous unstable medium. Therefore, this mechanism could operate in a variety of locally absolutely unstable flows. The corresponding nonlinear global mode has a front at the radius of onset of absolute instability when the disk edge is far from the front. This front moves radially outwards when the Reynolds number at the disk edge is reduced. It is shown that the laminar–turbulent transition front also behaves in this manner, possibly explaining the scatter in observed transitional Reynolds numbers.

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Email address for correspondence: j.j.healey@maths.keele.ac.uk
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J. M. Chomaz , P. Huerre & L. G. Redekopp 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Math. 84, 119144.

E. C. Cobb & O. A. Saunders 1956 Heat transfer from a rotating disk. Proc. R. Soc. Lond. A 236, 343351.


C. Davies , C. Thomas & P. W. Carpenter 2007 Global stability of the rotating-disc boundary layer. J. Engng Math. 57, 219236.

B. I. Federov , G. Z. Plavnik , I. V. Prokhorov & L. G. Zhukhovitskii 1976 Transitional flow conditions on a rotating disk. J. Engng Phys. 31, 14481453.

N. Gregory , J. T. Stuart & W. S. Walker 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. A 248, 155199.




J. J. Healey 2007 aInstabilities of flows due to rotating disks: preface. J. Engng Math. 57, 199204.


R. E. Hunt & D. G. Crighton 1991 Instability of flows in spatially developing media. Proc. R. Soc. Lond. A 435, 109128.

R. Kobayashi , Y. Kohama & Ch. Takamadate 1980 Spiral vortices in boundary layer transition regime on a rotating disk. Acta Mech. 35, 7182.



M. R. Malik , S. P. Wilkinson & S. A. Orszag 1981 Instability and transition in rotating disk flow. AIAA J. 19, 11311138.

N. Meunier , M. R. E. Proctor , D. D. Sokoloff , A. M. Soward & S. M. Tobias 1997 Asymptotic properties of a nonlinear αω-dynamo wave: period, amplitude and latitude dependence. Geophys. Astrophys. Fluid Dyn. 86, 249285.



B. Pier , P. Huerre , J. M. Chomaz & A. Couairon 1998 Steep nonlinear global modes in spatially developing media. Phys. Fluids 10, 24332435.

A. M. Soward 1977 On the finite amplitude thermal instability of a rapidly rotating fluid sphere. Geophys. Astrophys. Fluid Dyn. 9, 1974.

A. M. Soward & C. A. Jones 1983 The linear stability of the flow in the narrow gap between two concentric rotating spheres. Q. J. Mech. Appl. Math. 36, 1942.

S. M. Tobias , M. R. E. Proctor & E. Knobloch 1998 Convective and absolute instabilities of fluid flows in finite geometries. Physica D 113, 4372.

S. Wang & Z. Rusak 1996 On the stability of an axisymmetric rotating flow in a pipe. Phys. Fluids 8, 10071016.

S. P. Wilkinson & M. R. Malik 1985 Stability experiments in the flow over a rotating disk flow. AIAA J. 23, 588595.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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