Journal of Fluid Mechanics

Papers

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

J. J. HEALEYa1 c1

a1 Department of Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK

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.

(Received May 10 2010)

(Revised July 12 2010)

(Accepted July 12 2010)

(Online publication September 28 2010)

Key words:

  • absolute/convective instability;
  • boundary layer stability

Correspondence:

c1 Email address for correspondence: j.j.healey@maths.keele.ac.uk

Metrics