Growth of Spiral Vortices in a Globally Unstable Region on a Rotating Disk

Lee Keunseob*, Nishio Yu, Izawa Seiichiro, Fukunishi Yu
Department of Mechanical Systems Engineering, Tohoku University, Sendai, Miyagi, Japan

© 2018 Keunseob et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mechanical Systems Engineering, Tohoku University, Sendai, Miyagi, Japan; Tel: +81227956929; Fax: +81227956927; E-mail:



Instabilities on a rotating disk flow can be classified into two distinct groups, convective instability and global instability. Contrary to the convective instability, many characteristics of the global instability are left unknown despite of a lot of researches.


The study investigates the characteristics of the globally unstable mode.


Numerical simulation is carried out by a finite difference method. The simulation code solves the full Navier-Stokes perturbation equations and the continuity equation.


Four cases with azimuthal domain sizes of 2π/10, 2π/70, 2π/80 and 2π/90 are compared. In all cases, a short-duration wall-normal random suction and blowing is introduced from the wall at the beginning of the computation. In the computation for the wider size 2π/10 domain, wavenumber components of 70, 80 and 90 are all found to co-exist in the flow field, with the wavenumber 80 component being much stronger than the other two components. The strength of the wavenumber 80 component is equivalent to the narrower domain case. For the other two wavenumber components of 70 and 90, the strengths in the wider domain case are much lower compared to the corresponding narrower domain cases. When the same wavenumber components are compared between the wider and narrower domain computations, no difference can be found, indicating that each wavenumber component grows by the global instability.


The results imply that the amplitude saturation levels of wavenumber components 70 and 90 are suppressed by the wavenumber 80 component through the nonlinear effect.

Keywords: Global instability, Rotating-disk flow, Three-dimensional boundary layer, Nonlinear effect, Numerical simulation, Speral vortices.