Lyapunov-stability of solution branches of rotating disk flow

K.M.P. Eeten, van, J. Schaaf, van der, G.J.F. Heijst, van, J.C. Schouten

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
163 Downloads (Pure)

Abstract

This paper investigates the stability of solutions to the problem of viscous flow between an infinite rotating disk and an infinite stationary disk. A random perturbation, satisfying the Von Kármán similarity transformation, is applied to the steady velocity profiles for four solution branches, after which the disturbance propagation is tracked as a function of time. It was found that three of the four solution branches (including the Batchelor solution) were Lyapunov-stable and the development of the Lyapunov-coefficients as a function of the Reynolds number was determined. Stewartson-type of flow was found to be unstable and developed into a flow field corresponding to the Batchelor-solution. The mechanism with which the non-viscous core in this latter type of flow acquired its angular momentum was identified as being dominated by radial convection towards the axis of rotation.
Original languageEnglish
Article number073602
Pages (from-to)073602-1/13
Number of pages13
JournalPhysics of Fluids
Volume25
Issue number7
DOIs
Publication statusPublished - 2013

Fingerprint Dive into the research topics of 'Lyapunov-stability of solution branches of rotating disk flow'. Together they form a unique fingerprint.

Cite this