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

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Samenvatting

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.
Originele taal-2Engels
Artikelnummer073602
Pagina's (van-tot)073602-1/13
Aantal pagina's13
TijdschriftPhysics of Fluids
Volume25
Nummer van het tijdschrift7
DOI's
StatusGepubliceerd - 2013

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