Stability of solution branches in infinite rotating disc flow

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

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Abstract

This paper investigates the stability of solutions to the problem of viscous flow between an infinite rotating disc and an infinite stationary disc. In the early 50’s of the previous century, two distinct and mutually incompatible solution branches were found: a Batchelor1 type of flow, and a Stewartson2 type of flow. In 1981, Holodniok et al.3 showed that a multitude of distinct solution branches could be obtained, as a function of the Reynolds number, including the two earlier solutions. In this work, a random disturbance in the steady velocity profiles for five solution branches is applied at t = 0, after which the disturbance propagation, ¿(t), defined as the squared difference of the azimuthal velocity at time t with the steady state azimuthal velocity, is determined. The Lyapunov exponents are then determined as a function of the Reynolds number. It was found that three of the five solution branches (including the Batchelor solution) are Lyapunov stable. The Stewartson solution, on the other hand, was found to have a positive Lyapunov exponent and diverged from its initial state to a Batchelor type of flow. The mechanism with which the non-viscous core obtains its angular momentum during this transition was identified as being dominated by radial convection from larger radii towards the axis of rotation.
Original languageEnglish
Title of host publication9th European Fluid Mechanics Conference, 9-13 September 2012, Rome, Italy
Publication statusPublished - 2012
Eventconference; European Fluid Mechanics Conference 9 -
Duration: 1 Jan 2012 → …

Conference

Conferenceconference; European Fluid Mechanics Conference 9
Period1/01/12 → …
OtherEuropean Fluid Mechanics Conference 9

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