Lyapunov-stability of solution branches of rotating disk flow
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 Karman similarity transformation, is applied to the steady velocity profiles for four solution branches, afte...
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| Veröffentlicht in: | Physics of fluids (1994) 2013-07, Vol.25 (7) |
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| container_issue | 7 |
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| container_title | Physics of fluids (1994) |
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| creator | van Eeten, KMP van der Schaaf, J van Heijst, GJF Schouten, J C |
| description | 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 Karman 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. |
| doi_str_mv | 10.1063/1.4812704 |
| format | Article |
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A random perturbation, satisfying the Von Karman 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. 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| fulltext | fulltext |
| identifier | ISSN: 1070-6631 |
| ispartof | Physics of fluids (1994), 2013-07, Vol.25 (7) |
| issn | 1070-6631 0031-9171 1089-7666 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1642307059 |
| source | AIP Journals Complete; AIP Digital Archive; Alma/SFX Local Collection |
| subjects | Angular momentum Convection Disturbances Fluid dynamics Fluid flow Rotating disks Similarity Transformations |
| title | Lyapunov-stability of solution branches of rotating disk flow |
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