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Mode Expansion of Viscous and Viscoelastic Taylor‐Couette Flow in Finite Gaps
Author(s) -
Berger HansReinhard
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20000801440
Subject(s) - couette flow , taylor–couette flow , taylor series , viscoelasticity , mathematics , laminar flow , taylor number , trigonometric series , mathematical analysis , taylor dispersion , flow (mathematics) , mechanics , physics , geometry , thermodynamics , diffusion
The Taylor‐Couette flow of viscous and viscoelastic second‐order fluids is examined by a low‐dimensional truncated expansion of trigonometric functions. Tie influence of gap width between the cylinders is included up to second order. By comparing the results for the critical Taylor number, obtained from the series expansion, with numerical results from linear stability calculation the truncation is validated with an error of less than two percent. The dynamics of the truncated system of ordinary differential equations describe well the transition from laminar to Taylor‐vortex flow, but no further bifurcations to more complex flows are found. The reason for this behaviour is assumed to be due to the omission of non‐axisymmetric disturbances.