A low‐dimensional spectral approach for the nonlinear overstability of purely elastic fluids
Bibliographic record
Abstract
Abstract The conditions for the emergence and stability of finite amplitude purely elastic (non‐inertial) overstability are examined for axisymmetric Taylor–Couette flow of an Oldroyd‐B fluid in the narrow‐gap limit. The study is a detailed account of the formulation and results published previously [Khayat, Phys. Rev. Lett. 1997; 78 : 4918]. The flow field is obtained as a truncated Fourier representation for velocity, pressure and stress in the axial direction, and in terms of symmetric and antisymmetric Chandrasekhar functions along the radial direction. The Galerkin projection of the various modes onto the conservation and constitutive equations leads to a closed low‐dimensional nonlinear dynamical system with 20o of freedom. In contrast to our previous model that was based on the simplifying rigid‐free boundary conditions [Khayat, Phys. Fluids A 1995; 7 : 2191], the present formulation incorporates the more realistic rigid–rigid boundary conditions, and is capable of capturing quantitatively the flow sequence observed in the experiment of Muller et al. [ J. Non‐Newtonian Fluid Mech. 1993; 46 : 315] for a highly elastic (Boger) fluid under conditions of negligible inertia. Existing linear analysis results are first recovered by the present formulation, which predict the exchange of stability between the circular Couette flow and oscillatory Taylor vortex flow via a postcritical Hopf bifurcation as the Deborah number exceeds a critical value. The stability conditions of the limit cycle are determined using the method of multiple scales. The present nonlinear theory predicts, as experiment suggests, the growth of oscillation amplitude of the velocity and the emergence of higher harmonics in the power spectrum as the Deborah number increases. Good agreement is obtained between theory and experiment. Copyright © 2002 John Wiley & Sons, Ltd.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
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