Bistability and hysteresis induced by form drag in nonlinear subcritical and supercritical double-diffusive Lapwood convection in shallow porous enclosures
Bibliographic record
Abstract
This paper considers natural Lapwood convection in a shallow porous cavity filled with a binary fluid. The investigation is mainly focused on the nonlinear behaviour of subcritical convection and the bistability phenomenon caused by the combined effects of porous medium form drag and double-diffusive convection. The Dupuit–Darcy model, which includes the effect of the form drag at high Reynolds flow, is used to describe the convective flow in the porous matrix. The enclosure is subject to vertical temperature and concentration gradients. The governing parameters of the problem under study are the Rayleigh number, $R_{T}$ , the buoyancy ratio, $\unicode[STIX]{x1D711}$ , the Lewis number, $Le$ , the form drag coefficient, ( $1/P_{r}^{\ast }$ ), where $P_{r}^{\ast }$ is a modified Prandtl number, and the aspect ratio of the cavity, $A$ . An analytical solution, valid for shallow enclosures ( $A\gg 1$ ), is derived on the basis of the parallel flow approximation. Among other things, this work focuses on the effects of the form drag parameter on the convective flows that occur when the thermal and solutal buoyancy forces are opposing each other. For this situation, in the absence of the form drag effect, the onset of motion is known to occur at a subcritical Rayleigh number, $R_{TC}^{sub}$ , which depends upon $\unicode[STIX]{x1D711}$ and $Le$ only. The effects of $P_{r}^{\ast }$ on $R_{TC}^{sub}$ and on the subsequent convective heat and mass transfer rates are found to be significant. A new bistability phenomenon arises when the onset of subcritical convection is shifted close to or beyond the threshold of supercritical convection, whether heating or cooling isothermally or upon applying constant heat and solute fluxes, regardless of the enclosure aspect ratio value. It is demonstrated, on the basis of linear stability theory, that the form drag parameter has a stabilizing effect and considerably affects the threshold for Hopf bifurcation, $R_{TC}^{Hopf}$ , which characterizes the transition from steady to unsteady convection. In the range of governing parameters considered in this study, the heat, solute and flow characteristics predicted by the analytical model are found to agree well with the numerical study of the full governing equations.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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
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