On numerical stability analysis of double-diffusive convection in confined enclosures
Bibliographic record
Abstract
The onset of thermosolutal convection and finite-amplitude flows, due to vertical gradients of heat and solute, in a horizontal rectangular enclosure are investigated analytically and numerically. Dirichlet or Neumann boundary conditions for temperature and solute concentration are applied to the two horizontal walls of the enclosure, while the two vertical ones are assumed impermeable and insulated. The cases of stress-free and non-slip horizontal boundaries are considered. The governing equations are solved numerically using a finite element method. To study the linear stability of the quiescent state and of the fully developed flows, a reliable numerical technique is implemented on the basis of Galerkin and finite element methods. The thresholds for finite-amplitude, oscillatory and monotonic convection instabilities are determined explicitly in terms of the governing parameters. In the diffusive mode (solute is stabilizing) it is demonstrated that overstability and subcritical convection may set in at a Rayleigh number well below the threshold of monotonic instability, when the thermal to solutal diffusivity ratio is greater than unity. In an infinite layer with rigid boundaries, the wavelength at the onset of overstability was found to be a function of the governing parameters. Analytical solutions, for finite-amplitude convection, are derived on the basis of a weak nonlinear perturbation theory for general cases and on the basis of the parallel flow approximation for a shallow enclosure subject to Neumann boundary conditions. The stability of the parallel flow solution is studied and the threshold for Hopf bifurcation is determined. For a relatively large aspect ratio enclosure, the numerical solution indicates horizontally travelling waves developing near the threshold of the oscillatory convection. Multiple confined steady and unsteady states are found to coexist. Finally, note that all the numerical solutions presented in this paper were found to be stable.
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How this classification was reachedexpand
Full frame machine prediction
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".