Thermally Enhanced Motions of Variable‐Inflow Surface Gravity‐Driven Flows
Bibliographic record
Abstract
In this paper, we report on theoretical and numerical studies of models for suddenly initiated variable‐inflow surface gravity currents having temperature‐dependent density functions when these currents are subjected to incoming radiation. This radiation leads to a heat source term that, owing to the spatial and temporal variation in surface layer thickness, is itself a function of space and time. This heat source term, in turn, produces a temperature field in the surface layer having nonzero horizontal spatial gradients. These gradients induce shear in the surface layer so that a depth‐independent velocity field can no longer be assumed and the standard shallow‐water theory must be extended to describe these flow scenarios. These variable‐inflow currents are assumed to enter the flow regime from behind a partially opened lock gate with the lock containing a large volume of fluid whose surface is subjected to a variable pressure. Flow filament theory is used to arrive at expressions for the variable inflow velocity under the assumptions of an inviscid and incompressible fluid moving through a small opening under a lock gate at one end of a large rectangular tank containing the deep slightly more dense ambient fluid. Finding this time‐dependent inflow velocity, which will then serve as a boundary condition for the solution of our two‐layer system, involves solving a forced Riccati equation with time‐dependent forcing arising from the surface pressure applied to the fluid in the lock. The results presented here are, to the best of our knowledge, the first to involve variable‐inflow surface gravity currents with or without thermal enhancement and they relate to a variety of phenomena from leaking shoreline oil containers to spring runoff where the variable inflow must be taken into account to predict correctly the ensuing evolution of the flow.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".