Self‐Similarity and the Evaluation of Long‐Time Nonhydrostatic Effects in Compositionally Driven Gravity Flows in Deep Surroundings
Bibliographic record
Abstract
In the study of compositionally driven gravity currents involving one or more homogeneous fluid layers, it has been customary to adopt the hydrostatic assumption for the pressure field in each layer which, in turn, leads to a depth‐independent horizontal velocity field in each of these layers and significant simplifications to the governing equations. Under this hydrostatic paradigm, each layer will then have its motion governed by the well‐known reduced dimension shallow‐water equations. For the so‐called ‐layer or reduced gravity shallow‐water equations, similarity solutions for fixed volume gravity currents released in rectangular geometry have been found. Very few attempts have been made to evaluate contributions arising from the possible loss of hydrostatic balance in the context of the problems treated using the classic shallow‐water approach. Where such attempts have been pursued, they have usually been carried out in a time‐independent context or using layer‐averaged equations and very small amplitude disturbances. The vast majority of these studies into nonhydrostatic effects do not include any relevant numerical work to assess these effects. In this paper, we develop an approach for evaluating nonhydrostatic contributions to the flow field for bottom gravity currents in deep surroundings and rectangular geometry. Our approach makes no assumptions on the amplitudes of the disturbances and does not depend on layer‐averaging in the governing equations. We seek asymptotic expansions of the solutions to the Euler equations for a shallow fluid by using the small parameter δ2, where δ is the aspect ratio of the flow regime. At leading order the equations enforce hydrostatic balance while those obtained at first order retain certain nonhydrostatic effects which we evaluate. Our method for evaluation of these first‐order contributions employs the self‐similar nature of the solution to the leading‐order equations in the new first‐order equations without any vertical averaging procedures being employed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.003 |
| 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 | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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
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".