The sensitivity of internal solitary waves to localized patches of mixing
Bibliographic record
Abstract
While most theoretical work on internal waves idealizes the stratification, geophysical stratifications are typically much more complicated. We build on recent work on nearly linear stratifications by adopting perturbations that take the form of a localized patch of mixing. We present a data-centric framework that seeks to identify which locations and widths of a mixing patch yield the largest effect on the structure of exact waves (computed via the Dubreil-Jacotin-Long equation), linear waves (computed via the longwave Taylor-Goldstein equation), and evolving nonlinear waves (via time-dependent simulations using the incompressible Navier-Stokes equations). We find that the vertical structure functions of linear waves are most sensitive to perturbations below (above) the pycnocline when the pycnocline is above (below) mid-depth; furthermore, as the pycnocline approaches mid-depth, the depth of the perturbation layer with the greatest impact approaches the depth of the pycnocline. In contrast, the centre streamwise velocity profile of a DJL wave is perturbed most by layers above (below) the pycnocline when the pycnocline is above (below) mid-depth. Finally, we present the results of simulations of evolving nonlinear waves, where we compare pairs of cases with and without a perturbation layer. Despite the presence of an initial patch of unstable fluid, the perturbation layer is sustained during the simulation; nevertheless, slight Rayleigh-Taylor instabilities are observed within and about the perturbation layer. Modulations in the horizontal velocity field about the leading solitary wave are compared with the results of the linear and DJL analyses.
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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 | 0.006 |
| 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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".