Trapped internal waves over topography: Non-Boussinesq effects, symmetry breaking and downstream recovery jumps
Bibliographic record
Abstract
It is well-known that in certain parameter regimes, the steady flow of a density stratified fluid over topography can yield large amplitude internal waves. We discuss an embedded boundary method to solve the Dubreil-Jacotin-Long (DJL) equation for steady-state, supercritical flows over topography in an inviscid, stratified fluid. The DJL equation is equivalent to the full set of stratified steady Euler equations and thus the waves we compute are exact nonlinear solutions. The numerical method presented yields far better scaling with increase in grid size than other iterative methods that have been used to solve this equation, and this in turn allows for a more thorough exploration of parameter space. For waves under the Boussinesq approximation, we contrast the properties of trapped waves over hill-like and valley-like topography, finding that the symmetry of freely propagating solitary waves when the stratification is reflected across the middepth is not present for trapped waves. We extend the derivation of the DJL equation to the non-Boussinesq case and discuss the effect of the new, non-Boussinesq terms on the structure of the trapped waves, finding that the sharp transition between large and small amplitude waves observed under the Boussinesq approximation is much more gradual when the Boussinesq approximation is relaxed. Finally, we demonstrate the existence of asymmetric steady states over hill-like topography where the flow is subcritical upstream of the topography but transitions to supercritical somewhere over the hill. Waves in this new class of exact solutions are related to so-called downstream recovery jumps predicted on the basis of hydrostatic (shallow water) theories, but when breaking does not occur the recovery jump does not stop propagating downstream and an asymmetric state across the topography maximum is reached for long times.
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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| 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
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".