The nonlinear evolution of internal tides. Part 2. Lagrangian transport by periodic and modulated waves
Bibliographic record
Abstract
We examine Lagrangian transport by a nonlinearly evolving vertical mode-1 internal tide in non-uniform stratification. In a companion paper (Sutherland & Dhaliwal, J. Fluid Mech., 2022, in press) it was shown that a parent internal tide can excite successive superharmonics that superimpose to form a solitary wave train. Despite this transformation, here we show that the collective forcing by the parent wave and superharmonics is effectively steady in time. Thus we derive relatively simple formulae for the Stokes drift and induced Eulerian flow associated with the waves under the assumption that the parent waves and superharmonics are long compared with the fluid depth. In all cases, the Stokes drift exhibits a mixed mode-1 and mode-2 vertical structure with the flow being in the waveward direction at the surface. If the background rotation is non-negligible, the vertical structure of the induced Eulerian flow is equal and opposite to that of the Stokes drift. This flow periodically increases and decreases at the inertial frequency with maximum magnitude twice that of the Stokes drift. When superimposed with the Stokes drift, the Lagrangian flow at the surface periodically changes from positive to negative over one inertial period. If the background rotation is zero, the induced Eulerian flow evolves non-negligibly in time and space for horizontally modulated waves: the depth below the surface of the positive Lagrangian flow becomes shallower ahead of the peak of the amplitude envelope and becomes deeper in the lee of the peak. These predictions are well-captured by fully nonlinear numerical simulations.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 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".