Investigation of the viscous reconnection phenomenon of two vortex tubes through spectral simulations
Bibliographic record
Abstract
This paper aims to shed further light on the viscous reconnection phenomenon. To this end, we propose a robust and efficient method in order to quantify the degree of reconnection of two vortex tubes. This method is used to compare the evolutions of two simple initial vortex configurations: orthogonal and antiparallel. For the antiparallel configuration, the proposed method is compared with alternative estimators and it is found to improve accuracy since it can account properly for the formation of looping structures inside the domain. This observation being new, the physical mechanism for the formation of those looping structures is discussed. For the orthogonal configuration, we report results from simulations that were performed at a much higher vortex Reynolds number (ReΓ ≡ circulation/viscosity = 104) and finer resolution (N3 = 10243) than previously presented in the literature. The incompressible Navier-stokes equations are solved directly (Direct Numerical Simulation or DNS) using a Fourier pseudospectral algorithm with triply periodic boundary conditions. The associated zero-circulation constraint is circumvented by solving the governing equations in a proper rotating frame of reference. Using ideas similar to those behind our method to compute the degree of reconnection, we split the vorticity field into its reconnected and non-reconnected parts, which allows to create insightful visualizations of the evolving vortex topology. It also allows to detect regions in the vorticity field that are neither reconnected nor non-reconnected and thus must be associated to internal looping structures. Finally, the Reynolds number dependence of the reconnection time scale Trec is investigated in the range 500 ≤ ReΓ ≤ 10 000. For both initial configurations, the scaling is generally found to vary continuously as ReΓ is increased from Trec∼ReΓ−1 to Trec∼ReΓ−1/2, thus providing quantitative support for previous claims that the reconnection physics of two vortices should be similar regardless of their spatial arrangement.
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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 | 0.000 |
| 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".