Towards the Inviscid Limit: A New Perspective on TKE in Forced Burgers Turbulence
Bibliographic record
Abstract
In the realm of fluid dynamics, understanding the details of turbulent kinetic energy (TKE) behavior under varying conditions remains crucial.This study revisits the classic problem of forced Burgers turbulence, specifically examining the influence of Reynolds number on TKE, in light of historical assertions that TKE is independent of Reynolds number variations (if they are large enough).Contrary to the long-standing claims made by D.T.Jeng and W.C.Meecham in 1972, our investigation discusses a nuanced relationship between Reynolds number and TKE.By employing sinusoidal forcing with a zero initial velocity field, we carefully analyse the transition of TKE as the system approaches the limit of vanishing viscosity.Our results unambiguously indicate that, with an increase in Reynolds number, TKE exhibits a convergence towards the inviscid solution, suggesting a dependence on viscosity that has not been fully acknowledged in previous studies.This perspective enriches our understanding of turbulence dynamics by highlighting the critical role of viscosity, as it diminishes.Our research serves as a cornerstone for re-evaluating theoretical approaches to turbulence, particularly in modelling and simulation frameworks that have probably overlooked the subtleties of viscosity's influence on TKE.By drawing attention to these complexities, we pave the way for more accurate predictions and a deeper comprehension of turbulent flows across a wide spectrum of applications.
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 | 0.000 |
| 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".