Anomalous Dissipation and the Turbulent Cascade: A Variational Free-Energy Derivation of Kolmogorov Scaling
Fuente:
Zenodo
Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
|
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866902332075147264 |
|---|---|
| author | Geiger, Lukas |
| author_facet | Geiger, Lukas |
| contents | A variational principle yields the Kolmogorov energy spectrum as the unique minimiser of a scale-resolved free-energy functional. Anomalous dissipation follows under the Downhill Flux Condition (DFC). The DFC hierarchy provides a concrete DNS falsification protocol. Published in English and German. <p><strong>Changelog:</strong> </p><h3>Changes in Version 1.1 (March 2026)</h3><p>Numerical validation + new theoretical results.</p><ul><li><strong>Major:</strong> Numerical verification of Theorem 3.1: F[E_K41]=0 exactly, 300/300 perturbation tests confirm strict convexity</li><li><strong>Major:</strong> DFC recast as energetic stability class (not pointwise axiom)</li><li><strong>Major:</strong> Finite-N spectral gap via shell-model Markov structure (GOY/SABRA)</li><li><strong>Minor:</strong> AI disclosure, location standardized, De Lellis-Brue bibitem</li><li><strong>DE/EN:</strong> Both versions synchronized</li></ul><p></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19087413 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Anomalous Dissipation and the Turbulent Cascade: A Variational Free-Energy Derivation of Kolmogorov Scaling Geiger, Lukas A variational principle yields the Kolmogorov energy spectrum as the unique minimiser of a scale-resolved free-energy functional. Anomalous dissipation follows under the Downhill Flux Condition (DFC). The DFC hierarchy provides a concrete DNS falsification protocol. Published in English and German. <p><strong>Changelog:</strong> </p><h3>Changes in Version 1.1 (March 2026)</h3><p>Numerical validation + new theoretical results.</p><ul><li><strong>Major:</strong> Numerical verification of Theorem 3.1: F[E_K41]=0 exactly, 300/300 perturbation tests confirm strict convexity</li><li><strong>Major:</strong> DFC recast as energetic stability class (not pointwise axiom)</li><li><strong>Major:</strong> Finite-N spectral gap via shell-model Markov structure (GOY/SABRA)</li><li><strong>Minor:</strong> AI disclosure, location standardized, De Lellis-Brue bibitem</li><li><strong>DE/EN:</strong> Both versions synchronized</li></ul><p></p> |
| title | Anomalous Dissipation and the Turbulent Cascade: A Variational Free-Energy Derivation of Kolmogorov Scaling |
| url | https://doi.org/10.5281/zenodo.19087413 |