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The study demonstrates Kolmogorov scaling using a variational principle in turbulent systems, suggesting implications for energy dynamics.
A variational principle yields the Kolmogorov k−5/3 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 versions. Part of the Functional Stability Theory (FST) programme. Changes in Version 1.3 (March 2026) No substantive changes (already journal-grade). Recompiled with latest cross-references. Changes in Version 1.2 (March 2026) Critical: Fixed placement Changes in Version 1.1 (March 2026) Major: Numerical verification of Theorem 3.1: F[E_K41]=0 exactly, 300/300 perturbation tests confirm strict convexity Major: DFC recast as energetic stability class Major: Finite-N spectral gap via shell-model Markov structure (GOY/SABRA)
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Lukas Geiger (2026) studied this question.
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