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Kolmogorov's 5/3 law and beyond

Turbulence Scaling

Can the empirically observed scaling exponents of high-Reynolds-number turbulence be derived from first principles?

Progress

40%

Framework paper drafted

Current approach

Grade decomposition of the energy cascade; scaling exponents emerge from grade-truncation at fixed Reynolds number.

Status notes

Connects to Navier–Stokes work via shared grade decomposition. Anomalous exponents not yet derived.

Direct contributions

1 paper

Physics Working Paper Lean

Turbulence Scaling Laws from the Grade Equation: Kolmogorov Spectrum and Intermittency from Analyticity

We derive the Kolmogorov energy spectrum $E(k) \sim \varepsilon^{2/3} k^{-5/3}$ and anomalous intermittency corrections to the structure function exponents $\zeta_p$ from the Grade Equation — a universal structural decomposition theorem for analytic dynamical systems. The derivation proceeds in three steps.

12,483 words 3 claims