Chapter 25: Turbulence: Energy Cascades and Structural Reinterpretation

Turbulence is the most common dynamical regime in the macroscopic universe: stellar convection zones, interstellar gas, accretion disks, and planetary atmospheres are all turbulent. The orthodox Kolmogorov–Obukhov theory (1941) describes turbulence statistically, predicting the k^{-5/3} energy spectrum from dimensional analysis and the assumption of a self-similar inertial range. The theory is spectacularly successful—and entirely phenomenological. It does not explain why the cascade is self-similar, why the exponent is -5/3, or what turbulence is at a structural level.

This chapter reinterprets turbulence within the τ-framework. The Kolmogorov energy cascade becomes a typed budget redistribution: the mobility component μ of the defect tuple transfers budget from large to small primorial scales. The enstrophy cascade is the vorticity dual: the component ν transfers budget from small to large scales. The self-similarity of the inertial range follows from the self-similarity of the primorial tower. The exponent -5/3 is recovered as a consequence of the 4-component budget geometry.

Scope: τ-effective (structural reinterpretation, cascade mechanism); conjectural (quantitative exponents, intermittency corrections).