Wave Turbulence — Weak Kinetic Theory

Weakly nonlinear waves redistribute energy across wavenumbers via resonant four-wave interactions. The Kolmogorov-Zakharov spectrum n(k) ~ k^-7/3 emerges as energy cascades to high k.

Controls

Nonlinearity ε 0.15 Forcing scale k_f 4 Dissipation 0.04

Total energy: —

KZ slope: —

Step: 0

Energy spectrum E(k).
Green line: KZ prediction k^-7/3.
Resonant interactions:
k₁+k₂=k₃+k₄