Weak Wave Turbulence

Nonlinear dispersive waves interact via resonant triads (3-wave) or quartets (4-wave). Energy cascades through scales following the Zakharov kinetic equation. Power-law spectrum E(k) ~ k^-α analogous to Kolmogorov.

Resonance: ω₁ + ω₂ = ω₃, k₁ + k₂ = k₃. Zakharov (1965): exact power-law stationary solutions.

Nonlinearity ε 0.10 Dispersion α 1.00 Forcing k 2 Damping scale 24

Energy spectrum log E(k) vs log k

Spectral slope: measuring...

Kolmogorov-Zakharov slope: E(k)~k^-4 (deep water gravity)