Helical Kelvin waves on vortex filaments · E(k) ∝ k⁻³ spectrum · quantum turbulence
Kelvin waves are helical perturbations of a superfluid vortex line. Dispersion: ω_k = (κk²/4π)·ln(1/ka).
Nonlinear interactions cascade energy to smaller scales (larger k), creating a Kelvin wave spectrum E(k) ∝ k⁻³.
This is distinct from Kolmogorov turbulence (k⁻⁵/³). At the quantum scale a ≈ ξ (healing length), phonons are emitted.
The cascade connects the classical Richardson cascade to quantum dissipation via vortex reconnections.