  Kelvin waves (kelvons)--helical waves on quantized vortex lines--are the
normal modes of vortices in a superfluid. At zero temperature, the only
dissipative channel of vortex dynamics is phonon emission. Starting with the
hydrodynamic action, we derive the Hamiltonian of vortex-phonon interaction,
thereby reducing the problem of the interaction of Kelvin waves with sound to
inelastic elementary excitation scattering. On the basis of this formalism, we
calculate the rate of sound radiation by superfluid turbulence at zero
temperature and estimate the value of short-wavelength cutoff of the turbulence
spectrum.
