Decay of superfluid turbulence at a very low temperature: The radiation of sound from a Kelvin wave on a quantized vortex

In an earlier paper [Phys. Rev B 61, 1410 (2000)] concerned generally with grid turbulence in superfluid ${}^{4}\mathrm{He},$ we discussed the mechanisms by which such turbulence might decay at a very low temperature. One such mechanism involves generation of Kelvin waves on quantized vortex lines that are present in the turbulent superfluid component, and the loss of energy from these waves by radiation of sound. An inadequate theory of this radiative process is replaced here by a more rigorous treatment. The speculative conclusions in our earlier paper are not substantially changed.