Emission of phonons by vortex filaments and the decay of a turbulent state in the Bose condensate

A turbulence decay mechanism in the Bose condensate (superfluid liquid) that is associated with the emission of acoustic waves upon reconnection of vortex filaments is studied. An approach based on the master equation for the length distribution of vortex loops is developed. Evolution equations for the density of the vortex filaments in the quasistationary and non-quasistationary regimes are derived. The decay law is compared to the numerical simulation results.