Interaction of Weakly Nonlinear Second Sound Waves with a Vortex Tangle in Helium II

We generalize the analysis of second sound nonlinear waves to include the case in which a turbulent tangle of superfluid vortices is present in the flow. In the limit of weakly nonlinear perturbations the analysis reduces to examining the effect of friction arising from a given vortex tangle on a propagating wave, so that the considered model describes temperature waves propagating in a background of constant quantized vorticity. The obtained analytical solution yields a simple criterion showing that a localized disturbance develops into the temperature discontinuity provided the gradient of the initial disturbance exceeds a critical value; the latter is found as a function of temperature and superfluid vortex line density.