Numerical computation of a thermal shock wave in He II

The application of a direct numerical computation to superfluid phenomena was attempted. The propagation of a thermal shock wave was numerically simulated by applying a finite-difference method to the two-fluid equation for superfluid helium (He II). Typically, three types of thermal shock waves, namely a frontal shock, a back shock and a double shock, are well simulated, all of which grew from a finite-amplitude second sound wave. The result, however, suggested the necessity for introducing the effect of the interaction of a shock with a tangled mass of quantized vortices to the governing equation in the breakdown state, i.e. in the superfluid turbulent situation. The effect was taken into account on the basis of the Gorter-Mellink mutual friction formula, or on the basis of the equation of the vortex line density evolution proposed by Vinen. The computational results were found to agree qualitatively with experimental data.