Cascade process of vortex tangle dynamics in superfluid ${}^4$He without mutual friction

Recently the Kelvin wave cascade process in superfluid ${}^4$He at very low temperatures was discussed. In this mechanism, the dynamics of the waves on the vortex lines plays an important role. In order to investigate this mechanism, we study numerically the dynamics of the waves on the reconnected vortex lines using the full Biot-Savart law. This work shows the reconnection of two vortices leads to the waves on the reconnected vortex lines. To discuss the energy of the waves on the vortex lines, the energy spectrum of the superflow before and after the reconnection is calculated.