Discontinuity Evolution and Sonic Propagation for Superfluidity Hydrodynamics with Small Superfluid Entropy

Abstract

In this paper, we have studied discontinuity evolution and sonic propagation for the two-fluid model with small superfluid entropy in the framework of hydrodynamics. General features of the transverse mode and the longitudinal mode are provided. The fourth sound and the sixth sound are identified as the propagation of discontinuity, in agreement with earlier theoretical studies. Moreover, the growth equation is obtained to describe the decay and growth of the discontinuity propagating along its normal trajectory. The solution is in an integral form and various cases are discussed. Important discriminations between the case of fourth sound and that of sixth sound are also presented, which may be meaningful for future's experiments to identify the sixth sound and the small superfluid entropy.