I. Numerical Solution of the Superfluid Shock Jump Conditions. II. Experimental Investigation of the Liquid Helium II-Vapor Interface

Abstract

Numerical Solution of the Superfluid Shock Jump Conditions The four fundamental conservation equations of superfluid mechanics may be integrated across a one-dimensional discontinuity (shock wave) propagating into undisturbed helium II to yield a set of four algebraic equations (jump conditions) which, when supplemented by thermodynamic state information, establish the equilibrium flow state behind the shock wave for a given wave speed and undisturbed flow state ahead of the shock. These jump conditions have been solved numerically for 19 points on the helium II p-T diagram with upstream Mach number as the independent parameter. Representative results of the calculations are presented for pressure shocks, temperature raising shocks, and temperature lowering shock. The results are compared to previous analytical approximate solutions to test the validity of those approximation. They are also compared to experimental data for shock waves in helium II as a means of testing the correctness of the full, nonlinear two-fluid equations. Experimental Investigation of the Liquid Helium II-Vapor Interface An apparatus was designed and constructed to measure the linear reflection and transmission coefficients for weak second sound shocks impinging upon the liquid-vapor interface of helium II. The measured reflection coefficients reproduce the work of previous authors, giving values which are roughly 20% higher than those predicted by thermodynamic equilibrium theory. The transmitted pressure wave speed was measured, and was found to be sonic within the limits of experimental precision. Therefore strength could not be deduced from time of flight measurements. Direct amplitude measurements of this weak wave were prevented by the film which coats the sensors in the vapor. For these reasons, the attempted transmission coefficient measurements were unsuccessful.