Shock waves in superfluid helium

Exact solutions of the equations of motion of liquid helium II can be compared to experiments to test Landau's two-fluid theory. The best flows with which to conduct such tests are those in which amplitudes and gradients are large and in which the calculations and measurements are free from wall effects, e.g., shock waves. The four fundamental conservation equations of superfluid mechanics have been 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 shocks. The results are compared to previous analytical approximate solutions to test the validity of those approximations. 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