Landauâ€™s equations for the two-fluid model of liquid helium II are us ed as the basis for an investigation of the properties of thermal wave propagation. A number of assumptions are made which reduce the four original equations to a system of two non-linear partial differential equations valid to first order in the relative velocity of the two components. These equations are analogous to Riemannâ€™s equations which describe pressure waves in a classical fluid.

This system of equations, when reduced to just one space dimension is shown to be hyperbolic and a set of characteristics and invariants is found. A particularly simple, one-dimensional problem is then formulated and an explicit solution is given. This solution is then studied in detail to show the distortion of a temperature pulse as it propagates and also to show effects such as non-linear breaking.

Subsequently, the restrictive assumptions are eliminated individually and the equations are then valid to second order in the relative velocity; the effects of including thermal expansion and using the relative velocity as a thermodynamic variable are given. Also, some effects due to the interaction of first and second sound are investigated. In all cases, the results are compared with other results based on equations differing from the Landau equations and with results found by using perturbation techniques.

Finally, equations based on the same Landau equations are derived and discussed which describe steady state shock (discontinuous) solutions.

Suggestions for further theoretical and experimental work are made.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Hsieh, Din-Yu}, }