CONTACT AND PRESSURE BALANCE STRUCTURES IN 2-FLUID COSMIC-RAY HYDRODYNAMICS

The role of cosmic-ray-modified contact discontinuities and pressure b alance structures in two-fluid cosmic-ray hydrodynamics in one Cartesi an space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fu ndamental wave modes of the two-fluid cosmic-ray hydrodynamic equation s in the long-wavelength limit consist of the backward and forward pro pagating cosmic-ray-modified sound waves, with sound speed dependent o n both the cosmic-ray and thermal gas pressures; the contact discontin uity; and a pressure balance mode in which the sum of the cosmic ray a nd thermal gas pressure perturbations is zero. The pressure balance mo de, like the contact discontinuity is advected with the background flo w. The interaction of the pressure balance mode with the contact disco ntinuity is investigated by means of the method of multiple scales. Th e thermal gas and cosmic-ray pressure perturbations satisfy a linear d iffusion equation, and entropy perturbations arising from nonisentropi c initial conditions for the thermal gas are frozen into the fluid. Th e contact discontinuity and pressure balance eigenmodes both admit non zero entropy perturbations in the thermal gas, whereas the cosmic-ray- modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmo des, and examples are given in which there is a transfer of entropy be tween the two modes. In particular, N-wave type density disturbances a re obtained which arise as a result of the entropy transfer between th e two modes. A weakly nonlinear geometric optics perturbation expansio n is used to study the long timescale evolution of the short-wavelengt h entropy wave and the thermal gas sound waves in a slowly varying, la rge-scale background flow. The weakly nonlinear geometric optics expan sion is also used to generalize previous studies of a squeezing instab ility for short-wavelength sound waves in the two fluid model, by incl uding a weakly nonlinear wave steepening term that leads to shock form ation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks, and compression and rarefaction wave s with the solar wind termination shock are briefly discussed.