Properties of longitudinal flux tube waves - II. Limiting shock strength behavior

We extend our previous work on analytic evaluations of properties of longitudinal tube waves to waves propagating in gravitational atmospheres. We derive an expression for the limiting shock strength and discuss the behavior of the shock strength in tubes of different geometry. It is found that a height-independent value for the limiting strength is attained for constant cross-section tubes and exponential tubes, whereas for wine-glass tubes the limiting shock strength increases with height due to the increase of the tube cross section. The limiting shock strength is well reproduced by time-dependent Simulations. The derived limiting shock strength as well as the energy dissipation rate of the waves show significant similarities to acoustic waves. The limiting shock strength allows to estimate the heating potential of waves in the absence of detailed time-dependent computations.