Prolongation of the rise time of the compression wave generated by a high-speed train entering a tunnel

An analysis is made of the large-amplitude compression wave formed when a high speed train enters a tunnel whose entrance is 'vented' by perforations in the tunnel walls. The vents are designed to increase the rise time of the wave in order to alleviate shock formation in a long tunnel by progressive nonlinear steepening of the wavefront. The wave emerges from the far end as an impulsive 'micro-pressure wave', and the presence of shocks increases its propensity to cause significant structural damage and environmental annoyance. Detailed predictions are given for a 'tunnel' consisting of a thin-walled circular cylinder, of the type frequently used in model-scale experiments. A finite length of the cylinder entrance is perforated with an axisymmetric distribution of circular apertures. The apertures are equivalent to a distribution of sources, and it is shown that the profile of the compression wavefront can be greatly extended, so that the wave amplitude increases smoothly and linearly, by 'shading' the aperture distribution to make the effective source strengths approximately uniform along the perforated zone. The maximum compression wave rise time that can be obtained by this means is equal to the time of passage of the front of the train through the perforated section.