The compression wave produced by a high-speed train entering a tunnel

An analytical investigation is made of the compression wave produced when a highspeed train enters a tunnel. The wave propagates ahead of the train within the tunnel at about the speed of sound. In very long tunnels it is transformed by nonlinear steepening into a shock whose amplitude is about 1 or 2% of atmospheric pressure. The emergence of the shock from the far end of the tunnel produces an environmental disturbance analogous to the sonic boom generated by an aircraft in supersonic flight. In this paper the train is modeled by a continuous distribution of monopole sources whose strengths are determined by the train nose profile. The initial wavelength greatly exceeds the tunnel diameter at typical train Mach numbers of about 0.2 and the analytical problem of wave generation by interaction of the monopoles with the tunnel can be solved by use of a compact Green's function. The functional form of Green's function depends on the tunnel entrance geometry and on the proximity of other inhomogeneities, such as embankments, buildings and bridge structures. Detailed predictions are given for axisymmetric 'trains' entering a long circular cylindrical tunnel. The results are found to be in excellent agreement with experimental data. for this configuration available in the literature.