THE COMPRESSION WAVE PRODUCED BY A HIGH-SPEED TRAIN ENTERING A TUNNEL

An analytical investigation is made of the compression wave produced w hen a highspeed train enters a tunnel. The wave propagates ahead of th e train within the tunnel at about the speed of sound. In very long tu nnels it is transformed by nonlinear steepening into a shock whose amp litude is about 1 or 2% of atmospheric pressure. The emergence of the shock from the far end of the tunnel produces an environmental disturb ance analogous to the sonic boom generated by an aircraft in supersoni c flight. In this paper the train is modeled by a continuous distribut ion of monopole sources whose strengths are determined by the train no se 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 ca n 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 an d bridge structures. Detailed predictions are given for axisymmetric ' trains' entering a long circular cylindrical tunnel. The results are f ound to be in excellent agreement with experimental data. for this con figuration available in the literature.