The compression wave generated by a high-speed train entering a tunnel is studied theoretically and experimentally. It is shown that the pressure rise across the wavefront is given approximately by

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where ρo, U, M, [Ascr ]o and [Ascr ] respectively denote the mean air density, train speed, train Mach number, and the cross-sectional areas of the train and the uniform section of the tunnel. A monopole source representing the displacement of air by the train is responsible for the main pressure rise across the wave, but second-order dipole sources must also be invoked to render theoretical predictions compatible with experiment. The principal dipole is produced by the compression wave drag acting on the nose of the train. A second dipole of comparable strength, but probably less significant in practice, is attributed to ‘vortex sound’ sources in the shear layers of the back-flow out of the tunnel of the air displaced by the train.

Experiments are performed that confirm the efficacy of an ‘optimally flared’ portal whose cross-sectional area S(x) varies according to the formula

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where x is distance increasing negatively into the tunnel, [lscr ] is the prescribed length of the flared section, and [Ascr ]E is the tunnel entrance cross-sectional area, given by

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This portal is predicted theoretically to cause the pressure to increase linearly with distance across a compression wavefront of thickness ∼ [lscr ]/M, which is very much larger than in the absence of flaring. The increased wave thickness and linear pressure variation counteract the effect of nonlinear steepening of the wave in a long tunnel, and tend to suppress the environmentally harmful ‘micro-pressure wave’ radiated from the far end of the tunnel when the compression wave arrives. Our experiments are conducted at model scale using axisymmetric ‘trains’ projected at U ∼ 300 k.p.h. (M ≈ 0.25) along the axis of a cylindrical tunnel fitted with a flared portal. The blockage [Ascr ]o/[Ascr ] = 0.2, which is comparable to the larger values encountered in high-speed rail operations.