A cylindrical sound pulse in a rotating gas

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Abstract
This paper deals with the propagation of a sound pulse into a gas which initially has solid-body rotation and constant temperature, the initial pressure and density increasing outwards like ex, where x is the square of a certain dimensionless radial co-ordinate. The perturbations are due to a source-like disturbance on the axis of symmetry, which begins to act at time t = 0: most attention is paid to source strengths which vary in time like a Dirac pulse or a step function, but the following remarks apply generally.Immediately behind the wave front the perturbation velocity and temperature decay like e-½x, while the (absolute) perturbation pressure and density grow like e½x (the relative pressure and density increments, which are referred to local conditions in the undisturbed state, then also decay like e-½x). The rotation also introduces oscillations in flows which, with the same disturbance at the origin and no rotation, would vary monotonically with time at a given point.

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