Two-dimensional scattering from an impenetrable cylindrical obstacle in an acoustic quarterspace

The problem of sound scattering by an infinitely long hard or soft circular cylindrical obstacle suspended near a rigid corner is investigated. The separation of variables technique, the appropriate wave field expansions and the method of images along with the translational addition theorem for cylindrical wave functions are used to derive a closed-form analytical solution in form of infinite series. The analytical results are illustrated with a numerical example in which the cylindrical obstacle is positioned near the rigid boundary of a water-filled acoustic quarter-space. The backscattering form function amplitude and spatial distribution of the total acoustic pressure are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence and proximity of the cylinder to the rigid boundary are examined. Limiting case involving an infinite cylinder in an acoustic halfspace is considered and fair agreement with a well-known solution is established.