Backscattering from empty and water-filled tilted cylindrical shells due to leaky helical flexural waves: Comparison and ray theory

Abstract

For tilt angles smaller than the meridional ray coupling condition previously investigated [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785–794 (1998)], helical rays on empty and water-filled steel shells can significantly enhance the backscattering. These contributions are compared and modeled in the present work. Such contributions in the water-filled case are found to be weaker in amplitude, which is to be expected since additional energy is lost through radiation leaked to the inner fluid. A modified ray theory taking into account the increased radiation damping was compared with experimental results for the earliest helical wave arrival, yielding satisfactory agreement. However, the energy lost to the interior of the shell may be at least partially recovered, as internal rays can excite additional leaky waves on the shell. Contributions from rays with one internal chord inside the cylinder were superposed with those of the first helical wave, and the resulting backscattering amplitude was nearly that of the air-filled case for the first helical wave alone. This shows that we may regard the ray theory for the empty shell as an upper bound for corresponding amplitudes observed in the water-filled case. [Work supported by ONR.]