On the possibility of representing an acoustic field in shallow water as the sum of normal modes and quasimodes

Abstract

Using the example of a shallow-water acoustic waveguide with a homogeneous water layer of constant thickness H lying on a homogeneous fluid absorbing half-space (bottom), we obtain estimates of distance r from a source, for which it is possible to ignore the continuous spectrum for the mode description of the depth dependence of the intensity of a low-frequency sound field in the bottom layer. We have compared two discrete representations of the field using (1) the total set of normal modes and (2) the total set of normal modes and quasimodes. It is shown that in the case when there is at least one normal mode in the channel, additional allowance for quasimodes makes it possible by an order of magnitude to approximate the boundary of applicability of mode theory and on average establish it at a level of r ~ H or less. We explain the functional dependences of the contribution of the continuous spectrum to the total field on the waveguide parameters and find the conditions of its minimization. We present examples of description of the field in the bottom, where the advantage of using quasimodes at short distances is also demonstrated.