A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

Cross Orthogonality Between Eigenfunctions and Conjugate Eigenfunctions of a Class of Modified Helmholtz Operator for Pekeris Waveguide

The eigenfunctions of the modified Helmholtz operator have no orthogonality in a bounded domain with a perfectly matched layer (PML), which makes it difficult to calculate the coordinates under two different local bases when the marching algorithm is applied. In this paper, we derive the conjugate eigenfunctions of the operator and discuss the cross orthogonality between the eigenfunctions and their conjugate eigenfunctions. On the other hand, we derive a simple formula for calculating the coordinates under the local base. The numerical results indicate that this method is effective.

Low frequency bottom reverberation in a Pekeris waveguide with Lambert’s rule

The requirement by modern navies to predict sonar performance in shallow water, whether for use in research, planning or operations, led to an initiative for the validation of reverberation models in the form of two Reverberation Modeling Workshops at the University of Texas at Austin in November 2006 and May 2008 [J. S. Perkins and E. I. Thorsos, Update on the reverberation modeling workshops, J. Acoust. Soc. Am. 126 (2009) 2208]. The problem considered here (Problem XI, from the 2006 workshop) requires the computation of reverberation versus time in a Pekeris waveguide with Lambert scattering from the seabed. Results from eigenray, normal mode and (hybrid) continuum methods are presented and compared for the time window 0.05[Formula: see text]s to 1000[Formula: see text]s after pulse transmission. Approximate analytical solutions are used to provide insight into the expected behavior of the reverberation and establish regimes of validity of numerical models. In situations where the regimes of validity of different methods coincide, the solutions of models applying these methods overlap. The overlapping solutions agree with each other within ±[Formula: see text]0.3[Formula: see text]dB. Their purpose is to provide a baseline against which future model improvements can be assessed and quantified.