Numerical estimates of acoustic fields in the ocean generated by moving airborne sources

Abstract

We investigate the underwater acoustic field in the stratified ocean generated by moving in the air sources. We obtain asymptotic formulas expressed in terms of the retarded time and the Doppler-shifted frequency. The spectral parameter power series method is implemented to find the wave numbers of the propagating modes, their group velocity and an analytic form of the acoustic field in the ocean. Some numerical results are presented. ARTICLE HISTORY

Spectral parameter power series representation for solutions of linear system of two first order differential equations

“…In contrary, Dirac-based approach requires only O(n) steps greatly reducing computation time if one needs large number of eigenvalues. We would like to point out that the method proposed in [16] is better suited for computing large sets of eigenvalues, nevertheless the SPPS representation is simpler and still being used for numerous applications, see, e.g., [4], [5], [6], [23], [26].…”

“…The spectral parameter power series (SPPS) representation for solutions of second-order linear differential equations [14], [17] has proven to be an efficient tool for solving (analytically and numerically) and studying a variety of problems, see the review [13] and recent papers [4], [5], [6], [11], [23], [26]. The SPPS method starts with a non-vanishing solution of the equation for one fixed value of the spectral parameter and by performing a series of recursive integrations produces coefficients of the Taylor series of the solution with respect to the spectral parameter.…”