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ACOUSTIC DETECTION PREDICTION STUDIES. PART III. NORMAL MODE THEORY POINT SOURCE,
GENERAL DYNAMICS GROTON CT ELECTRIC BOAT DIV
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HIS REPORT PRESENTS A CONSOLIDATION OF WORK ON THE NORMAL MODE SOLUTIONS OF THE COMPLEX WAVE EQUATION FOR UNDERWATER SOUND PROPAGATION AND EXTENDS THIS WORK TO INCLUDE A GENERALIZED VELOCITY-DEPTH PROFILE. In order to make the analysis tractable for arbitrary sound velocity profiles, the total water depth is characterized by separation into regions dependent on the shape of the velocity profile. Solutions of the wave equation for velocity potential are developed by the standard separation of variables technique for partial differential equations. This results in the solution being expressed as a product of Bessel functions, or more explicitly, Hankel functions of the first and second kind, and of a function of the depth variable obtained by use of the Wenzel-Kramers-Brillouin WKB method. Calculation of the velocity potential from the theoretical solutions, and sound intensity, which is proportional to the square of the absolute value of the potential, requires knowledge of the frequency of the sound, source depth, and velocity as a function of depth. No specific calculations or applications are given. Author
APPROVED FOR PUBLIC RELEASE