Ph.D Student Ph.D Thesis Bar-Adon Shulamit Nonlinear Models for Acoustic Wave Propagation in Water Department of Agricultural Engineering ASSOCIATE PROF. Giora Rosenhouse

Abstract

The thesis develops a mathematical model for the underwater acoustic field, caused by an underwater acoustic source, using measurable physical parameters, with expected better accuracy than that of previous models. It is based on the continuity and Euler equations, solved analytically for the general case of an underwater acoustic source without simplifying assumptions such as constant density or small perturbations.

The expression derived for the pressure field depends on density only, varying as a function of both time and position. The research uses the solution of the Euler Equation, commonly used as a flow equation, as a theoretical model to describe the propagation of the acoustic wave at sea.

Since the source effects, the fluid, and their combined influence are included in the solution, its generality leads to cumbersome and lengthy expressions, functions of time and location that are not necessarily direct or even linear. Certain effects are not known specifically (e.g., the effect of the source, which decays with distance linearly, exponentially, or otherwise). Consequently, the expression driven here is not limited to any particular mathematical expression.

Incorporating the continuity equation into an Euler equation general solution yields the pressure field equation as a function of density only, which is measurable and thus applicable. The solution is a general relation between density, velocity and the pressure field, following the corollary from the Stone-Weierstrass Theorem.

The generality and flexibility of the final equation can be applied to various fluids as well as a wide variety of acoustic phenomena. As the two basic equations, i.e., the equation of continuity and the Euler equation, are the basic equations of fluid mechanics, the solution obtained can be applied also in this area.

In cases where experiments confirm that the model is sufficiently accurate, its application to practical problems is likely to be relatively simple as it is based only on density parameters, changes in the density, and their influences.

The solution is illustrated for two cases.