### ASA 125th Meeting Ottawa 1993 May

## 5pUW4. Exact mode representation of sound propagation in a shallow-water
wedge with a penetrable bottom.

**Dezhang Chu
**

**
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*Dept. of Appl. Ocean Phys. and Eng., Woods Hole Oceanogr. Inst., Woods
Hole, MA 02543
*

*
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A new solution for the acoustic wave propagating in a wedge-shaped
shallow-water waveguide with a penetrable bottom ((rho)[sub 1](not equal
to)(rho)[sub 2], c[sub 1](not equal to)c[sub 2]) is presented. By using a
special transformation of range function (Bessel function), the inherent
nonseparable problem can be converted to a pseudoseparable one. The solution is
exact and is expressed as a summation of wedge mode sets, i.e., each eigenvalue
corresponds to a set of eigenfunctions. There are several advantages of the
present method over the conventional coupling mode method: (1) since the
cylindrical coordinates corresponding to wedge modes are used, the media are
bounded in angular direction 0(implied by)(theta)(implied by)(pi); therefore,
the mode spectrum of the exact solution only contains discrete modes. (2) The
diffracted wave from wedge apex is included automatically. The contribution of
the diffracted wave to the total field is important when kr<<1, where k is the
wave number and r is the range from the wedge apex. (3) The mode coefficients
are obtained through recursive formulas instead of solving M linear equations
simultaneously, where M is the number of modes. When c[sub 1]=c[sub 2], the
problem becomes separable and for each eigenvalue, only the primary
eigenfunction corresponding to a conventional wedge mode remains nonzero.
Hence, the solution smoothly reduces to that for an isovelocity/density
contrast wedge [D. Chu, J. Acoust. Soc. Am. 87, 2442--2450 (1990)]. Numerical
computations are presented to show the effect of mode coupling in terms of
different geometrical and physical parameters.