### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 2pUW15. Mode vector parabolic equation.

**Ahmad T. Abawi
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W. A. Kuperman

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*Marine Phys. Lab., Scripps Inst. of Oceanogr., Univ. of California,
San Diego, La Jolla, CA 92093-0238
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**Michael D. Collins
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*Naval Res. Lab., Washington, DC 20375
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**Michael B. Porter
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*New Jersey Inst. of Technol., Newark, NJ 07102
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A mode vector parabolic equation (MVPE) is derived for the propagation of
normal modes in the ocean waveguide. This model, which includes mode coupling,
is a generalization of the adiabatic mode PE [M. D. Collins, 2269
(1993)]. The main features of this model are: (1) It is based on an initial
value differential equation which propagates normal modes rather than a method
that involves matching solutions at interfaces. (2) The solution vector whose
components are the amplitude of the modes is not derived from a procedure
involving a reference wave number and thus each vector component is locally
accurate around each mode. (3) It agrees with previous benchmark solutions. (4)
The model is tractable in three dimensions. MVPE has three parts: Spatial
derivative of the mode amplitudes, eigenvalue, and coupling coefficients
matrices. The latter two are precomputed; the coupling matrix is based on
McDonald's formulation in terms of environmental parameters which is summarized
in [McDonald et al., 2357 (1994)]. The system of equations can either
be solved by matrix inversion or iteration. To illustrate the method, the
solution to the problem of propagation of waves in a two-dimensional wedge is
presented in detail.