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

## 2pUW16. Application of the mode vector parabolic equation to the
3-dimensional wedge problem.

**Ahmad T. Abawi
**
W. A. Kuperman

**
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*Marine Phys. Lab., Scripps Inst. of Oceanogr., Univ. of California, San
Diego, La Jolla, CA 92093-0238
*

*
*
The MVPE [Abawi et al., this session] is applied to the problem of
propagation of waves in a 3-dimensional coastal wedge and the results are
compared with those when horizontal coupling is neglected and with the results
obtained from conventional 3-dimensional methods. The components of the
solution vector are the amplitudes of the vertical modes which are coupled in
both range and azimuth. The coupling matrices for both range and azimuth are
precomputed by the method summarized in [McDonald et al., 2357
(1994)]. In the absence of mode coupling, the solution reduces to the solution
of the adiabatic mode parabolic equation [M. D. Collins, 2269 (1993)].
The system of equations are numerically solved by the Crank--Nicholson finite
difference method. For a single vertical mode, this system of equations closely
resembles a system of discretized parabolic equation in range and azimuth. For
multiple modes, the matrices involved are band diagonal with the coupling
matrices appearing in their diagonal. The size of these matrices are thus equal
to the number of points in azimuth times the number of vertical modes. When the
physics of the problem is contained in a subset of coupled modes, this method
offers additional advantages in numerical computation over the conventional
3-dimensional methods.