885095986

2:30

3UW5. High resolution and cfficient oceanographic and acoustic modeling of propagation through mesoscale oceanie features. L. S.

Gardincr. B. R. Frcdcrick, T. A. Chmielewski, P. Bilazarian, and W, F. Mitchell (General Electric Co., Adv. Techno]. Lab., ATL Bldg., Moorestown Corp. Ctr., Moorestown, NJ 08057)

A procedurę is presented for combining the output of advanced multilcvel “primitive equation" dynamie oceanographic forecast models with high tidelity underwater acoustic propagation models. This procedurę is appropriate for the dcvelopmcnt of realistic predictions of acoustic transmissions through complicated mesoscale features, such as cur-rents, rings, eddies, and fronts. Eaamples of oceanographic predictions using the Princeton dynamie ocean model dcveloped by Mellor and Blumberg are displayed graphically for a dataset of the Gulf of Mexico. Results pertinent to data interpolation, the identification of mesoscale oceanie features, and 3-D visualization are presented. Ocean data are converted to sound-speed profiles for this region and are intcrfaccd to a range-dependent parabolic equation (PE) propagation loss model. Asa low-frcquency acoustic source is moved successively from shallow to deep water in the Gulf of Mexico, results are given that illustrate large variations in propagation loss to a receiver located in dccp water. The relative contributions of bathymetry and mesoscale oceanie features to these variattons are analyzed. Finaliy, a scheme for speeding up PE calculations by utilizing the massively parallcl computational capabili-lies of the Connection Machinę at GE/ATL is discusscd.

2:45-3:00

Break

3:00

3UW6. Derivation of one-way wave equations for vector wave propagation problems. Louis Fishman (Dept. of Math. and Comp. Sc i., Colorado School of Mines, Golden, CO 80401)

The recent application of pseudodifferential and Fourier integral operators and functional integral methods to the factored scalar Helm-holtz equation has resulted in extended parabolic wave theorics, corrc-sponding path integral Solutions, and a numerical marching algorithm for a variety of acoustic wave propagation problems. These known tcch-niques are applied here to vector wave equations (Maxwel)'s and elas-ticity), resulling in ncw first-order Wcyl pseudodi (teren tial equations, which are recognized as exact one-way wave equations for transversely inhomogeneous environments. Perturbation treatments of the appropriate Weyl composition equations for the operator symbol matrix yicld high-frequency and other asymptotic wave theorics. Unlike the scalar Helmholtz equation casc, the one-way vector equations (and a scalar analog provided by the Klein-Gordon equation of relativistic physics) require the solution of generalized quadratic operator equations. While these operator Solutions do not have a simple formal representation as in the straightforward (acoustic) square root case, they are convenicntly constructed in the Weyl pseudodifferential operator calculus. This is an cxact formulation at the levcl of the wave field—no special symmetry and/or far-field assumptions are madę. (Work supported by NSF, AFOSR, ONR-1

3:30

3UW8. A complex ray method using asymptotic expansions applied to the penetrable wedge. Grant B. Deane (Marinę Phys. Lab., Scripps Inst. of Oceanography, La Jolla, CA 92093)

The acoustic field in a sioping, isovelocity waveguide (the penetrable wedge) is found by extension and application of a complex ray model. The pressure is computed as a sum of ray fields, each of which is expressed as an asymptotic expansion of a piane wavc integral cvaluatcd using the method of steepest descent. A geometrical interpretation of the method is given which should be possible to extend to threc-dimensional environmcnts.

3:45

3UW9. Magnus expansion and split-step PE error analysis. F. J. Ryan (Ocean and Atmos. Sci. Div., Codę 541, Naval Ocean Systems Ctr., San Diego, CA 92152-5000)

A practical problem involved with implementing parabolic wave equation (PE) Computer codes is the optiinal selection of depth mesh and rangę step-size. Efficiency rcquires that a varying rangę step-sizc be used. An objeclive method for automatic rangę step-size selection in split-step PE codes can be derivcd by an error budget analysis based upon the Magnus expansion of an exponential operator. The method will be described and examples shown for PE propagation in range-dependent environments.

3:15

3UW7. Generating eigenray tubes from two Solutions of the wave equation. James B. Bowlin (Woods Hole Oceanographic Inst., Dept. of Appl. Ocean Phys. and Eng., Woods Hole, MA 02543)

A method is presented for calculating the paths taken by sound betwcen a source and receiver. These paths, which are called eigenray tubes. are obtuincd from two Solutions of the wave cquation at finite frequency, one propagated from the source and the other propagated from the receiver. The results are not restricted to the high frequency limit as is the case with classical ray traces. This generalization of classical ray tracing could be an important new tool in acoustic tomog-raphy.

4:00

3UW10. Stability analysis of a higher-order time-domain paraxial approximation. B. J. Orchard, W. L. Siegmann, M. J. Jacobson, G. J. Habetler (Dept. Math. Sci., R.P.I., Troy, NY 12180-3590), and Michac) D. Collins (Naval Rcs. Lab., Washington, DC 20375)

The global and local stability of an nth-order time-domain paraxial approximation (TDPA„) to an acoustic wave equalion (M. D. Collins, J. Acoust. Soc. Am. 86, 1097-1102 (1989)] is resolved. An operator splitting technique and the Trotter product formula are used to deter-mine the conditional (i.e., parameter dependent) stability of the com-plete paraxial operator from the stability of the individual diffractive, refractive, and dissipative components. The local stability of a finite difference implementation of the TDPA„ is analyzed using Von Neu-

1895

J. Acoust. Soc. Am., Vol. 89, No. 4, Pt. 2, April 1991

121 st Meeting: Acoustical Society of America

1895