885095985

TUESDAY AFTERNOON, 30 APRIL 1991

LIBERTY B, 1:25 TO 4:45 P.M.

Session 3UW

Underwater Acoustics: Propagation

Evan K. Westwood, Chair

Applied Research iMhoraiories, Uniuersity of Texas, Austin, Texas 78713

Chair*s Introduction—1:25

Contributed Papers

1:30

3UW1. A modificd perturbation approach for calculating the vertical wave function required in normal modę theory. Robert Zingarelli and M. F. Wcrby (NOARL, Theorel. Acoust. Codę 221, Stennis Space Center, MS 39529)

Perturbation approaches are useful when one wishes to solve a problem that does not difler significantly from a known solution. The con-ventional approach to derive perturbation methods is to begin with a solvable solution x, and then to cxpand the desired solution in terms of first- and higher-order contributions of the perturbing component— with a smali coefficient €—which differs from the exact solution only by the perturbing component. Then first-order perturbation theory is ob-tained by dropping higher powers of e. In quantum physics this method is referred to as Fermi's second golden rulc. This method can often fail as will be demonstrated and it can lead to erroneous results. This work reports on a new and refined perturbation method based on complete-ness considcrations in which the exact expansion solution in matrix form is set up. Gauss-Seidel iteration is then employed and shows that the first iteration leads to an improved first-order perturbation theory, the sccond iteration leads to an improved second-order perturbation theory, etc. The method is illustrated with a few examples in which the old and new methods are compared with the exact solution for the case of vertical wave functions for variable speed profiles perturbed about an isovelocity case.

1:45

3UW2. On calculation of the acoustic field in a water layer with variable depth placed on a liquid half-space. Valery B. Galancnko (Dept. of Acoust., Kiev Polytech. Inst., Prospect Pobedy 39, Kiev, 252056, USSR)

The wave problem for the variable depth Pekeris waveguide with special cross sections is discussed by means of the cross-section method. The wave field is expandcd as the sum of a senes and integrated with a regular kernel or by summing a senes of modę components only. Both are equivalent to the usual expansion as sums of coupled modes and waves of continuous spectra. A system of coupled difTerential and inte-gral equations or an equivalent set of differential equations only is ob-tained. Some numerical rcsults are presented and it is shown that modę reflection coefficients for a near-coast wedge with a typical bottom are less than 0.03 if the incident angle 0 = 0.03 and they inerease to 0.8 when 0 = 60.

2:00

3UW3. A high-order adaptive integration method for wave propagation in range-independent fluid-solid media. Sven Ivansson and llkka Karasalo (Dept. of Hydroacoust. and Seismol., Swedish Dcfence Res. Est., S-17290 Sundbyberg, Swedcn)

A high-order, adaptive method is described for computing the wave field in a laterally homogencous fluid-solid medium by Henkel-transform integration. A technique for numerical quadrature is used, where trapezoidal or Filon sums obtained with scveral step sizes are combined by polynomial or Bulirsch-Stoer rational interpolation to inerease the order of convergence and to obtain error estimates. This techmque is combined with adaptive interval ha!ving, maintaining a hierarchy of subintervals, meshes, and function values in a stack to eliminate duplicate function evaluations. Computational results from an underwater acoustics application are presented, showing impressive gains in efficiency and accuracy in comparison to traditional nonadap-tive methods. Wave-field computations with tight accuracy demands are of interest, specifically in the context of benchmark calculations and program verification. With the method presented, about five additional correct digits are obtained by inereasing the computational work by a factor of two. Of particular interest is the observation that the Filon technique seems really attractive only in conjunction with the adaptive approach.

2:15

3UW4. Simulating acoustic fields with a lattice gas model for waves.

S. K. Numrich, R. A. Krutar, R. K. Squier (U.S. Naval Res. Lab., Washington, DC 20375-5000), and i. Pearson (Los Alamos Natl. Lab., Los Alamos. NM 87545)

Lattice gas modcls have bcen useful in simulating complicated field behavior and arc particularly well suited to take advantage of massively parallel Computer architectures. As an alternativc to the traditional computational methods used in acoustics, a lattice gas model based on the wavc cquation has bccn implcmcntcd on a Omncciion Machinę and used to simulate acoustic phenomena. The model has been successful in simulating independently driven point sources, functioning singly, as pairs and arranged in both traditional linę arrays and a variety of alter-native configurations. The implementation of the model can also handle rigid and pressure release boundaries as well as changes in sound speed. Both scattering and propagation are directly computed in the same model. Once a phenomenon, a boundary condition or sound speed change, has been correctly modeled, it can be placed at any point or in any area anywhere in the field. The model then produces the time evolution of the pressure field evcrywhere in the modeled region. The results are shown as video tapes of that time evolution or snapshots of the entire field at some instant of time. (Work supported by ONT.J

1894

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

121st Meetiog: Acoustical Society of America

1894