• The Journal of the Acoustical Society of Korea
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• v.15 no.2
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• pp.72-78
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• 1996

This thesis deals with a method to solve a two-and-one-half-dimensional ($2\frac12$ D) problem, which means that the ocean environment is two-dimensional whereas the source is fully three-dimensionally propagating, including three-dimensional refraction phenomena and three-dimensional back-scattering, using two-dimensional two-way parabolic equation method combined with Fourier synthesis. Two dimensional two-way parabolic equation method uses Galerkin's method for depth and Crank-Nicolson method and alternating direction for range and provides a solution available to range-dependent problem with wave-field back-scattered from discontinuous interface. Since wavenumber, k, is the function of depth and vertical or horizontal range, we can reduce a dimension of three-dimensional Helmholtz equation by Fourier transforming in the range direction. Thus transformed two-dimensional Helmholtz equation is solved through two-way parabolic equation method. Finally, we can have the $2\frac12$ D solution by inverse Fourier transformation of the spectral solution gained from in the last step. Numerical simulation has been carried out for a canonical ocean environment with stair-step bottom in order to test its accuracy using the present analysis. With this spectral parabolic equation method, we have examined three-dimensional acoustic propagation properties in a specified site in the Korean Straits.

• The Journal of the Acoustical Society of Korea
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• v.36 no.1
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• pp.1-11
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• 2017

In this study, novel approximate form of the square-root operator of three dimensional acoustic Parabolic Equation (3D PE) is proposed using a rational approximant for two variables. This form has two advantages in comparison with existing approximation studies of the square-root operator. One is the wide-angle capability. The proposed form has wider angle accuracy to the inclination angle of ${\pm}62^{\circ}$ from the range axis of 3D PE at the bearing angle of $45^{\circ}$, which is approximately three times the angle limit of the existing 3D PE algorithm. Another is that the denominator of our approximate form can be expressed into the product of one-dimensional operators for depth and cross-range. Such a splitting form is very preferable in the numerical analysis in that the 3D PE can be easily transformed into the tridiagonal matrix equation. To confirm the capability of the proposed approximate form, comparative study of other approximation methods is conducted based on the phase error analysis, and the proposed method shows best performance.

• Journal of KSNVE
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• v.7 no.2
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• pp.215-222
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• 1997

The flow and acoustic fields due to a vortex ring interaction with a rigid sphere are simulated numerically. The flow field is regarded as three-dimensional inviscid and incompressible. The vorticity is assumed to be concentrated inside the finite core of vortex filament. The vortex filament curve, described by parabolic blending curve function, is used to effectively solve the modified Biot-Savart equation. The interaction between a vortex ring and a rigid sphere using the parabolic blending curve is calculated. The trajectory of the vortex ring is obtained with several different initial positions between the ring and the sphere. The force variations acting on the sphere are calculated by using the boundary integral method. Finally, we can also obtain the acoustic signals at the far field observation positions from the force variations acting on the rigid surface. We can find that the dipole axis of the directivity patterns are rotated during the interacting phenomena.

• The Journal of the Acoustical Society of Korea
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• v.41 no.2
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• pp.131-142
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• 2022

In order to examine the possibility of horizontal simulations of acoustic waves on the environments of big water depth variations, this study introduces a 3-dimensional model based on the pababolic equation. The model gives approximated solutions by separating the cross- and non cross-terms in the equation. Assuming artificial bathymetry (25 km × 4 km) with a source frequency 75 Hz, the simulations give clear horizontal refractions on the transmission loss distributions. The degree of refractions shows non-linear increase along the propagating range and proportional increase with water depth along the cross range. Another simulations with the real bathymetry (25 km × 8 km) also give clear horizontal refractions. The horizontal distributions present little difference with the depth resolution variations of the same data source because the model gives interpolations over the depth data before simulations. Meanwhile, the horizontal distributions show big difference with those of different data sources.