Acoustic Propagation in a Wedge-Shaped Ocean with Perfectly Reflecting Boundaries

The notion of environmentally adaptive, curvilinear, uncoupled normal modes is developed by writing the Helmholtz equation in curvilinear coordinates. The depth-dependent vertical scaling function provides some coordinate freedom missing from the Cartesian formulation. This freedom permits adaptation of the normal mode approach to variable depth and variable sound-speed problems for environments that change slowly in range. A W.K.B. approximation to the eigenfunctions shows modal decoupling can be realized when the vertical scaling function is chosen equal to the reciprocal of the depth-dependent vertical wave number of the lowest mode. Numerical simulations demonstrate that a requirement for constant inter-modal ratios of the vertical wave number is valid throughout several wedges with different bottom boundary conditions. The horizontal refraction of such modes agrees closely with analytic solutions. For a wide-angle wedge, the acoustic field agrees qualitatively well with the benchmark solution of Dean and Buckingham [J. Acoust. Soc. Am. 93, 1319-1328 (1993)].

Section: Introductionmentioning

confidence: 93%

Environmentally adaptive wedge modes

Mignerey

2000

“…For evolution along a gradient, as will be seen, the physical coordinates look like angular coordinates in a wedge, and the correct solution should look locally like some wedge mode. 21,22 The same interference effects that result in geometric dilution of wedge modes necessarily also affect the phase advance. It will be seen that the latter effect can be incorporated by effectively shifting n(x) by terms proportional to its range derivatives.…”

Section: One-way Evolutionmentioning

confidence: 99%

Benchmarking virtual backscatter in parabolic evolution

Smith

1997

A perturbative method has recently been presented for improving parabolic equations to account for intermediate backscattering induced by slow range dependence of the acoustic index of refraction. In realistic cases, it yields solutions to the full wave equation from a truly one-way algorithm, and generalizes a number of special results of this kind which have been known for many years. Numerically validating the method, though, involves certain unique difficulties, because the physical corrections it introduces to local evolution are accompanied by medium dependence of the projection operator that defines the input and output wave fields. A method for benchmarking is presented here, which permits numerical isolation of range-local effects from the endpoint projections, and also from particular details of the choice of one-way model used. To illustrate that the physical content of the new terms can be sensibly validated in this manner, an exact solution is considered, where they are shown to correct the ''idealized'' one way equation on which current parabolic algorithms are based. This solution is used to illustrate the relation of energy conservation to one-way evolution in the presence of slow range dependence. In particular, it demonstrates that energy conservation alone is not a sufficient requirement to produce correct parabolic evolution, even when it pertains.

“…Such a geometry approximates the region of an ocean over a continental slope, and a significant effort has gone into studying this problem. [10][11][12][13][14][15][16][17][18][19][20][21] Wedge-shaped waveguides find applications in other fields as well, such as electromagnetics. [7][8][9][22][23][24] The case of a point source in a three-dimensional wedge with perfectly reflecting boundaries and homogeneous medium leads to a separable PDE.…”

Section: Introductionmentioning

confidence: 99%

“…[7][8][9][22][23][24] The case of a point source in a three-dimensional wedge with perfectly reflecting boundaries and homogeneous medium leads to a separable PDE. Buckingham derived an exact solution 10,11 for the case where both boundaries are pressurerelease surfaces, and Frisk 25 did so for the case of one pressure release and one rigid boundary. In both cases, the solution is characterized by a decomposition into independently propagating normal modes with curved wave fronts that are circular arcs.…”

Section: Introductionmentioning

confidence: 99%

Broadband modeling of downslope propagation in a penetrable wedge

Yudichak

Royal

Knobles

et al. 2006

Sound propagation in a wedge-shaped environment with a penetrable bottom is simulated with broadband adiabatic mode, coupled mode, and parabolic equation model computations. Simulated results are compared to measured data taken in a tank experiment by Tindle et al. The coupled mode formalism is shown to predict, in agreement with that experiment, that modal wave fronts in penetrable wedges are approximately circular arcs centered at the apex of the wedge for a source near the apex. It is also shown that for wedge angles up to 6 degrees, the received waveforms are well approximated by the adiabatic waveforms time-shifted by a depth-dependent interval to account for the curvature of the modal wave fronts. A small deviation from circularity in the modal wave fronts is possibly observed in the 6 degrees case.