A Normal Mode Theory of an Underwater Acoustic Duct by Means of Green's Function

Deavenport, R. L.

doi:10.1002/rds196616709

Cited by 23 publications

(7 citation statements)

References 24 publications

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“…( , , ) is the spatial Green's transfer 15 function satisfying the following elliptic Helmholtz wave equation:…”

Section: Algorithm To Implement the Duhamel Convolutionmentioning

confidence: 99%

Time-Dependent Modeling of Underwater Explosions by Convolving Similitude Source with Bandlimited Impulse from the CASS/GRAB Model

Deavenport¹,

Gilchrest²

2015

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The authors thank John M. Tattersall (formerly of NUWC Division Newport) for introducing the bandlimited transfer function, Joseph O. Fayton (Code 7021) and Stephen E. Turner (Code 7023) for their careful review and suggestions, and Bert E. Neales (Code 7023) for his continuing service and assistance with the MATLAB prototyping. Reviewed and SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)Naval Undersea Warfare Center Division 1176 Howell Street Newport, RI 02841-1708 SPONSORING/MONITOR'S ACRONYM NUWC SPONSORING/MONITORING REPORT NUMBER DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTThe research documented in this report was conducted to develop a time-dependent pressure computational model for an explosive source in an underwater acoustic waveguide. This objective was accomplished by convolving a time-dependent (similitude) source with the farfield impulse response from the Comprehensive Acoustic System Simulation/Gaussian Ray Acoustic Bundle (CASS/GRAB) model. The impulse response was found by performing an inverse fast Fourier transform of the frequency-dependent, bandlimited transfer function (Green's function) from CASS/GRAB. The bandlimited transfer function is determined using the CASS/GRAB amplitudes and phases over a range of frequencies. The result of this convolution is a time-dependent pressure field that satisfies the time-dependent hyperbolic wave equation with boundary conditions, which, in turn, produces a time series from the explosive source. In addition to describing the conduct of this investigation, this report presents the algorithm developed for the computational model and provides a comparison of measured and modeled data. SUBJECT TERMS

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“…( , , ) is the spatial Green's transfer 15 function satisfying the following elliptic Helmholtz wave equation:…”

Section: Algorithm To Implement the Duhamel Convolutionmentioning

confidence: 99%

Time-Dependent Modeling of Underwater Explosions by Convolving Similitude Source with Bandlimited Impulse from the CASS/GRAB Model

Deavenport¹,

Gilchrest²

2015

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“…An inverse scattering theory, on the other hand, starts from the scattering data and reconstructs-the profile function.) Epstein's direct scattering theory [ 81 is helpful in this regard, since the scattering results are precisely known; it also has been widely used (e.g., see [ 9 ] ) . An estimate of N is thus obtained for the approximate reconstruction of any of a wide range of electron distributions, which could, in principle, proceed analogously to the threepole case.…”

Section: ~ -Mmentioning

confidence: 99%

“…where f(r1) is given by (9). The three additional conditions required can be obtained from the original integral equation 3.…”

Section: Inverse Scattering Theory: Three-pole Casementioning

confidence: 99%

The applicability of an inverse method for reconstruction of electron-density profiles

Reilly

Jordan

1981

IEEE Trans. Antennas Propagat.

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“…When this change is sufficiently slow, the modes do not interact significantly, and thus each mode can be tracked separately. This so-called adiabatic approximation has been used extensively in underwater sound [Deavenport, 1966;Nagl et al, 1978] and atmospheric acoustic waves [Pierce, 1965]. Only quite recently has the importance of mode conversion been appreciated when dealing with nonuniform natural wave guides [Bahar and Wait, 1963;Wait, 1968Wait, , 1974Bahar, 1971;McDaniel, 1977;Cho and Wait, 1978;Rutherford and Hawker, 1979; E. Ledinegg et al, private communication, 1975].…”

Section: Introductionmentioning

confidence: 99%

Coupled mode analysis for a nonuniform tropospheric wave guide

Wait¹

1980

Radio Science

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We employ a two‐dimensional cylindrical model to analyze the normal modes in a laterally nonuniform tropospheric duct. The utilization of the impedance boundary condition at the earth's surface permits us to use a complete field representation in terms of discrete modes only. These modes are chosen to be locally orthogonal so that a tapered‐type nonuniformity can be handled with a systematic accounting of the mode conversion. Explicit formulas are given for the coupling coefficients. It is shown that the general coupled mode analysis reduces to the appropriate form when dealing with an abrupt but small lateral change of the refractive index structure. This step model had been treated previously using a nonrigorous mode matching procedure that neglected reflected waves at the outset.

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A Normal Mode Theory of an Underwater Acoustic Duct by Means of Green's Function

Cited by 23 publications

References 24 publications

Time-Dependent Modeling of Underwater Explosions by Convolving Similitude Source with Bandlimited Impulse from the CASS/GRAB Model

Time-Dependent Modeling of Underwater Explosions by Convolving Similitude Source with Bandlimited Impulse from the CASS/GRAB Model

The applicability of an inverse method for reconstruction of electron-density profiles

Coupled mode analysis for a nonuniform tropospheric wave guide

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