B. Edward McDonald

Comparison of data and model predictions for Heard Island acoustic transmissions

Propagation paths and signal characteristics from the Heard Island Feasibility Test are modeled using a combination of adiabatic mode theory, coupled mode theory, and parabolic equation (PE) methods. Adiabatic mode theory predicts the horizontal propagation paths (including small grazing angle reflections from bathymetry), group travel times, and estimates of signal loss due to bottom interaction. The PE calculations are performed primarily to illustrate modal coupling near sharp oceanic fronts and bathymetry intruding into the sound channel. They are carried out in depth and range along selected horizontal ray paths. For the Heard Island to Christmas Island path, we carry out a time domain pulse transmission using coupled mode equations. The result gives a pulse envelope in approximate agreement with observations.

Echoes from vertically striated subresonant bubble clouds: A model for ocean surface reverberation

A surface reverberation model for acoustic frequencies below several kHz is proposed based on weak scatter from inhomogeneities whose geometry is descriptive of recent ocean observation [e.g., Farmer and Vagle, J. Acoust. Soc. Am. 86, 1897 (1989)]. Scatterers in this model are vertical cylinders of elliptical cross section representing either filamentary‐ or sheetlike subresonant microbubble clouds whose population decreases exponentially with depth. This geometry approximates intermediate‐aged fossils of breaking waves and/or convective processes. Born approximation (weak scatter) results from this model show substantial agreement with observed surface backscatter cross sections as a function of wind speed, grazing angle, and acoustic frequency in the range 0.2–20 kHz. It is demonstrated that almost all the high‐frequency weak backscatter in the model is specular reflection from surfaces of volume scatterers. Some preliminary speculations involving Langmuir circulation are offered for the application of ...

Jovian acoustics and Comet Shoemaker–Levy 9

A technique for solving three‐dimensional ocean acoustics problems is modified to handle Jovian acoustics problems and applied to model propagation from the impact sites of the fragments of Comet Shoemaker–Levy 9. The adiabatic mode parabolic equation is generalized to media with fluid flow for the case of low Mach number. The vertical dependence of sound speed and density and the latitude dependence of the zonal winds are known from Voyager data. The acoustic model predicts that energy that radiated from the impact sites was vertically concentrated within a sound channel that includes the cloud layers and horizontally concentrated into intense caustics by refraction associated with wind shear. Although nonlinear effects are important near the impact sites, the spatial distribution of energy should be qualitatively represented by the linear acoustics results.

THREE-DIMENSIONAL EFFECTS IN GLOBAL ACOUSTICS

Low‐frequency ocean acoustics problems are solved in three dimensions over the entire globe. Adiabatic mode solutions are obtained at 1 Hz using the parabolic equation method by marching through both the oceans and the continents from the location of the source to the antipode. The examples indicate that azimuthal coupling can be important for global‐scale problems. One of the examples illustrates the broadening of a shadow behind the Hawaiian Islands by horizontal refraction. The other examples involve sources at the locations of the sources used in the Perth–Bermuda and Heard Island experiments.

Enhanced sound transmission from water to air at low frequencies.

Excitation of acoustic radiation into the air from a low-frequency point source under water is investigated using plane wave expansion of the source spectrum and Rayleigh reflection/transmission coefficients. Expressions are derived for the acoustic power radiated into air and water as a function of source depth and given to lowest order in the air/water density ratio. Near zero source depth, the radiation into the water is quenched by the sources acoustic image, while the power radiated into air reaches about 1% of the power that would be radiated into unbounded water.

High-angle formulation for the nonlinear progressive-wave equation model☆

Abstract The nonlinear progressive-wave equation (NPE) model has been reformulated for wider propagation angle accuracy. The wide angle NPE results from range-integrating the second order time domain nonlinear wave equation rather than reducing it to a first order equation in time as in the original NPE. The numerical implementation of the second order NPE retains two time levels rather than one. The resulting model is refered to as NPE2. Benchmark tests reveal RMS errors in the model are reduced by nearly a factor of 10 for moderately high propagation angles as compared to errors in similar tests of the first order NPE.

Bathymetric and volumetric contributions to ocean acoustic mode coupling

Ocean acoustic mode coupling matrix elements are investigated assuming weak range dependence in both the sound‐speed profile and bathymetry. The range‐dependent environmental variables are taken as known, and explicit integral expressions for the matrix elements are derived. The expressions contain separate volumetric and bathymetric terms arising from range dependence in the water column and bathymetry, respectively. The bathymetric terms lead to an algebraic connection between rates of modal ray curvature (horizontal refraction) due to bathymetry and energy loss rate due to bottom absorption. Theoretical evidence that a signal refracted by shallow bathymetry may show decreasing bottom absorption with increasing mode number is presented.

Nonlinear pulse propagation in shallow-water environments with attenuating and dispersive sediments

A hybrid treatment for wide-angle paraxial propagation that includes effects of both sediment dispersion and weak nonlinearity has been developed. A Fourier transform approach is used to combine effects of refraction, diffraction, and sediment dispersion in the frequency domain, and nonlinear effects in the time domain. A nonlinear wide-angle time-domain equation developed recently is first split into linear and nonlinear component equations. The linear equation is decomposed into its discrete frequency-domain counterparts. Sediment attenuation and dispersion are incorporated using a complex wave number along with a frequency-dependent formula for phase velocity to satisfy causality. The numerical implementation consists of first decomposing a broadband source into its frequency components and propagating them over a range step using a wide-angle parabolic equation. Fourier synthesis is used to reconstruct the signal which is then corrected to account for nonlinear effects in the time domain. Numerical ex...

Weak shock interaction with a free‐slip interface at low grazing angles

Theoretical/numerical investigations with the nonlinear progressive wave equation (NPE) model predict qualitative differences between behavior of a planar weak shock and a linear acoustic wave of similar time signature incident downward at small grazing angle onto a free‐slip interface between two fluids. For the linear case, the model agrees well with an appropriate analytic benchmark solution. For the nonlinear cases considered, initial conditions evolve toward (a) supercritical reflection (steady wave with no Mach stem development) or (b) subcritical reflection (self‐similar behavior with Mach stem development). When the horizontal phase speed c0 of the incident wave barely exceeds the linear sound speed cL of the lower medium, an intermediate state can be obtained in which the incident shock discontinuity terminates on the interface; wave energy below the interface runs ahead and reforms a deep penetrating shock ahead of and below the interface disturbance. When c0 is below cL, the shock discontinuity...

Parabolic equation modeling of azimuthally advected gravity waves

Abstract An adiabatic mode solution is derived for azimuthally advected gravity waves. Horizontal variations in the medium are assumed to be sufficiently gradual so that the coupling of energy between modes can be neglected. The wind speed is assumed to be small relative to the wave speed. The mode coefficients satisfy the same horizontal wave equation for both gravity and acoustic waves, which satisfy three-dimensional wave equations that are fundamentally different. The horizontal wave equation can be solved efficiently with the parabolic equation method. The adiabatic mode solution is used to model the propagation of gravity waves in the atmosphere of Jupiter.