Jacqueline Naze Tjøtta

An analytical model for the nearfield of a baffled piston transducer

The linearized sound field from a baffled piston source (radius a, wavenumber k) in a dissipative fluid is considered. A simplified parabolic equation is derived (for ka ≫ 1) and solved analytically. The solution matches a plane collimated beam in the vicinity of the source and has the Bessel function directivity in the farfield. The nearfield‐farfield transition region is studied. The range of validity of the parabolic equation is discussed. Its exact solution is shown to be the first term of an expansion in powers of (ka)−2 for the solution of the Helmholtz equation. The higher‐order terms are secular at distances of order a(ka)1/3 from the piston. The analytical results obtained for the linearized field can be used to calculate the effects of nearfield oscillations on nonlinear effects generated in soundbeams. (For example, see Paper GG1, by the same authors, in this Program.) [Work supported in part by the Office of Naval Research.]

Theoretical study of the penetration of highly directional acoustic beams into sediments

Recently Muir, Horton, and Thompson [J. Sound Vib. 64, 539–551 (1979)] presented results of an experimental study of the penetration of directional acoustic beams into bottom sediments. We consider here the linearized theory of the refracted soundfield produced by a highly directional beam on a bottom sediment. A simplified equation valid for k′a tanθa ≫ 1 (k wavenumber in the sediment, k′ wavenumber in the overlaying water, a width of the incident beam at the interface, θa angle of the acoustic axis with the normal to the interface) is derived and solved analytically subject to the nondissipative boundary condition at the interface. The radiation field is found to be similar to that of a phase shaded piston source. The solution is valid whenever the characteristic length of the diffraction effects, which is of order (a;/k′ sin2θa1/2, is small compared to the attenuation length in the sediment; this is the case in the experiment referred to. When k′ sinθa < k, the refracted soundfield is a beam with axis ...

Performance of the parametric receiving array: Effects of misalignment

The difference frequency sound field from two concentric but misaligned, axisymmetric, planar transducers in a nondissipative and nondispersive medium is developed as a special case of the general theory [Garrett et al., J. Acoust. Soc. Am. 75, 769–779 (1984)]. Effects of misalignment of pump, source, and hydrophone on the performance of the parametric receiving array are quantified in numerical examples. These include the effect of interaction in the nearfields of both pump and source transducers. The results show that the best performance is obtained for good alignment, high pump frequency, and placement of the hydrophone within or not far from the source nearfield.

Reflection and Refraction of Parametrically Generated Sound at a Water-Sediment Interface

The results of an experimental study of the penetration of highly directional acoustic beams into bottom sediments were recently reported by Muir, Horton, and Thompson [J. Sound Vib. 64, 539–551 (1979)]. Of special interest was the behavior of a narrow beam generated by a parametric source. We have considered this problem theoretically. Simplified equations for the reflected and refracted beams at the water-sediment interface are derived and solved analytically subject to the nondissipative boundary conditions. The range of validity is discussed. Results are presented that seem to explain the experimental observations.

Nonlinear equations of acoustics in inhomogeneous fluids

The propagation of finite amplitude sound waves produced by real sources in an inhomogeneous and thermoviscous fluid is considered. A governing nonlinear equation in the sound pressure amplitude is derived using the methods of singular perturbations. It consistently accounts for the effects of diffraction, dissipation, nonlinearity, and inhomogeneity, and represents a generalization of the parabolic equation valid for a homogeneons fluid (Khokhlov‐Zabolotskaya‐Kuznetsov equation) discussed in a previous work [Naze Tjotta and Tjotta, J. Acoust. Soc. Am. 69, 1644–1652 (1980)]. The equation also applies to the case of sound beams produced by strongly curved sources, for example, focusing and defocusing sources. The relationship to the equations of classical ray theory is discussed. [Work supported by The Norwegian Research Council for Sciences and Humanities (NAVF), the IR&D program of ARL:UT, and VISTA/STATOIL, Norway.]

Scattering of a plane wave at a plane boundary presenting an impedance discontinuity

The scattering of a sound wave by a boundary presenting an impedance discontinuity has been the object of many theoretical investigations based on the Wiener‐Hopf method. Although the method provides an exact solution, the expressions obtained are involved and not very useful in the vicinity of the boundary. The present work addresses the simple case of a plane wave incident on a plane boundary that is made up of two half‐planes. One of the half‐planes is perfectly rigid, the other is pressure release. The boundary between the two half‐planes is a straight line, and the medium over the boundary is a lossless fluid. It is shown that a simple analytical solution can be obtained by taking advantage of the symmetry properties of the problem. The solution is expressed in terms of one‐dimensional integrals that can be evaluated numerically. Numerical results for the sound pressure and velocity are presented. The case where the incident plane wave is replaced by a sound beam is briefly discussed. [Work supported...

A version of NPE for nonlinear propagation of ultrasonic pulses in focused field

The NPE (nonlinear progressive wave equation) and associated computer program are a time domain representation that was developed by McDonald and Kuperman to study waveguide problems. The present work extends the earlier studies [Too and Ginsberg (1989–1990)], which developed a modified version of NPE in terms of axisymmetric cylindrical coordinates to describe propagation of finite‐amplitude sound beams. In the present studies, a new version of NPE is studied in which axisymmetric spherical coordinates are employed to describe propagation of axisymmetric convergent and divergent waves. The present problem concerns nonlinear pulse propagation in a focused field. In order to initialize the moving window convected by NPE, a linear spherical wave assumption is made adjacent to the transducer; i.e., inside the converging beam, the input field is represented as a linear spherical wave, while outside the beam, the input field is considered to be zero. Temporal waveforms are computed on‐ and off‐axis and are com...

Nonlinear model equations for waves in a stratified fluid

The present work is a theoretical study of the combined propagation of acoustic and internal waves of finite amplitude in a stratified fluid. The motion is described within the framework of a thermoviscous fluid, although relaxation effects can be readily accounted for. Model equations are derived under the assumption of weak nonlinearity. The nonlinear terms combine to form source terms in two coupled, governing equations in the pressure and vertical particle velocity or displacement. Examples are given that show effects of nonlinear coupling between acoustic and internal waves. Generation of vorticity and steady flow (acoustic streaming), and their interaction with the sound field, is also discussed briefly. [Work supported by The Norwegian Research Council for Science and Humanities (NAVF) and VISTA/STATOIL, Norway.]

Effects of boundary conditions on the propagation and interaction of finite amplitude sound beams

Weak nonlinearity in the propagation and interaction of real sound beams in a lossless fluid is considered. Special emphasis is given to the effects produced by various boundary conditions at the sound sources and other bounding surfaces. Asymptotic formulas and numerical results are presented for the second harmonic, and for the scattered sum and difference frequency sound generated by two harmonic beams that intersect at an arbitrary angle. The results are derived from a general theory presented earlier [see Naze Tjotta and Tjotta, J. Acoust. Soc. Am. 83, 487–495 (1988)], which is valid for any source separation and amplitude distribution. In situations where the parabolic approximation is not legitimate (large angles, broad beams), properly accounting for the boundary conditions may be crucial. [Work supported by the IR&D program of ARL:UT, ONR, and VISTA/STATOIL, Norway.]

Effects of absorption on the scattering of sound by sound

The scattering of sound by sound in a lossless fluid was discussed at an earlier meeting [Berntsen et al., J. Acoust. Soc. Am. Suppl. 1 83, S4 (1988), and Darvennes and Hamilton, J. Acoust. Soc. Am. Suppl. 1 83, S4 (1988)]. Here, the effects of absorption are included. The Khokhlov‐Zabolotskaya‐Kuznetsov equation is used to derive farfield asymptotic results for the sum and difference frequency sound due to the noncollinear interaction of real sound beams radiated from displaced sources. There are two main contributions to the nonlinearly generated sound in the farfield: the continuously pumped sound and the scattered sound. Weak absorption affects neither the locations nor the relative amplitudes of the pumped and scattered difference frequency sound. Strong absorption attenuates the pumped difference frequency sound faster than the scattered difference frequency sound. The scattered sum frequency sound is always attenuated faster than the pumped sum frequency sound, and there may be shifts in the locati...