Three-dimensional Wave Field Research Articles

A contrast source method for nonlinear acoustic wave fields in media with spatially inhomogeneous attenuation

Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.

Spatial Frequency Clustering in Nonlinear Dust-Density Waves

Self-excited density waves were studied in a strongly coupled dusty plasma of a radio-frequency discharge under microgravity conditions. The spatiotemporal evolution of the complicated three-dimensional wave field was investigated and analyzed for two different situations. The reconstructed instantaneous phase information of the wave field revealed a partial synchronization within multiple distinct domains. The boundaries of these regions coincide with the locations of topological defects.

Computation formulas by FFT of the nonlinear orbital velocity in three-dimensional surface wave fields

Accurate representations of the surface potential and the orbital velocity of nonlinear water waves are obtained, given the spatial wave-elevation field and its time derivative along two-dimensional sections of the ocean surface. The effect of a horizontal current is accounted for. The method is three-dimensional. The kernel of an integral equation and its right-hand side, both nonlinear functions of the elevation, are obtained in series expansions, and expressed explicitly by Fourier transform (FFT). Calculations for a periodic sine-wave and non-periodic model directional irregular wave field over swaths (wave slope in the range ±0.3 in both cases) illustrate the formulas. The Gibbs phenomenon along the boundaries affects the very high-order contributions in the non-periodic case.

Surface and deep ducting of sound parallel to strong nonlinear internal wave fronts.

Acoustic ducting effects observed in a nonlinear internal wave field on the shelf of the South China Sea northeast of Tung-Sha Island (water depth of ∼120 m) are investigated. Environmental measurements from stationary instruments in the area show that the nonlinear internal waves have large amplitudes (over 40 m) and strong curvature. A principal component interpolation method is used to reconstruct the time-dependent three-dimensional internal wave field. A three-dimensional parabolic equation model is then employed to simulate monochromatic 400-Hz acoustic propagation parallel to the internal wave fronts for comparison to field data. The passing internal waves alternately elevate and depress the thermocline to form strong three-dimensional near-bottom acoustic ducts between the wave troughs and strong surface ducts of mixed layer water in the wave troughs. These alternating, depth-dependent acoustic ducts create asynchronous, vertically-bifurcated sweeping beams of ducted acoustic energy. The three-dimensional acoustic propagation modeling results are shown to mimic the field observations to a strong degree and elucidate the propagation physics in this highly complex environment.

The phase difference effects on 3-D structure of wave pressure acting on a composite breakwater

In designing the coastal structures, the accurate estimation of the wave forces on them is of great importance. In this paper, the influences of the phase difference on wave pressure acting on a composite breakwater installed in the three-dimensional (3-D) wave field are studied numerically. We extend the earlier model [Hur, D.S., Mizutani, N., 2003. Coastal Engineering 47, 329–345] to simulate 3-D wave fields by introducing 3-D Navier–Stokes solver with the Smagorinsky's sub-grid scale (SGS) model. For the validation of the model, the wave field around a 3-D asymmetrical structure installed on a submerged breakwater, in which the complex wave deformations generate, is simulated, and the numerical solutions are compared to the experimental data reported by Hur, Mizutani, Kim [2004. Coastal Engineering (51, 407–420)]. The model is then adopted to investigate 3-D characteristics of wave pressure and force on a caisson of composite breakwater, and the numerical solutions were discussed with respect to the phase difference between harbor and seaward sides induced by the transmitted wave through the rubble mound or the diffraction. The numerical results reveal that wave forces acting on the composite breakwater are significantly different at each cross-section under influence of wave diffraction that is important parameter on 3-D wave interaction with coastal structures.

Internal wave fields generated by a translating body in a stratified fluid: an experimental comparison

Uniform approximations for the combined permanent and transient start-up waves produced by the impulsive motion of a body in a density-stratified fluid are calculated. These new approximations to the wave field remove the unphysically diverging fluid velocities and phase shifts near the boundary of the causality envelope associated with previous non-uniform approximations. The calculated wave field is compared to experimental measurements of the wave field generated by towing a spherical body through a linearly stratified fluid. Synthetic schlieren, a technique previously used only to analyse two-dimensional or axisymmetric flow, is developed further to allow comparison with this fully three-dimensional wave field. In particular, breadth averaging across the tank is employed. Good agreement is found between the theoretical and experimental results in the far field.

Effect of scattering of elastic harmonic waves in the far zone by a spatial crack

A three-dimensional wave field formed owing to diffraction of low-frequency waves on a curved crack in an infinite elastic solid at a large distance from the defect is studied by the method of boundary integral equations. Direction diagrams of the scattered field versus the excentricity of the crack surface and wavenumber are obtained for different directions of incidence of planar longitudinal waves onto a gently sloping spheroidal crack.

A three-dimensional wave field over a bidirectionally periodic ripple bottom

For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is developed to the second order so that the Bragg resonance effect of the ripple bottom on the free-surface wave can be analyzed. Both the resonant and non-resonant cases are treated and the singular behavior at resonance is avoided. This theory is successfully verified by reducing to simpler situations. Then, the analytical results for the special case of a unidirectional sinusoidal bottom are compared with experimental data for validation.

Automated trinocular stereo imaging system for three-dimensional surface wave measurements

A novel automated trinocular stereo imaging system (ATSIS) is developed for non-intrusively measuring the temporal evolution of three-dimensional wave characteristics. The system consists of three progressive digital cameras to provide three independent stereo-pairs, i.e. left–right, left–center, and center–right, for accurately estimating depth of a scene. A third camera assists to resolve correspondence problems due to specular reflection on the water surface and provides additional constraints on image matching, dramatically reducing the chance of a mismatch. An oblique configuration for the trinocular system effectively increases spatial coverage, allowing observations of wave phenomena over a broad range of spatial scales. The height resolution is increased with the optical axes of the cameras pointed at an oblique angle with respect to vertical surface wave displacements. A new exterior calibration procedure is developed in this paper to determine the orientation of cameras in the field. Field experiments demonstrate that ATSIS can robustly measure hundreds of matched image points in seconds, allowing fast extraction of the temporal evolution of a three-dimensional surface wave field.

Estimates of Energy Dissipation Rates in the Three-Dimensional Deep Ocean Internal Wave Field

Using the “Eikonal Approach” (Henyey et al., 1986), we estimate energy dissipation rates in the three-dimensional Garrett-Munk internal wave field. The total energy dissipation rate within the undisturbed GM internal wave field is found to be 4.34 × 10−9 W kg−1. This corresponds to a diapycnal diffusivity of about 0.3 × 10−4 m2s−1, which is less than the value 10−4 m2s−1 required to sustain the global ocean overturning circulation. Only when the high vertical wavenumber, near-inertial current shear is enhanced can diapycnal diffusivity reach ∼10−4 m2s−1. It follows that the energy supplied at low vertical wavenumbers and low frequencies is efficiently transferred to high vertical wavenumbers and near-inertial frequencies in the mixing hotspots in the real ocean.

A three-dimensional numerical modeling of multidirectional random wave diffraction by rectangular submarine pits

A three-dimensional numerical model of multidirectional random wave diffraction by rectangular submarine pits has been investigated theoretically in the uniform water depth. In the exterior region, the three-dimensional Green function has been us ed for the solution of the velocity potential and its derivative in fluid interface between regions. The form of the Fourier expansion has also been utilized for the solution of the velocity potential in the interior region. The Mitsuyasu directional spectrum has been di scretized to specify the incident wave conditions for obtaining linear diffraction solutions, and then subsequent cumulative superposition is performed to obtain the random wave results. The results of the present model have been compared with those of previous theoretical studies for both regular and random wave diffraction by single or multiple pits. reasonable agreement was consistently obtained in all cases. In accordance with good agreement from these comparisons, the present numerical model may accurately be utilized to predict the three-dimensional wave field around multiple submarine pits or navigation channels.

Deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on a sloping bed

This study investigates the wave deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on the slope. Experiments were conducted in a three-dimensional wave basin equipped with a multi-directional random wave generator. Measurements of the free surface elevations around an impermeable submerged breakwater were carried out using 19 capacitance-type wave gages. In addition, a numerical model is proposed in three-dimensional random wave field. It is shown that the numerical results reproduce the general trend of the experimental results well. Investigations are made to study the effect of the spreading parameter S max and bottom topography (bottom slope and submerged breakwater) on the wave deformation. It is pointed out that concentration of wave energy with larger values of the spreading parameter S max is located within narrow limits in onshore side of the submerged breakwater. Furthermore, the supplementary discussion is made by means of numerical results.

Surface acoustic waves on a sphere with divergent, focusing, and collimating beam shapes excited by an interdigital transducer

The surface acoustic wave (SAW) device on a ball is expected to provide high-performance sensors. Since we must deal with three-dimensional wave fields for precise design of ball SAW devices, numerical methods, such as the finite element method, will require too many elements. Therefore, we applied an analytical solution to a practical calculation of the full-field acoustic waves. For an IDT aperture of 6° and 80° with a wave number parameter of 45, the SAW has a divergent beam and a focusing beam, respectively. For an intermediate aperture of 30°, the SAW forms a collimating beam. This calculation confirmed the possibility of an extremely sensitive sensor with diffraction-free SAWs without disturbance by spurious bulk waves.

Observations of inertial waves in a rectangular basin with one sloping boundary

Inertial waves in a homogeneous rotating fluid travel along rays that are inclined with respect to the rotation axis. The angle of inclination depends solely on the ratio of the wave frequency and twice the angular frequency. Because of this fixed angle, the waves can become focused when reflected at a sloping wall. In an infinitely long channel with a sloping wall, the repeated action of focusing may lead to the approach to a limit cycle, the so-called wave attractor, where the energy is concentrated. This effect is studied in the laboratory in a rectangular tank with one sloping wall, placed excentrically on a rotating table. The waves are excited by modulation of the background rotation. Several frequency ratios are used to study different wave attractors and one standing wave. The observations consist mainly of particle image velocimetry data in horizontal and vertical cross-sections in one half of the basin. The attractors are observed in the vertical cross-sections. They show continuous phase propagation, which distinguishes them from the standing wave where the phase changes at the same time over the whole cross-section. However, particle motion of inertial waves is three-dimensional and the actual basin is not an ideal twodimensional channel but is of finite length. This implies that the waves must adapt to the vertical endwalls, although a prediction of the nature of these adaptations and the structure of the three-dimensional wave field is at present lacking. For critical waves, whose rays are parallel to the slope, clear three-dimensional behaviour is observed. The location of most intense motion along this critical slope attractor changes in the horizontal direction and horizontal phase propagation is observed, with a wavelength between 1/5 and 1/4 of the basin length. For the other attractors there is little evidence of phase propagation in the horizontal direction. The motion along the attractor is however stronger near the vertical endwalls for attractors with wave rays of slopes close to 1 or larger. The standing wave and the other attractors are more clearly visible near 1/5 of the tank length.

3D scattering of waves by a cylindrical irregular cavity of infinite length in a homogeneous elastic medium

The three-dimensional (3D) wave field scattered by an irregular, cylindrical cavity of infinite length contained in a homogeneous elastic medium illuminated by a dilatational point load is obtained. This model is used to evaluate the effect of the cross-sectional geometry of the cavity on the waves propagating in its vicinity. It particularly highlights the identification of the normal modes excited both in the frequency and time domain. The solution is formulated using the boundary element method for a wide range of frequencies and spatially harmonic line loads, which are then synthesized to obtain the time responses. The 3D solution is obtained as a summation of two-dimensional responses for different axial wavenumbers. The responses in the frequency vs. axial-wavenumber domains are presented, allowing the recognition, identification, and physical interpretation of the variation of the wave field when five irregular cross-sections are used, namely a circle, an oval, a thin oval, a kidney and a boomerang.

BENCHMARK SOLUTIONS FOR 3-D SCATTERING FROM CYLINDRICAL INCLUSIONS

The solutions for two-dimensional diffracting objects with simple geometry such as a cylindrical inclusion are frequently used as benchmark solutions to test the accuracy of numerical schemes, such as the Finite Elements Method and the Boundary Elements Method, and to better understand the wave propagation around inclusions. The importance of having benchmark solutions available is greater in the case of the evaluation of three-dimensional scattered fields, given its increase in complexity. In this work, analytical-numerical solutions are used to evaluate the three-dimensional wave field elicited by monopole sources in the vicinity of a fluid-filled cylindrical cavity drilled through an unbounded homogeneous elastic medium. This model is used to assess the effects of the position of the source and receiver, on the propagation of both axisymmetric and nonaxisymmetric wave modes. Both frequency versus axial-wave number responses and time-domain transients are presented.

Benchmark Solutions for 3-D Scattering from Cylindrical Inclusions

The solutions for two-dimensional diffracting objects with simple geometry such as a cylindrical inclusion are frequently used as benchmark solutions to test the accuracy of numerical schemes, such as the Finite Elements Method and the Boundary Elements Method, and to better understand the wave propagation around inclusions. The importance of having benchmark solutions available is greater in the case of the evaluation of three-dimensional scattered fields, given its increase in complexity. In this work, analytical-numerical solutions are used to evaluate the three-dimensional wave field elicited by monopole sources in the vicinity of a fluid-filled cylindrical cavity drilled through an unbounded homogeneous elastic medium. This model is used to assess the effects of the position of the source and receiver, on the propagation of both axisymmetric and nonaxisymmetric wave modes. Both frequency versus axial-wave number responses and time-domain transients are presented.

Wigner function for highly convergent three-dimensional wave fields

The angle-impact Wigner function for highly convergent three-dimensional scalar wave fields is derived directly by use of the three-dimensional generalized optical transfer function rather than from a six-dimensional Wigner function. The angle-impact Wigner function is a real four-dimensional function from which the intensity at any point in space is readily determined.

3-D wave propagation in fluid-filled irregular boreholes in elastic formations

Different seismic testing techniques rely on the propagation of acoustic waves in fluid-filled boreholes from sources placed within the borehole and in the solid media. The interpretation of the signals recorded relies on understanding how waves propagate in the borehole and its immediate vicinity. It is known that very complex wave patterns can arise, depending on the distance between the source and the receiver, and their placement and orientation relative to the axis of a circular borehole. The problem becomes more complex if the cross-section is not circular, conditions for which analytical solutions are not known. In this work, the Boundary Element Method (BEM) is used to evaluate the three-dimensional wave field elicited by monopole sources in the vicinity of a fluid-filled borehole. This model is used to assess the effects of the receiver position on the propagation of both axisymmetric and non-axisymmetric wave modes when different borehole cross-sections are used. Both frequency vs. axial-wave number responses and time-domain responses are calculated.

The three-dimensional transfer function and phase space mappings

Abstract For paraxial wave-fields in two dimensions, it is known that the defocused OTF is given by a section through the ambiguity function. This is no longer true for high aperture fields. It is shown that there is a simple relationship, even for high aperture fields, between the two-dimensional (one transverse and one longitudinal) generalized OTF and the spectral correlation function. The connection with the Wigner distribution function is also discussed. The generalization to three-dimensional wavefields is also considered.