Modulation of acoustic phase by internal-wave vertical velocity

Acoustic holography underpins the number of modern acoustics applications. The usage of multi-focal acoustic holograms with phased array transducers (PATs) in ultrasonic tactile displays and acoustic levitation are increasing, and achieving a high-quality hologram are of significant interest. Inspired by the latest optical hologram optimizer, we developed a novel acoustic hologram optimizer for PATs called Diff-PAT [T. Fushimi, K. Yamamoto, and Y. Ochiai, “Acoustic hologram optimisation using automatic differentiation”]. Diff-PAT is based on a gradient-descent algorithm and automatic differentiation. The performance of Diff-PAT was numerically evaluated using three array configurations and it achieved superior accuracy over the conventional optimizers. For example, when two focal points are generated with 196 ultrasonic (40 kHz) transducers; the state of art optimizer (with phase and amplitude modulation) based on Eigensolver has an average error of 4.07 % where Diff-PAT (with only phase modulation) achieve average error of 0.0174%. These results show that amplitude and phase modulation may not be necessary for PATs to be successful. Furthermore, we demonstrate the versatility of Diff-PAT by applying it to binary acoustic holograms, simultaneous modulation of acoustic amplitude and phase at the target plane, and phase plates. [Work supported by Pixie Dust Technologies, Inc., Diff-PAT is patent pending (JP2020-167367A).]

The underlying physics that generates the excitations in the global low-frequency, < 5.3 mHz, solar acoustic power spectrum is a well known process that is attributed to solar convection; However, a definitive explanation as to what causes excitations in the high-frequency regime, > 5.3 mHz, has yet to be found. Karoff and Kjeldsen (Astrophys. J. 678, 73-76, 2008) concluded that there is a correlation between solar flares and the global high-frequency solar acoustic waves. We have used the Global Oscillations Network Group (GONG) helioseismic data in an attempt to verify Karoff and Kjeldsen (2008) results as well as compare the post-flare acoustic power spectrum to the pre-flare acoustic power spectrum for 31 solar flares. Among the 31 flares analyzed, we observe that a decrease in acoustic power after the solar flare is just as likely as an increase. Furthermore, while we do observe variations in acoustic power that are most likely associated with the usual p-modes associated with solar convection, these variations do not show any significant temporal association with flares. We find no evidence that consistently supports flare driven high-frequency waves.

The reference wave phase was modulated with a sinusoidal vibrating mirror attached to a Piezoelectric Transducer (PZT), the integration was performed by a CCD, and the charge storage period of the CCD image sensor was one-quarter period of the sinusoidal phase modulation. With the frequency- synchronous detection technique, four images (four frames of interference pattern) were recorded during one period of the phase modulation. In order to obtain the optimum modulation parameter, the values of amplitude and phase of the sinusoidal phase modulation were determined by considering the measurement error caused by the additive noise contained in the detected values. The PZT oscillation was controlled by a closed loop control system based on PID controller. An ideal discrete digital sine function at 50Hz with adjustable amplitude was used to adjust the vibrating of PZT, and a digital phase shift techniques was used to adjust vibrating phase of PZT so that the phase of the modulation could reach their optimum values. The CCD detector was triggered with software at 200Hz. Based on work above a small coherent signal masked by the preponderant incoherent background with a CCD detector was obtained.

This paper investigates the modal acoustic power by a cascade of flat-plate airfoils interacting with homogeneous, isotropic turbulence. Basic formulation for the acoustic power upstream and downstream is based on the analytical theory of Smith and its generalization due to Cheong et al. The acoustic power spectrum has been expressed as the sum of cut-on acoustic modes, whose modal power is the product of three terms: a turbulence series, an upstream or downstream power factor and an upstream or downstream acoustic response function. The effect of these terms in the modal acoustic power has been examined. For isotropic turbulence gust, the turbulent series are only reducing factor of the modal acoustic power. The power factor tends to reduce the modal acoustic power in the upstream direction, although the power factor is liable to increase the modal acoustic power in the downstream direction. The modes close to cut-off are decreasing strongly, especially in the downstream direction. Therefore the modes close to cut-off don't contribute highly to the radiated acoustic power in the downstream direction, although the modal acoustic pressure is high for these modes.

Interest in modeling internal gravity waves in littoral regions was stimulated by the discovery of anomalous transmission loss in the Yellow Sea, predicted by Zhou and Rogers in 1991 to be caused by solitary wave propagation along the acoustic transmission path. Over the past 20 years, we have been modeling acoustic wave/solitary internal wave interactions and an overview and perspective of some of this work, illustrated by examples, will be presented. The relationship between internal waves and the scintillation index, horizontal refraction of acoustic energy, oceanographic waveguide focusing, mode coupling between acoustic and internal wave modes, and the effect of internal waves on acoustic field uncertainty are discussed. Some thoughts on the future of 4-D simulation of acoustic/internal wave interactions and modeling in the context of incomplete environmental knowledge are considered. [Work supported by the Office of Naval Research.]

In “sound transmission through a fluctuating ocean,” Flattxe et al. described saturation of a single acoustic path as that path becoming a number of interfering uncorrelated micropaths due to refraction by internal waves. The probability density function of intensity becomes exponential with a scintillation index of 1.0. In deep water, however, full saturation is not achieved due to weak scattering and absorption. Mid‐frequency (1–10 kHz) data from the Shallow Water 2006 Experiment are used to determine single‐path intensity statistics. At a range of 1 km in water 80 m deep, an acoustic path is isolated that went through two upper turning points separated by a single bottom reflection. The data were collected during a period when large nonlinear internal waves were absent. The scintillation index calculated from the data increases with frequency until reaching a maximum of 1.2 around 6 kHz. It then decreases to 1.0, suggesting that single‐path saturation can be achieved at mid‐frequencies in shallow water. The probability density functions of intensity at various frequencies show a trend toward exponential. Because shallow water internal waves are dominated by the first mode, uncorrelated micropaths are an unlikely mechanism for producing the observed saturation. [Work supported by ONR.]

High‐resolution global ocean models forced by atmospheric fields and tides are beginning to display realistic internal gravity wave spectra, especially as model resolution increases. This paper examines internal waves in global simulations with 0.08° and 0.04° (~8 and 4 km) horizontal resolutions, respectively. Frequency spectra of internal wave horizontal kinetic energy in the North Pacific lie closer to observations in the 0.04° simulation than in the 0.08° simulation. The horizontal wave number and frequency (K‐ω) kinetic energy spectra contain peaks in the semidiurnal tidal band and near‐inertial band, along with a broadband frequency continuum aligned along the linear dispersion relations of low‐vertical‐mode internal waves. Spectral kinetic energy transfers describe the rate at which nonlinear mechanisms remove or supply kinetic energy in specific K‐ω ranges. Energy is transferred out of low‐mode inertial and semidiurnal internal waves into a broad continuum of higher‐frequency and higher‐wave number internal waves.

An acoustic experiment to measure the sound field during internal wave activity was conducted in the South China Sea. During the experiment, a train of strong internal solitary waves (ISWs) moved from the acoustic source to the receiver array along the acoustic path, and the propagation direction of the ISWs train was almost parallel to the acoustic path. Here, a study of the characteristics and physical mechanisms of the acoustic temporal coherence in this scenario is reported. The temporal coherence was analyzed by using the simulation results and experimental data. The results show that the temporal correlation coefficients oscillate quasi-periodically with both time and time delay, and the predominant oscillation periods are the same as the periods of the ISWs. The predominant fluctuation frequencies of the sound field correspond to some specific modes and lead to the periodicity of the temporal correlation coefficients. In the shallow layer, the spectrum structures of the temporal correlation coefficients are simpler because of the fewer effective modes.

A three-dimensional, multi-level model was used to study the energy dissipation of semidiurnal internal Kelvin waves due to their interaction with bottom topography. A simplified topography consisting of a channel with an additional shallow bay was used to clarify the wave’s scattering process. When the first mode semidiurnal internal wave given at an open boundary arrives at the bay mouth, higher-mode internal waves are generated at a step bottom of the bay mouth. As a result, the energy of the first mode internal Kelvin wave is effectively decayed. The decay rate of the internal Kelvin wave depends on both the width and length of the additional bay. The maximum decay rate was found when a resonance condition occurs the bay, that is, the bay length is equal to a quarter of wave length of the first mode internal wave on the shallow region. The decay rate in the wide bay cases is higher than that in a narrow case, due to a contribution from the scattering due to the Poincare wave that emanates from the corners of the bay head. The decay rate with the additional bay is 1.1–1.8 times that of the case without the additional bay. The decay rate due to the scattering process is found to be of the same order as that of the internal and bottom friction.

Accurately identifying the types and formation mechanisms of seafloor bedforms is crucial for understanding sediment transport and deposition on continental margins, and assessing seafloor stability for marine geohazard evaluation. This study, using high-resolution bathymetric, 2-D/3-D seismic and sediment core data, investigates sediment waves at the heads of the Shenhu Canyon System in the northern South China Sea. These sediment waves have wavelengths up to 1.4 km and heights reaching 50 m, exhibiting continuous internal reflections and an upslope migration trend. Sediment samples reveal that these waves are predominantly composed of silt (73.21%−88.45%). Our findings suggest that internal waves, particularly those at diurnal frequencies, are the primary driver for the formation of these sediment waves. In critical and near-critical areas, the interaction of internal waves with the seafloor induces strong energy dissipation, which enhances bottom mixing and facilitates sediment resuspension and transport, leading to the formation of sediment waves. The variation in sediment wave scale is linked to differences in internal wave conditions, energy, and slope morphology. In the northeastern canyon heads (C11−C19), near-critical/critical conditions of diurnal internal waves, higher initial internal wave energy, and longer slopes enhance sediment resuspension, forming larger sediment waves. Conversely, reflective conditions, lower wave energy, and shorter slopes in the central (C8−C10) and southwestern (C1−C7) canyon heads limit sediment resuspension and transport, resulting in smaller or no sediment waves. These results provide new insights into sediment wave formation adjacent to submarine canyon heads, highlighting the significant role of internal waves in shaping continental margin geomorphology.

The simultaneous photometric and spectroscopic observations of the RR Lyrae variables in the globular cluster, M3, published in Jurcsik et al. (2017, Paper I) made it possible to perform Baade–Wesselink (BW) analysis of a large sample of Blazhko stars for the first time. The BW distances of Blazhko stars turned out to be unreliable, as significantly different distances were obtained for the stars of the Blazhko sample and also for the same star in different modulation phases. Even the results of small modulation–amplitude Blazhko stars may be doubtful. This result warns that the application of the BW method to Blazhko stars is not trustworthy. Keeping the distance fixed for each Blazhko star in each modulation phase, a significant difference between the spectroscopic and the photometric radius (Rsp, Rph) variations is detected. The phase and amplitude variations of Rsp follow the changes of the light curve during the Blazhko cycle but the Rph curve seems to be not (or only marginally) affected by the modulation. The asynchronous behaviour of Rsp and Rph supports the interpretation of the Blazhko effect as a depth-dependent phenomenon, as the spectroscopic radius variation reflects the radial displacement of the line-forming region high in the atmosphere, while the photospheric radius variation is derived from the information of the observed visual-band light emitted mostly by the lower photosphere. The stability of Rph may be interpreted as a strong argument against the non-radial-mode explanation of the Blazhko phenomenon.

Vertical two‐dimensional numerical experiments incorporating Garrett‐Munk (GM) internal waves are conducted to investigate tide‐induced near‐field mixing over a finite‐amplitude sinusoidal seafloor, conventionally attributed to the breaking of high‐wavenumber internal tidal waves. Turbulent mixing is characterized by tidal excursion parameter ( Te ) and topographic steepness parameter ( Sp ) measuring tidal current strength and seafloor slope gradient, respectively. Under strong tidal currents ( Te &gt; 1), high‐wavenumber internal lee waves propagate upward from the seafloor. Even when Te and Sp are set to produce nearly the same upward energy flux, the vertical profile of mixing hotspots varies with Sp . For Sp 0.2, near‐inertial currents above the seafloor rapidly amplify by absorbing energy of internal lee waves from below, hindering their upward propagation and creating “short mixing hotspots.” For Sp &lt; 0.2, these near‐inertial currents diminish, allowing internal lee waves to propagate upward and interact with the GM background internal waves, creating “tall mixing hotspots.”

Internal waves are ubiquitous oceanographic features that occur in various forms across the world’s oceans. They manifest themselves as interface waves across ocean density layers that represent the interplay between buoyancy and gravitational forces, and are typically classified as linear and nonlinear internal waves. Nonlinear internal waves are characterized by isopycnal displacements that can exceed 30 m, and current velocities that approach 1 m/s. Internal wave energy converters, if developed, could have the advantage of no surface expression and provide for the availability of renewable ocean energy in regions of scant surface wave energy resources.&#x0D; Here, internal wave energies were computed at two locations: the New Jersey continental shelf and the coast of Central California. The available energy resource calculated for internal waves was then compared against surface gravity wave resources at each of these locations. Results suggest that the internal wave energy flux is comparable to that of surface waves on the New Jersey continental shelf during the summer of 2006 but is two orders of magnitude lower than that of surface waves in Central California during the summer of 2017. When expressed in terms of forces on a cylindrical structure, internal wave forces are an order of magnitude lower than that of surface waves on identically sized cylinders. However, the forces of the two resources are comparable when the diameter of the cylinder is doubled for the internal wave calculations. This suggests that while a larger energy converter would be required to harness internal wave energy, the larger size could be a reasonable tradeoff for advantages such as the lack of surface expression and the availability of energy in regions of limited surface wave energy resources.&#x0D; These results could potentially pave the way for longer-time scale characterization of internal waves and the development of devices to harness this energy resource (thereby powering the Blue Economy), while augmenting the portfolio of marine renewable energy resources. Further, the dominance of internal wave energy resources during summer seasons when the water column is stratified can augment the surface wave energy resource that can be diminished during the summer season.

The work presents a ray acoustic based analysis of the effect of ocean internal waves and its fluctuations on acoustic wave propagation. In the present work, it is shown that consideration of only perfect internal waves simplifies the real problem, disregarding the fluctuations of internal waves. The focus of the paper is to study numerically the influence of internal wave fluctuations and the role of an initial ray angle onto underwater acoustic propagation. In the present formulation the eikonal equation is considered in the form of a second order, nonlinear ordinary differential equation with harmonic excitation due to internal wave. The harmonic excitation is taken imperfect, i.e., with a random phase modulation due to Gaussian white noise. The amplitude and wavelength of the acoustic waves are used as the principle signal characteristics in bifurcation analysis. The regions of instability are identified using the bifurcation and phase diagrams. The effect of internal waves phase modulation is demonstrated by means of comparison of the numerical data obtained in the present work with data, obtained perfect internal wave. The preliminary analysis shows very strong dependence of acoustic propagation on intensity of fluctuations.

We review the evolution of modulation formats designed for direct detection, from on-off keying intensity modulation (IM) of a single polarization to three-dimensional formats where the intensity of both polarizations and the interpolarization phase are all independently modulated. We present the transmitter and receiver architectures capable of modulating an increasing number of dimensions, all orthogonal to each other. We detail the digital signal processing for Stokes vector receivers capable of recovering all three dimensions of a lightwave via self-beating direct detection, performing simultaneously polarization derotation and mitigation of intersymbol interference. We also analyze two different transmitter architectures modulating all three dimensions where the interpolarization phase is modulated over two levels using either a direct phase modulator (DPM) or a binary phase modulator, also called a BPSK modulator. We study the impact of increasing the bandwidth efficiency from 4 to 5 b/symbol by adding two level modulation of the interpolarization phase of a dual-polarization 4-level pulse amplitude modulation (PAM4) signal on the signal quality of the PAM4 IM on the polarization bearing the phase modulator by modeling the optical fields generated by both architectures. Assuming equal quality of the driving signals to the PAM4 and phase modulator, we show that a DPM minimizes the impact on PAM4 for short reach direct detect systems operating close to the zero dispersion wavelength where chromatic dispersion is negligible.