Propagation In Deep Water Research Articles

High-Order Boussinesq Equations for Water Wave Propagation in Porous Media

To accurately capture wave dynamics in porous media, the higher-order Boussinesq-type equations for wave propagation in deep water are derived in this paper. Starting with the Laplace equations combined with the linear and nonlinear resistance force of the dynamic conditions on the free surface, the governing equations were formulated using various independent velocity variables, such as the depth-averaged velocity and the velocity at the still water level and at an arbitrary vertical position in the water column. The derived equations were then improved, and theoretical analyses were carried out to investigate the linear performances with respect to phase celerity and damping rate. It is shown that Boussinesq-type models with Padé [4, 4] dispersion can be applied in deep water. A numerical implementation for one-dimensional equations expressed with free surface elevation and depth-averaged velocity is presented. Solitary wave propagation in porous media was simulated, and the computed results were found to be generally in good agreement with the measurements.

A two-layer viscous Boussinesq-type model for surface waves: Derivation, analysis, numerical implementation, and verification

A two-layer viscous Boussinesq-type model is developed to simulate the wave energy dissipation during wave propagation in deep water. The viscous terms are incorporated into both the dynamic and kinematic boundary conditions at the free surface, and the corresponding analytical solution of the second-order amplitude has been derived for the first time. The linear and nonlinear properties of the model are analyzed with different viscosity coefficients. When the viscosity coefficient is 1 × 10−4 m2/s, the linear phase velocity, decay rate, second-order amplitude, and velocity profiles of the viscous model are accurate for up to h/L0 (h is water depth, L0 is characteristic wavelength) ≈ 8.66, 5.86, 3.60, 3.60, and 7.51 within 1% error, respectively. The finite difference method is adopted for the numerical implementation of the model. To verify the linear and nonlinear properties of the model, computed results for linear waves and focused wave group in deep water are compared with linear analytical solutions and experimental data, respectively.

Pacific Echo: A deep ocean collaborative experiment

This paper summarizes experiments carried out using towed line arrays in the Pacific Echo sea trials. Although John Preston was not a participant, the experiments are examples consistent with his efforts in promoting collaborative research at sea with horizontal arrays. The overall goal of Pacific Echo was to study the impact of thin sediment ocean bottom environments on sound propagation in deep water. The objective of the experiments described here was to study the evolution of young oceanic crust. The hypothesis was that the sound speed of young basalt increased with age of the crust. Sound speed was inferred from low frequency measurements of the reflection coefficient versus grazing angle at sites of increasing distance from the deep ocean spreading center. The experiments introduced a novel design for measuring the reflection coefficients using two ships and small explosive charges. The signals at the array were spatially filtered to resolve the specular reflections as the ships opened range on set courses. The data provided estimates of both the compressional and shear wave speeds of the basalt. Results from the broadside reflection technique showed that sound speed increased with crustal age and were consistent with measurements obtained from conventional seismic reflection surveys.

Three-Dimensional Sound Propagation in the South China Sea with the Presence of Seamount

Seamounts have important effects on sound propagation in deep water. A sound propagation experiment was conducted in the South China Sea in 2016. The three-dimensional (3D) effects of a seamount on sound propagation are observed in different propagation tracks. Ray methods (BELLHOP N×2D and 3D models) are used to analyze and explain the phenomena. The results show that 3D effects have obvious impacts on a sound field within a horizontal refraction zone behind the seamount because some sound beams cannot reach the receiver for the horizontal refraction effects, which impacts the sound field within a certain angle range behind the seamount. The arrival structure results show that the eigenrays after horizontal reflection will arrive at the receiver earlier than those obtained from the two-dimensional (2D) model within the horizontal refraction zone behind the seamount. This means that the horizontal reflection effect of a seamount will cause the shortening of sound propagation paths. Finally, in the reflection zone in front of the seamount, the 2D and 3D TL results show that the shape of the reflection zone is similar to an “arch” type, and the horizontal refraction of sound waves has little effect on the TLs in the reflection zone of a seamount.

Uncertain Effects of Linear Internal Waves on Convergence Zone Propagation in Deep Water

Zhang, L.; Chen, W., and Liu, D., 2020. Uncertain effects of linear internal waves on convergence zone propagation in deep water. In: Zheng, C.W.; Wang, Q.; Zhan, C., and Yang, S.B. (eds.), Air-Sea Interaction and Coastal Environments of the Maritime and Polar Silk Roads. Journal of Coastal Research, Special Issue No. 99, pp. 296–309. Coconut Creek (Florida), ISSN 0749-0208.The use of the convergence zone effect is an important means of underwater long-range target detection. Many uncertain factors (ocean fronts, ocean eddies, etc.) can lead to uncertainties of the sound field in the convergence zone. Linear internal waves are usually produced in the deep ocean, causing fluctuations of the sound velocity which are otherwise stable. Over long distances, linear internal waves will have a great influence on the propagation of sound waves. In this paper, a model of sound velocity fluctuation caused by linear internal waves is established, and the sound velocity field within a certain depth and distance range is obtained. The transmission loss is calculated using the ray mode parabolic equation underwater sound propagation model. The Monte Carlo method is then used to simulate the uncertainty of the sound field in the generated convergence zone. The results shows that the loss of sound propagation varies greatly when an internal wave propagates through the convergence zone. The uncertainty of the sound field in different convergence zones varies, and the uncertainty of the sound field increases with convergence zone range.

Sensitivity of sound speed fluctuation on acoustic arrival delay of middle range in deep water

For middle range acoustic propagation in deep water, there exists mainly four types of ray arrivals, namely direct path arrival, one time surface-reflected (SR) arrival, one time bottom-reflected (BR) arrival and one time surface-reflected bottom-reflected (SRBR) arrival. With Bellhop ray model, sensitivity of sound speed fluctuation on the arrival delay of middle range in deep water was studied. Argo profiles in Philippine Sea were used to establish the Sound Speed Profile (SSP) fluctuation set with the Empirical Orthogonal Function (EOF) method. Numerical simulation suggests that when the source was closer to the sea surface, the relative delay structure was more sensitive to the SSP fluctuation, and that the SR arrival and the SRBR arrival were more sensitive to the fluctuation than the BR arrival. When receiver range increases from 20 km to 30 km, sensitivities of ray arrivals gradually increase. Acoustic arrival delay data in the Philippine Sea experiment was used to invert the SSP. The inverted result agrees with the measured data well, suggesting the arrival structure was a nice choice for acoustic tomography of middle range in deep water.

Numerical verification of a two-layer Boussinesq-type model for surface gravity wave evolution

A vertical two-dimensional numerical model is developed to demonstrate the application potential of the recently proposed two-layer Boussinesq-type equations, which have been theoretically shown to exhibit high accuracy in both linear and nonlinear properties, by the authors (Liu and Fang, 2016). Numerical implementation is established on a regular uniform grid, combined with finite differencing of the spatial derivatives and a composite fourth-order Adams–Bashforth–Moulton time integration. Initially, some idealized numerical experiments are designed to examine the fundamental aspects of the model, including the linear dispersion, linear shoaling gradient and highly nonlinear velocity profile. Next, challenging numerical experiments for the regular wave evolution over a submerged breakwater, bichromatic wave evolution in a long flume and focused wave group evolution in a short flume are carried out. The computed results are consistent with the experimental data. By simulating moderately and highly nonlinear wave propagation in deep water, we further investigate the effect of nonlinear terms in the governing equations on the numerical performance. The numerical test of the evolution process of highly nonlinear regular water waves shows that retaining third-order nonlinear terms in the governing equations can provide more accurate computational results.

An experiment of air-to-water sound propagation in deep water

The underwater sound propagation from an airborne source has been paid much attention recently. To explore the underwater sound propagation from an airborne source in deep water, an experiment was conducted in South China Sea. A vertical line array of hydrophones with depth from 100 meters to 3400 meters was anchored on the seabed to detect the sound of a loudspeaker. Two microphones were placed under the loudspeaker to measure the source level. Both continuous and linear frequency modulation wave signals with frequency from 100 Hz to 2000 Hz were transmitted by the loudspeaker. The distances between the loudspeaker and the vertical line array were from 5km to 14.5km. Comparing signal detected by underwater hydrophones with signal detected by microphones in air, transmission loss of is figured out. The transmission loss predicted by a wave number integration model OAST is compared with the experimental results.

Some examples of the application of high-performance computing for time-domain full-wave simulations in underwater acoustics using a spectral-element method

Being able to perform accurate time-domain full-wave simulations in underwater acoustics is important within the context of complex environments. Among the numerical methods that can be used to perform such types of simulations, the spectral-element method is a method of choice because it can take advantage of the possibilities offered by high-performance computing. This capability is very important because accurate numerical simulations require a high computational power. In this presentation we will show some examples of the use a spectral-element method for underwater acoustics applications. 2D simulations as well as 3D simulations will be considered for various configurations, illustrating the interest of performing such simulations. Shallow water propagation, deep water propagation as well as diffraction by objects in complex environments will be analyzed.

Horizontal refraction effects of seamounts on sound propagation in deep water

The seamounts usually have important effects on sound propagation in deep water. A sound propagation experiment was conducted in the South China Sea in 2016. One of the experimental goals is to investigate the three-dimensional(3D) effects of seamounts on sound propagation. Phenomena about horizontal refraction of acoustic waves are observed in different propagation tracks which go through the seamount along different directions when the source depth is 200 m. Ray methods (BELLHOP N×2D and 3D models) which can calculate sound field efficiently and show clear physical images, are used to analyze and explain the causes of the phenomena. The experimental and numerical results show that the convergent zone structures are destroyed by the direct blockage of seamount due to the multiple reflection of acoustic waves, which leads to the increase of transmission loss (TL), and horizontal-refraction zone with obvious boundaries appears behind the seamount. Some experiment phenomena cannot be explained by BELLHOP N×2D model in which the horizontal refraction effects are not taken into consideration. The experimental sound field structure behind the seamount is obviously different from N×2D model numerical result, i.e.the width of shadow zone based on the experimental data is wider than that calculated by N×2D model, and the width of strong horizontal-refraction zone from the experiment is narrower than the N×2D model result. Moreover, the TLs calculated by N×2D model is about 10 dB less than the experimental result in horizontal refraction zone. After analyzing the difference between experimental data and N×2D model numerical results by BELLHOP 3D model which contains the azimuth-coupling capability, it can be concluded that sound waves reach the receiver through horizontal refraction after the interaction with seamount when the source is located behind the seamount. The eigenrays obtained from 3D model are less than N×2D model numerical result because some of sound beams cannot reach the receiver as a result of the horizontal refraction effects, which leads to the experimental TLs larger than the numerical results calculated by N×2D model. Therefore, 3D effect of seamount has an obvious influence on sound field within a certain angle range behind the seamount, and the investigation of 3D effects of seamounts is meaningful for the sound propagation and target detection in deep water.

Sound propagation in deep water with an uneven bathymetry

Water depth has significant effects on sound propagation in underwater. A deep-water propagation experiment along two different tracks with the flat and uneven bottoms was conducted in the South China Sea in 2014. Some different propagation phenomena and horizontal-longitudinal correlations oscillation patterns were observed. Due to the reflection-blockage effects by a sea hill with height less than 1/10 water depth, transmission losses increase up to about 8 dB in the reflection area of the sea hill than that of flat bottom. Moreover, there is an inverted-triangle shadow zone with a maximal depth of 1500 m below the sea surface. The horizontal-longitudinal correlations in the reflection area of the sea hill do not show an obvious cyclical oscillation any longer as that in flat bottom environment. The differences of the transmission losses and the horizontal-longitudinal correlations oscillation patterns are explained by using the ray theory. [Work supported by the National Natural Science Foundation of China under Grant Nos. 11434012, 41561144006, and 11404366.]

Random matrix theory simulation of propagation through internal waves

Hegewisch and Tomsovic proposed using random matrix theory (RMT) to simulate the effect of internal wave scattering on long-range propagation in deep water [JASA, 2013]. They model mode propagation as the multiplication of a series of unitary propagator matrices whose statistics are derived using perturbation theory. A simplifying assumption facilitates the generation of broadband time series. One potential advantage of the RMT approach is that it requires fewer computations than a full wave simulation to produce a large set of statistical realizations of the received time series [Hegewisch & Tomosovic, Europhys. Lett. 2012]. Efficient simulation techniques are especially important for applications that require predictions of the timefront and/or its statistics at a large number of possible receiver ranges. For example, simulating data sets for acoustic gliders operating within a tomographic array is computationally intensive. While Hegewisch and Tomsovic illustrated the performance of their approach for one deep water simulation environment, they also highlighted the need for additional research. This talk investigates the feasibility of using RMT to efficiently simulate broadband time series for use in analysis of glider data. The underlying assumptions of the RMT approach will be assessed based on results of prior experimental work. [Work sponsored by ONR.]

The effects of the sloping bottom environment on sound propagation in deep water

Variation of bathymetry has large effects on sound propagation. An acoustic propagation experiment was conducted in the South China Sea. Some different propagation phenomena are observed for two different tracks with the flat bottom and the sloping bottom environments when the source depth is 131 m. Numerical analysis based on the ray methods is carried out to explain the causes of the differences. The experimental and numerical results show that when a sea hill with height of 320 m, which is less than 1/10 of water depth, exists at the range of sound beams with the grazing angles from 10° to 20° incident on bottom first time, an inverted-triangle shadow zone appears at the reflection-blockage area of the sea hill. Compared with the TLs results in the flat bottom environment, TLs increase up to about 8 dB in the corresponding area of the first shadow zone, and the abnormal TLs effects can reach to maximal depth of 1300 m. The first convergence zone caused by refractions of sound beams with small grazing angles within 10° from the water above the axis of sound channel is lost. There are only the sound beams refracted back from water below the axis of sound channel. It’s quite different from the convergence-zone structure in deep water with flat bottom. Thus, the accuracy of bathymetry is meaningful for sound propagation and target detection in deep water.

The reflection and shadow effects of seamounts on sound propagation in deep water

The seamounts have enormous effects on sound propagation in deep water. Some abnormal propagation phenomena were observed for two different tracks with the flat bottom and the seamounts bottom environments. A propagation experiment was conducted in the South China Sea in 2014. The effects of seamounts on sound propagation were analyzed by using the wideband signals. It’s observed that, in the first shadow zone about 28 km, the transmission loss (TL) for the environment with the seamounts was decreased up to 7 dB compared with the TL for the environment without the seamounts, due to the reflection effects of the seamount. And in the first convergence zone about 56 km, the TL was increased more than 30 dB for the shallow source. It was because that most of the deep refraction waves were blocked by the seamount. In the reflection zone of seamount, the TL increased as the depth of the receiver became deeper for less of sound rays could arrival and most of the grazing angles became bigger. Moreover, the TL difference between receiver depth 170 and 1868 m was nearly 10 dB. At the range more than 30 km, the TL trends were consistent as receiver depth vary from 170 to 1868 m, because it can be equivalent to that all the rays were reject from the top of the seamount. The numerical TLs and pulse arrival structures can match with experimental results well. Abnormal TLs and pulse arrival structures at different ranges are explained by using ray and wave theory.

Sound propagation in deep water with a sloping bottom

Variation of bathymetry has a large effect on the sound propagation in deep water. An acoustic propagation experiment is carried out in the South China Sea. Some different propagation phenomena are observed for two different tracks in the flat bottom and the sloping bottom environments. Numerical analysis based on the parabolic equation model RAM (range-dependent acoustic model) is performed to explain the causes of the differences. The experimental and numerical results show that the transmission losses (TLs) decrease down to about 5 dB above the slope due to the reflection of the bottom, with a high-intensity region appearing below the sea surface. When a sea hill with a height of 320 m, which is less than 1/10 of water depth, exists in the incident range of sound beams on bottom first time, the sound beams are blocked due to the reflection of the sea hill. Then their propagating directions are changed, which makes an inverted-triangle shadow zone appearing in the reflection area of the sea hill. Compared with the TL results in the flat bottom environment, TLs increase up to about 8 dB in the corresponding area of the first shadow zone, and the abnormal TL effects can reach a maximal depth of 1500 m. Consequently, the shadow amplification effect caused by a small variation of bathymetry in deep water for long-range/large-depth sound propagation should receive enough attention. Furthermore, the convergence-zone structure in the sloping environment is different from that in deep water with flat bottom. The first convergence zone caused by refractions from the water above the axis of sound channel disappears. There are only the sound beams refracted back from water below the axis of sound channel. The numerical simulations show that the reflection-blockage of sound beams caused by the sloping bottom is significant. When the source is located somewhere above the slope, sound beams with large grazing angles can be reflected by the sloping bottom, and only some sound beams with small grazing angles can be refracted in the water without touching the slope and then come into the depth range of the vertical line array (VLA), forming the first part of the convergence zone refracted back from water. As the source moves farther from the VLA, the reflection-blockage of the sloping bottom becomes stronger. Sound beams are all reflected by the slope at a depth of about 3000 m, and they go through below the VLA, which leads to the absence of the first convergence zone caused by refractions from the water above the axis of sound channel. Therefore, the accuracy of bathymetry is meaningful for the sound propagation and target detection in deep water.

The Effects of Seamounts on Sound Propagation in Deep Water**Supported by the National Nature Science Foundation of China under Grant Nos 11434012 and 11174312.

A propagation experiment was conducted in the South China Sea in 2014 with a flat bottom and seamounts respectively by using explosive sources. The effects of seamounts on sound propagation are analyzed by using the broadband signals. It is observed that the transmission loss (TL) decreases up to 7 dB for the signals in the first shadow zone due to the seamount reflection. Moreover, the TL might increase more than 30 dB in the converge zone due to the shadowing by seamounts. Abnormal TLs and pulse arrival structures at different ranges are explained by using the ray and wave theory. The experimental TLs and arrival pulses are compared with the numerical results and found to be in good agreement.

Numerical modelling of the wave energy in Galway Bay

A coupled modeling system was implemented to characterize the wave conditions and assess the wave energy potential at Galway Bay using WAVEWATCH IIII (WWIII) for wave generation and deep water propagation and SWAN model for wave propagation in intermediate and shallow water. Wind fields were taken from ECMWF's ERA Interim data base. Validation tests were carried out for the period between 2007 and 2010 with buoy data so that the model's performance could be evaluated.The wave parameters considered for the comparisons in the time domain are significant wave height and mean period. Statistical analysis of the results is made and its time series evolution is also presented. For the energy assessment an evaluation of the spatial distribution of wave power is done and, since Galway Bay is a quarter scale test site for wave energy devices, statistical results were presented for three years of data, providing statistics of the expected wave energy resource in the Bay.

Deep water acoustic propagation in the northern Philippine Sea: Comparison of observed ray travel times with a non-acoustic state estimate

Six transceivers and one distributed vertical line array (DVLA) receiver were moored in the northern Philippine Sea from April 2010 to May 2011 for low-frequency (325 Hz and below), deep water propagation experiments. The shortest range was about 130 km and the longest about 640 km. A 2009 equipment test yielded travel times between a moored source and a more limited DVLA at about 185 km range along one of the 2010–2011 paths. Experimental goals included understanding the impacts of fronts, eddies, and internal tides on acoustic propagation and determining the utility of acoustic measurements for ocean state estimation. This presentation will report on comparisons between ray travel times computed in a state estimate for the Northern Philippine Sea excluding the ray data, and observations from the 2009 and 2010–2011 experiments. The state estimate uses satellite sea surface height and sea surface temperature observations as well as Argo and XBT profiles. Ray arrival times calculated from the state estimate will be compared to observations as a simple estimate of the novel information present in the data.

Dispersion of tsunamis: does it really matter?

Abstract. This article focuses on the effect of dispersion in the field of tsunami modeling. Frequency dispersion in the linear long-wave limit is first briefly discussed from a theoretical point of view. A single parameter, denoted as "dispersion time", for the integrated effect of frequency dispersion is identified. This parameter depends on the wavelength, the water depth during propagation, and the propagation distance or time. Also the role of long-time asymptotes is discussed in this context. The wave generation by the two main tsunami sources, namely earthquakes and landslides, are briefly discussed with formulas for the surface response to the bottom sources. Dispersive effects are then exemplified through a semi-idealized study of a moderate-strength inverse thrust fault. Emphasis is put on the directivity, the role of the "dispersion time", the significance of the Boussinesq model employed (dispersive effect), and the effects of the transfer from bottom sources to initial surface elevation. Finally, the experience from a series of case studies, including earthquake- and landslide-generated tsunamis, is presented. The examples are taken from both historical (e.g. the 2011 Japan tsunami and the 2004 Indian Ocean tsunami) and potential tsunamis (e.g. the tsunami after the potential La Palma volcanic flank collapse). Attention is mainly given to the role of dispersion during propagation in the deep ocean and the way the accumulation of this effect relates to the "dispersion time". It turns out that this parameter is useful as a first indication as to when frequency dispersion is important, even though ambiguity with respect to the definition of the wavelength may be a problem for complex cases. Tsunamis from most landslides and moderate earthquakes tend to display dispersive behavior, at least in some directions. On the other hand, for the mega events of the last decade dispersion during deep water propagation is mostly noticeable for transoceanic propagation.

Quantifying the mesoscale variability in the western subtropical countercurrent (STCC) and its impact on acoustic propagation

During spring 2010 to spring 2011, the acoustics community deployed an impressive star-shaped moored array in the Philippine Sea to study acoustic propagation in deep water and its relationship to the oceanographic variability at a wide range of space and time scales. In addition to the acoustics instrumentation, six of the moorings spaced from 200-650 km apart were densely instrumented with velocity (u, v), Temperature (T), Conductivity (C), and Pressure (P) sensors making them ideally suited to study the mesoscale ocean circulation as well. Previous work has shown that the preferred baroclinic eddy length scale in the western STCC is order 350 km with most eddies propagating westward. These new observations will allow estimation of the vertical structure of the eddies, their propagation speed, their kinetic and available potential energy, and their dynamic stability. This improved view of the STCC eddies will be shared with the acoustics team for use in quantifying the impacts of the eddy variability on the acoustic propagation.