Internal Waves In Shallow Water Research Articles

Structure of interferogram and hologram of non-moving source in presence of shallow water internal waves

The results of holographic signal processing of the oceanographic experiment SWARM-95 on the coast of New Jersey are presented in the paper. The used acoustic signals were obtained on stationary acoustic track (non-moving airgun source) in the presence of shallow water intensive internal waves (IIW). The IIW led to significant 3D acoustic effects [Badiey et al., JASA 117(2), 613–625]. Within framework of holographic signal processing [Pereselkov and Kuz’kin, JASA 151(2), 666–676] the source interferogram (sound intensity distributions in frequency-time coordinates) is analyzed by two-dimensional Fourier transform (2D-FT). The result of the 2D-FT is called the Fourier hologram (source hologram). In result of holographic signal processing, the two separated sets of spectral spots are obtained in hologram domain. The first set of spectral spots corresponds to sound field in nonperturbed waveguide (without of IIW). The second set of spectral spots in hologram corresponds to hydrodynamic field perturbation by IIW. This structure of the hologram allows the reconstruction of interferogram of nonperturbed field for waveguide in the absence of IIW. The error in the reconstruction of the nonperturbed interferogram is estimated. [Work supported by grant from the Russian Science Foundation 23-61-10024.]

Sparse reconstruction of acoustic interference fringes in shallow water and internal wave environment

To reduce the distortion of acoustic interference fringes caused by internal waves in shallow water, a sparse reconstruction method of acoustic interference fringes is proposed in this paper according to the coupled mode theory. The proposed method consists of two steps: 1) The interference fringes are approximated to the sum of several two-dimension sinusoids, which are sparsely reconstructed by the vector finite rate of innovation method. 2) According to coupled mode theory, two-dimension frequencies related to uncoupled mode pairs do not vary with the location of internal waves. However, two-dimension frequencies related to coupled mode pairs vary with the location of internal waves. So these frequencies are classified into two parts. The uncoupled mode pairs are used to recover the regular interference fringes and estimate the waveguide invariant in the background environment. The coupled mode pairs are used to track the locations of internal waves. The simulation results show that the proposed method can effectively provide interference fringe reconstruction, waveguide invariant estimation, and internal wave tracking in the internal wave environment.

Modes selection based on holographic interferometry in presence of intense internal waves in shallow water

A holographic method is proposed for sound field modes selection and estimating their parameters (amplitude, horizontal wavenumber, group velocity, absorption coefficient) in shallow water by single scalar receiver in presence of intense internal waves (IIW). It is taken into account that IIW leads to horizontal refraction and modes coupling. The offered holographic method is based on the two-dimensional Fourier transform (2D-FT) of the real part of the moving-source sound field in time–frequency domain. It is shown in the paper that different sound field modes create different focal spots in the hologram domain in presence of IIW. The relationship of the mode phases and group velocities with the coordinates of focal-spot peaks is derived. The hologram domain allows to reconstruct the selected mode field and mode parameters in presence of IIW. The results of modes selection within framework of the numerical experiments are presented in the paper. The modal parameters are estimated. Analysis of influence of IIW on mode selection and mode parameters estimations is performed. It is shown that the effects of horizontal refraction and modes coupling do not lead to loss of the identity of mode parameters of the received signal. [This study was supported by Russian Science Foundation grant no. 22-79-10233. E.S. Kaznacheeva’s numerical experiment was supported grant no. МК-6144.2021.4]

Influence of internal wave induced sound speed variability on acoustic propagation in shallow waters of North West Bay of Bengal

This study focuses on the influence of internal wave induced sound speed variability on acoustic propagation parallel to the coast in shallow waters of North West Bay of Bengal (BoB). An acoustic transmission and reception experiment had been conducted at the site during February 2018 with simultaneous acquisition of oceanographic data, to examine propagation characteristics. The 950 Hz signal from an anchored vessel was received by an array of hydrophones moored 50 km away, with a loss of ∼ 80–95 dB with respect to the source position, receiver depth and sound speed variability. Sound speed variations in the acoustic environment were simulated using a shallow water internal wave model called WAVE to characterize the acoustic environment. Derived internal wave features from oceanographic and acoustic observations from study location during the experiment period were used to simulate the internal wave acoustic environment. Sound propagation using BELLHOP model was carried out with a simulated internal wave sound speed environment for 950 Hz source frequency. Model and observed temporal variability of transmission loss with sound speed at both source depth and thermocline depth has been addressed. Transmission loss features are comparable with field observations and model limitations are reflected in the results thus showing errors between two approaches. Range dependent bathymetry and other ocean acoustic parameters influence transmission loss at the study location. Temperature and salinity are major parameters influencing sound speed fluctuation in shallow waters, and corresponding variations are reflected in transmission loss and propagation. Finally this study provides a quantitative support in transmission loss in both modeling and experimental approaches at the study location.

Low-Frequency Acoustic Propagation Through Crossing Internal Waves in Shallow Water

Crossing internal wave trains are commonly observed in continental shelf shallow water. In this paper, we study the effects of crossing internal wave structures on three-dimensional acoustic ducts with both theoretical and numerical approaches. We show that, depending on the crossing angle, acoustic energy, which is trapped laterally between internal waves of one train, can be either scattered, cross-ducted or reflected by the internal waves in the crossing train. We describe the governing physics of these effects and illustrate them for selected internal wave scenarios using full-field numerical simulations.

Stokes drift of plankton in linear internal waves: Cross‐shore transport of neutrally buoyant and depth‐keeping organisms

AbstractThe meroplanktonic larvae of many invertebrate and vertebrate species rely on physical transport to move them across the shelf to their adult habitats. One potential mechanism for cross‐shore larval transport is Stokes drift in internal waves. Here, we develop theory to quantify the Stokes velocities of neutrally buoyant and depth‐keeping organisms in linear internal waves in shallow water. We apply the analyses to theoretical and measured internal wave fields, and compare results with a numerical model. Near the surface and bottom boundaries, both neutrally buoyant and depth‐keeping organisms were transported in the direction of the wave's phase propagation. However, neutrally buoyant organisms were transported in the opposite direction of the wave's phase at mid depths, while depth‐keeping organisms had zero net transport there. Weakly depth‐keeping organisms had Stokes drifts between the perfectly depth‐keeping and neutrally buoyant organisms. For reasonable wave amplitudes and phase speeds, organisms would experience horizontal Stokes speeds of several centimeters per second—or a few kilometers per day in a constant wave field. With onshore‐polarized internal waves, Stokes drift in internal waves presents a predictable mechanism for onshore transport of meroplanktonic larvae and other organisms near the surface, and offshore transport at mid depths.

Parameter dependence of acoustic mode quantities in an idealized model for shallow-water nonlinear internal wave ducts.

Nonlinear internal waves in shallow water have significant acoustic impacts and cause three-dimensional ducting effects, for example, energy trapping in a duct between curved wavefronts that propagates over long distances. A normal mode approach applied to a three-dimensional idealized parametric model [Lin, McMahon, Lynch, and Siegmann, J. Acoust. Soc. Am. 133(1), 37-49 (2013)] determines the dependence of such effects on parameters of the features. Specifically, an extension of mode number conservation leads to convenient analytical formulas for along-duct (angular) acoustic wavenumbers. The radial modes are classified into five types depending on geometric characteristics, resulting in five distinct formulas to obtain wavenumber approximations. Examples of their dependence on wavefront curvature and duct width, along with benchmark comparisons, demonstrate approximation accuracy over a broad range of physical values, even including situations where transitions in mode types occur with parameter changes. Horizontal-mode transmission loss contours found from approximate and numerically exact wavenumbers agree well in structure and location of intensity features. Cross-sectional plots show only small differences between pattern phases and amplitudes of the two calculations. The efficiency and accuracy of acoustic wavenumber and field approximations, in combination with the mode-type classifications, suggest their application to determining parameter sensitivity and also to other feature models.

Sound propagation effects of near-seabed internal waves in shallow water

Computational modeling is used to examine effects of near-seabed nonlinear internal waves. Waves of this type have been observed many times on the South New-England Shelf and elsewhere. The waves appear to be common when the dominant vertical density gradient zone is near the seabed. Many observations have been with profilers that alias the waves, or with instruments fixed to the seafloor that provide snapshots of passing waves. We have recently observed these features in greater detail using acoustic remote sensing from a ship, and we are now in a position to model their effects on sound propagation. Results are presented for many frequencies and many source/receiver/wave geometries. An important question remains about along-crest coherence of the waves, which would govern ducting and other anisotropic propagation effects. These waves are not as well studied as waves linked to a near-surface pycnocline, which can be studied remotely with EM via surface signature. The strong density gradients found in many shallow water areas allow the internal waves to have high frequencies, creating rapidly changing acoustics thereby shortening acoustic coherence time. The related strong sound-speed gradients, found both near the surface and near the seabed, are responsible for the important acoustic effects of the waves.

Bottom attenuation estimation using sound intensity fluctuations due to mode coupling by nonlinear internal waves in shallow water.

Analyses of fluctuations of low frequency signals (300 ± 30 Hz) propagating in shallow water in the presence of nonlinear internal waves (NIWs) in the Shallow Water 2006 experiment are carried out. Signals were received by a vertical line array at a distance of ∼20 km from the source. A NIW train was moving totally inside of the acoustic track, and the angle between the wave front of the NIW and the acoustic track in the horizontal plane was ∼10°. It is shown that the spectrum of the sound intensity fluctuations contains peaks corresponding to the coupling of pairs of propagating modes. Analysis of spectra at different hydrophone depths, and also summed over depth allows the authors to estimate attenuation in the bottom sediments.

Sound intensity fluctuations as evidence of mode coupling due to moving nonlinear internal waves in shallow water

One of manifestation of mode coupling produced by moving nonlinear internal (NIW) waves is temporal fluctuations of intensity or amplitude. In spectrum of fluctuations measured during a few hours there are maximums at frequencies, corresponding to periodical (in time) interaction of moving NIW with periodical (in range) interference structure of the sound field. If velocity of NIW along acoustic track is v, then peaks are placed at frequencies Fmn~v(km-kn) , where km is propagation constant of mode m. Due to a few remaining modes in a long range propagation, spectrum should have peaks at a few predominating frequencies. In given work on the base of experimental data of ASIAEX 01 and the corresponding theoretical analysis, it is shown existence of predominating frequencies in spectrum of the sound intensity fluctuations in the presence of NIW moving along acoustic track of the length ~35 km. Both speed of NIW and scales of interference beating determine mentioned frequencies. Note that acoustic track consi...

Modeling the effects of linear shallow-water internal waves on horizontal array coherence.

The coherence length of a horizontal array is the maximum separation between two points where coherent processing gives useful gain when a distant source is at broadside. In shallow water, the coherence length is limited by the environmental variability caused by several relevant oceanographic processes. In the present study, a statistical model is developed that quantifies how one oceanographic process, linear internal waves, affects the coherence length. A key input to the ocean sub-model is the vertically integrated energy density of the internal wave field. The acoustic sub-model is based on the adiabatic normal mode approximation and so should be reasonable for frequencies under 1 kHz. Numerical calculations using environmental data from the Shallow Water 2006 Experiment (SW06) show how the coherence length of individual modes varies with consequent effects on array coherence. The coherence length is shown to be a strong function of where the source and array are positioned in the water column. For a bottom-mounted array above a moderately lossy seabed, the model predicts a coherence length that depends only weakly on range, an effect observed in field experiments.

The role of water column variability on three-dimensional sound propagation in shallow water

Simultaneous measurements of sound field and the sound speed profile perturbed by passage of internal waves in shallow water and the resulting modal evolution in space-time domain is reported. The waveguide modal behavior for broadband signals centered at 100, 200, and 300 Hz with the bandwidth of 60 Hz during the Shallow Water 2006 (SW06) experiment is studied using an L-shaped hydrophone array. Several cases are considered where the angle of the internal wave front with the acoustic track ranges from −8 to + 83 degrees. Mode filtering obtained from the vertical array and tracking the filtered mode along the horizontal array reveals that individual modes propagating between the source and receiver arrive at different angles. Using the method of vertical modes and horizontal rays the phase of the acoustic field is calculated and the change in the angle of arriving ray at the L-shaped array, that is the horizontal angle of refraction, is obtained. A 3D PE model is used for comparison between the calculations and the experimental data. [Work supported by ONR 322OA.]

Possibility of False Target Signals Induced by Reverberation Due to Internal Waves in Shallow Water

It is investigated that there exists the possibility of the false target signals induced by reverberation in an active sonar system due to the internal waves in shallow water. The rays down-refracted from the internal waves may generate strong bottom-reverberation signals, which can result in false target signals. Sound waves emitted from a source propagate 3-dimensionally. Therefore, the study of internal waves on the reverberation should be studied for azimuthal direction as well as 2-dimensional (r-z) plane. Internal-wave modelling was conducted, based on solitons which were predicted with the various conditions such as, the range of source-soliton, horizontal widths of soliton. Variable depth sonar (VDS) was assumed as a source, of which the depth was located in the minimum sound speed layer in a simulation environment. Finally, the simulation on the reverberation level with time was made based on ray-based reverberation model, and the results implied that several false-target signals could be displayed on the PPI(Plan Position Indicator) scope simultaneously with range from source to soliton, and the horizontal width of soliton.

Sound intensity fluctuations due to mode coupling in the presence of nonlinear internal waves in shallow water

Intensity fluctuations of the low frequency LFM signals (band 270–330 Hz) were observed in Shallow Water 2006 experiment in the presence of moving train consisting of about seven separate nonlinear internal waves crossing acoustic track at some angle (~ 80º). It is shown that spectrum of the sound intensity fluctuations calculated for time period of radiation (about 7.5 minutes) contains a few peaks, corresponding to predominating frequency ~6.5 cph (and its harmonics) and small peak, corresponding to comparatively high frequency, about 30 cph, which is interpreted by authors as manifestation of horizontal refraction. Values of mentioned frequencies are in accordance with theory of mode coupling and horizontal refraction on moving nonlinear internal waves, developed earlier by authors. [Work was supported by BSF.]

Estimating waveguide parameters using horizontal and vertical arrays in the vicinity of horizontal Lloyd’s mirror in shallow water

When shallow water internal waves approach a source-receiver track, the interference between the direct and horizontally refracted acoustic paths from a broadband acoustic source was previously shown to form Horizontal Lloyd’s mirror (Badiey et al. J. Acoust. Soc. Am. 128(4), EL141–EL147, 2011). While the modal interference structure in the vertical plane may reveal arrival time for the out of plane refracted acoustic wave front, analysis of moving interference pattern along the horizontal array allows measurement of the angle of horizontal refraction and the speed of the nonlinear internal wave (NIW) in the horizontal plane. In this paper we present a full account of the movement of NIW towards a source-receive track and how we can use the received acoustic signal on an L-shaped array to estimate basic parameters of the waveguide and obtain related temporal and spatial coherence functions particularly in the vicinity of the formation of the horizontal Lloyd mirror. Numerical results using Vertical Modes and Horizontal Rays as well as 3D PE calculations are carried out to explain the experimental observations. [Work supported by ONR 322OA.]

Sound fluctuations resulting from mode coupling in shallow-water internal waves

We conduct a theoretical analysis and numerical simulation of fluctuations of low-frequency signals propagating in shallow water in the presence of nonlinear internal waves moving approximately along the acoustic track. It is believed that mode coupling causes the fluctuations. We show that in the fluctuation spectra there are characteristic frequencies that are proportional to the motion velocity of solitons along the track. We calculate the sound field using single- and multimode sources and analyze the frequency-mode composition of the field responsible for the maximum and minimum fluctuations. We analyze the so-called dominant fluctuation frequency introduced previously by the authors, which corresponds to fluctuations with the maximum amplitude in the given frequency range and for the given set of modes. We compare the calculation results with estimates obtained previously by the authors within the framework of ray theory.

Effect of internal waves on the waveguide invariant distribution

Multipath propagation in the ocean waveguide results in constructive and destructive interference between the paths. The resulting interference pattern, mapped versus range and frequency, often exhibits striations, alternating bands of high and low intensity. In simple waveguides, the trajectory of these striations can often be described by a single scalar parameter, the so-called waveguide invariant. In more complicated waveguides, the concept can be generalized to create the waveguide invariant distribution. In the present work, the effects of shallow water internal waves on the waveguide invariant distribution are examined. It is shown how internal waves can blur otherwise sharp striations and flatten the waveguide invariant distribution. [Work supported by ONR.]

Reverberation clutter induced by nonlinear internal waves in shallow water

Clutter is related to false alarms for active sonar. It is demonstrated that, in shallow water, target-like clutter in reverberation signals can be caused by nonlinear internal waves. A nonlinear internal wave is modeled using measured stratification on the New Jersey shelf. Reverberation in the presence of the internal wave is modeled numerically. Calculations show that acoustic energy propagating near a sound speed minimum is deflected as a high intensity, higher angle beam into the bottom, where it is backscattered along the reciprocal path. The interaction of sound with the internal wave is isolated in space, hence resulting in a target-like clutter, which is found to be greater than 10 dB above the mean reverberation level.

SHOALING OF NONLINEAR INTERNAL WAVES ON A UNIFORMLY SLOPING BEACH

The internal waves in the two-layer systems have been numerically simulated by solving the set of nonlinear equations in consideration of both strong nonlinearity and strong dispersion of waves. After the comparison between the numerical results and the BO solitons, as well as the experimental data, the internal waves propagating over the uniformly sloping beach are simulated including the cases of the mild and long slopes. The internal waves show remarkable shoaling after the interface touches the critical level. In the lower layer, the horizontal velocity becomes larger than the local linear celerity of internal waves in shallow water just before the crest peak and the position is defined as the wave-breaking point when the ratio of nonlinear parameter to beach slope is large. The ratio of initial wave height to wave-breaking depth becomes larger as the slope is milder and the wave nonlinearity is stronger. The wave height does not increase so much before wave-breaking on the mildest slope.

The mode coupling and effect on ambient noise vertical directionality caused by internal waves in shallow water

Experiments show that internal waves can cause the fluctuation of the depth of thermocline in shallow water, which may bring about two results: one is the change of hit number of sound rays and sea bottom, the other is mode coupling. The former changes the sound intensity, and the latter changes the sound energy distribution. The previous studies show that internal waves cause mode coupling by changing the sound propagation paths, which can fill the noise notch. In the calculation, it is found that the notch is deepened when some solitary internal waves are present. The reason is that the sound wave excited by the distant sources which are located on the palne near the sea surface propagates through the soliton which is a single downward undulation. The mode coupling from low-order modes to higher-order modes happens first, then the reverse conversion occurs. However, the former coupling is stronger, the lower-order modes fall off and the filling ability is weakened, so the notch is deeper.