Ocean Propagation Research Articles

Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

We investigate a hydrodynamic equation system which—with some approximation—is capable of describing the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions of how the wave height and velocity behave in time and space for constant and linear seabed functions. First, we study waves on open water, where the seabed can be considered relatively constant, sufficiently far from the shore. We found original shape functions for the ocean waves. In the second part of the study, we also consider a seabed which is oblique. Most of the solutions can be expressed with special functions. Finally, we apply the most common traveling wave Ansatz and present relative simple, although instructive solutions as well.

Observations and Parametrization of the Turbulent Energy Dissipation Beneath Non-Breaking Waves

Here, for non-breaking short surface waves, we have experimentally determined the value of the turbulent eddy viscosity νT or its ratio νT*≡νT/ν, where ν is the water kinematic viscosity. The non-breaking wave-generated turbulent eddy viscosity νT was found to depend on the ratio of the wave period, T, to the microscale Kolmogorov time scale, τη. Our observations were consistent with νT*=1.46·(T/τη)−2.6 when (T/τη)<0.9. That implied that the νT*∝ϵ−1.3, where ϵ is the background turbulent energy dissipation rate. The near-surface turbulent flow associated with non-breaking waves was characterized by a short inertial subrange. The background turbulence appears to modulate the amount of energy the non-breaking waves dissipate locally and, consequently, the wave’s decay rate. Our results imply that the background turbulent flow acts as a lubricant, permitting waves to propagate further when traveling over a more energetic turbulent background flow. Our results have implications for the modeling of oceanic wave propagation or the air–sea exchange processes.

Exact solitary wave and numerical solutions for geophysical KdV equation

Tsunamis are strong waves, arisen from volcanic eruptions, landslides, or earthquakes sweeping across oceans. The geophysical Korteweg-de Vries (gKdV) equation which governs the tsunami wave propagation in oceans is investigated in this work using an improved exp(-F(η))-expansion method. Shooting and adaptive moving approaches are taken into account. We retrieve several new solitary solutions for the gKdV equation. The obtained solution from implementing shooting method is successfully used as an initial value for the adaptive approach which is utilized to construct the numerical solution of the proposed problem. The constructed exact solutions coincide with the obtained numerical solutions. The accuracy of the presented numerical approximations is discussed. We apply Fourier concept to explore the accuracy and stability of the numerical schemes which is unconditionally stable. A clear comparison between the analytic and numerical outcomes is presented via some 2D and 3D sketches which are depicted under special selections of some parameters. Moreover, we illustrate the relative error and CPU time for the numerical technique. The proposed approaches can be easily utilized to deal with other partial differential equations.

Estimation of Maximum Tsunami Heights Using Probabilistic Modeling: Bayesian Inference and Bayesian Neural Networks

Song, M.-J.; Kim, B.-H., and Cho, Y.-S., 2022. Estimation of maximum tsunami heights using probabilistic modeling: Bayesian inference and Bayesian neural networks. Journal of Coastal Research, 38(3), 548–556. Coconut Creek (Florida), ISSN 0749-0208. Although tsunamis may occur relatively infrequently, they can cause substantial loss of life and property damage. Most studies on tsunamis have focused on developing numerical models to describe ocean propagation and the associated run-up process because laboratory experiments are expensive. Probabilistic techniques have been used in various scientific and engineering fields with reasonable results. In this study, numerical simulations were performed for historical and virtual tsunami events to explore maximum tsunami heights. Bayesian inference and Bayesian neural networks were then employed to predict the maximum tsunami height. These results can be used to develop hazard maps for unexpected tsunami events.

A Block Sparse-Based Dynamic Compressed Sensing Channel Estimator for Underwater Acoustic Communication

Due to the complex ocean propagation environments, the underwater acoustic (UWA) multipath channel often exhibits block sparse time-varying features, and while dynamic compressed sensing (DCS) can mitigate the time-varying effects of the UWA channel, DCS-based algorithms have limited performance for the UWA channel with block sparsity. In this study, by formulating the UWA channel with blocks concatenation, a block sparse-based DCS approach (BS-CS) is proposed to explore the block and time-varying sparsity of UWA channel simultaneously. In detail, we firstly adopt a block sparse recovery algorithm, block orthogonal matching pursuit (BOMP), to compute the temporary estimate. Then, the CS approach is applied to compute the support additions, which are caused by the time-varying components of the UWA channel. Next, we use the selected support to perform the BOMP estimate, and obtain the estimated channel response. Finally, the numerical simulation and the sea experiment were carried out to verify the superior performance of the proposed BS-CS algorithm in the block sparse time-varying UWA channels.

The effect of compressed ice-shelf on acoustic-gravity wave propagation in a compressible ocean having elastic bottom

Acoustic-gravity wave propagation under a compressed ice-shelf is mathematically modelled under the assumption of small ice-shelf deflection, linearised compressible water wave theory, and ocean floor elasticity. The dispersion relation associated with the acoustic-gravity modes is derived. Special cases of the free surface gravity wave motion with a rigid and elastic bottom, and flexural-gravity wave motion with rigid ocean bottom are approximated by utilising the dispersion relation. The effect of ice-shelf thickness and compressive stress on the propagation speed is investigated for different acoustic-gravity modes. The pressure distribution along the water column and the ice-shelf due to different acoustic-gravity modes are illustrated. While ice thickness significantly alters the phase speed and pressure distribution, the compressive force generally has a negligible effect on the phase speed of acoustic-gravity modes. However, the compression has significant effect on the pressure distribution. A separate treatment for relatively low frequencies shows a significant impact of the compressive force on the spatial pressure distribution. The dominance of the leading acoustic-gravity modes on different physical characteristics is evident from their graphical representations. An orthogonality property for the depth-dependent functions of the velocity potential in the water region is established along with a few approximate forms. This mathematical model can be treated as a more general one that can unify several well-established models of acoustic-gravity wave propagation.

Stochastic electromagnetic Hermite-cos-Gaussian correlated Schell-model beams and their properties

The analytical expressions of the stochastic electromagnetic Hermite-cos-Gaussian correlated Schell-model (EHcGSM) beams are first shown. The propagation expressions of a stochastic EHcGSM beam in turbulent ocean are theoretically derived, and the evolutions in intensity and degree of polarization of which propagating in the turbulent ocean and free space are simulated and analyzed with numerical examples. The intensity of stochastic EHcGSM beams in free space has a multiple intensity distribution. However, the intensity distributions of the same beams propagating through turbulent ocean will overlap with each other due to the actions of the turbulent ocean. Moreover, degree of polarization of stochastic EHcGSM beams will change during which propagation in the turbulent ocean and free space, and the on-axis degree of polarization will gradually increase into maximum value and then decrease as the z increases.

Tracking deep-sea internal wave propagation with a differential pressure gauge array

Temperature is used to trace ocean density variations, and reveals internal waves and turbulent motions in the deep ocean, called ‘internal motions.’ Ambient temperature detected by geophysical differential pressure gauges (DPGs) may provide year-long, complementary observations. Here, we use data from four DPGs fixed on the ocean bottom and a high-resolution temperature sensor (T-sensor) 13 m above the seafloor as a square-kilometer array deployed offshore ~ 50 km east of Taiwan facing the open Pacific Ocean to examine the impact of temperature on DPG signals related to internal motions. The DPG signals correlate with T-sensor temperature variations between 0.002 and 0.1 mHz, but have time shifts partially caused by slow thermal conduction from the ambient seafloor to the DPG chamber and partially by internal motion propagation time across the array. Applying beamforming-frequency-wavenumber analysis and linear regression to the arrayed T-sensor and DPG data, we estimate the propagating slowness of the internal motions to be between 0.5 and 7.4 s m−1 from the northwest and northeast quadrants of the array. The thermal relaxation time of the DPGs is within 103–104 s. This work shows that a systematic scan of DPG data at frequencies < 0.1 mHz may help shed light on patterns of internal wave propagation in the deep ocean, especially in multi-scale arrays.

Observed Variability of Bottom‐Trapped Topographic Rossby Waves Along the Slope of the Northern South China Sea

AbstractStrong deep‐current variabilities with periods of 8–25, 16–40, and 30–80 days observed in the northern South China Sea (NSCS) are interpreted as topographic Rossby waves (TRWs) based on the moored observations from July 25, 2017 to August 13, 2018. The TRWs present significantly spatial distribution in the frequency and intensity, which are largely controlled by the mesoscale perturbations in the upper layer. Longer‐period (30–80‐day) TRWs observed to the west of the Dongsha Islands were excited by locally enhanced perturbations with the periods of 30–80 days in the upper ocean. The bottom currents in the periods of 8–25 days observed on the slope of the northeastern South China Sea (NESCS) were influenced by upper‐layer mesoscale perturbations on their northeastern side through TRW propagation in the deep ocean in addition to local processes. In the Luzon Strait, deep currents with the periods of 16–40 days were associated with locally strong perturbations in the upper layer. The distribution of the bottom current variability was closely related to the spatial variability of the upper‐layer fluctuations. The 8‐25‐day bandpass‐filtered surface eddy kinetic energy (EKE) was overall maximal in the Luzon Strait and weakened westward to the east side of the Dongsha Islands, which explained why TRWs with the periods of 8–25 days were more energetic in the Luzon Strait. The surface fluctuations with the periods of 30–80 days were dominant in the west of the Dongsha Islands, and triggered the strong TRWs with the frequency band.

The effect of the variability of wind forcing on ENSO simulation in an OGCM: case of canonical and protracted event

This study is an attempt to understand the onset and the evolution of canonical (typical length ~ 18–24 months; CE) and protracted El Niño (> greater than 3 years; PE) compared to the normal state (NS) in an ocean model. Indo-Pacific warm pool indicates higher sea surface temperature (SST) before the onset of strong CE compared to the NS and PE. The ocean model (MOM5.1.0) used in the study shows a systematic SST bias in the Indo-Pacific Ocean with warmer (cooler) temperatures in the western (eastern) Pacific during NS, CE, and PE exhibiting La Niña–like conditions. The model also exhibits deeper thermocline depth in the western equatorial Pacific Ocean during PE and CE than NS, indicating higher heat content values. Despite higher heat content in the western Pacific before the onset of El Niño, the difference in the variability of surface wind forcing during the preceding months determines the type of El Niño. The difference in surface wind forcing among the NS, PE, and CE states without altering the ocean state can modify the subsurface propagation in the equatorial Pacific Ocean. A change in longitudinal extent of upwelling Kelvin waves from western Pacific towards eastern Pacific along with the change in surface wind forcing decides the fate of El Niño. Based on the results of model experiments for 1948–2009, observed features of the recent protracted El Niño of 2014–2016 appear to be a blend of PE and CE in terms of ocean dynamics and surface wind forcing.

Mixed layer acoustic propagation with small scale ocean dynamics

The effects of dynamic oceanographic processes in the upper ocean mixed layer on acoustic propagation are investigated using at-sea sound speed observations and acoustic transmission simulations. The sound speed environment is based on a 400 m deep and 1000 km long East-West salinity and temperature transect that was collected during April of 2005 in the North Pacific where there is a mixed layer acoustic duct with a mean depth of 89 m. The deterministic baseline of this sound speed measurement is first estimated from the observations using a spatial lowpass filter with a cut off length scale of 50-km. The remaining small length scale variations in sound speed are assumed to have two physically distinct contributions: one due to the vertical displacement of isopycnals caused by eddies and internal waves and another due to compensating temperature and salinity anomalies along isopycnals termed spice. These two contributions can be separated yielding three distinct sound speed fields: i(1) the deterministic background; (2) thedisplacement field; and (3) the spice field. Acoustic transmission loss calculations are carried out on these three fields for frequencies of 400 and 1000 Hz for sources both in and below the mixed layer duct. Statistical and deterministic results for acoustic normal modes and full field transmission loss are presented, which quantify the relative importance of displacement and spice for acoustic propagation in the upper ocean.

Mid-frequency sound transmission in a deep ice-covered ocean at short and medium ranges

A model of propagation and reverberation in a deep Arctic ocean and a tentative interpretation of ICEX16 data are discussed. The data subset used for analysis was collected by a NPS team in the Beaufort Sea (∼3650 m depth) on 12 March 2016 using mobile EMATT transmitters which were moving under the ice in circular patterns from Ice Camp SARGO that provided various combinations of source-receiver ranges (∼1–10 km) and depths (45–183 m). Transmitted waveforms were sequences of 60 s-long segments comprised of 57 s-long CW pulses at various frequencies (2800, 2900, and 3000 Hz) and 3 s-long 2300–3000 Hz LFM sweeps. Sound speed profiles measured during the experiment showed two shallow ducts, at 0–75 m and 75–250 m water depths. The model developed considers multi-path propagation including multiple reflections and scattering from rough interfaces. The model-based analysis allows examining the spatial and time-frequency structure of recorded arrivals and their sensitivity to variations in water stratification and acoustic parameters of ice and ocean bottom. Preliminary results of the ICEX16 data-model comparisons are presented. Suggestions are considered for environmental measurements to provide necessary inputs and ground-truth for the acoustic model. A potential for enhanced remote sensing capabilities and optimal configurations for future experiments are discussed. [Work supported by ONR.]

Towards a field deployable alternative to underwater explosive charges

Underwater acoustic experiments and surveys often utilize underwater explosions to produce a high amplitude, broadband event capable of penetrating the seabed and propagating to long range. Although underwater explosive charges have been readily utilized for many decades, an alternative to explosives is of interest due to environmental and logistical concerns. Prior experimentation has demonstrated the viability of the Rupture Induced Underwater Sound Source (RIUSS) that utilizes an expendable diaphragm, known as a rupture disk, as an underwater acoustic source. The device functions by placing a rupture disk over a chamber and mechanically breaking the disk (either by striking on demand or via hydrostatic pressure) at a specified depth to produce high-amplitude, broadband waveforms. Recent experimentation has demonstrated the ability to perform ocean propagation measurements from a small, low cost fishing vessel in the New England Mud Patch by deploying expendable RIUSS units along with small, single channel acoustic moorings. Each of the acoustic moorings and expendable RIUSS units were deployed by hand, allowing the measurements to be gathered with few personnel in a low cost manner. Discussion will focus on recent advancements, fielded deployments, and comparison to related explosive charge propagation measurements. [Work Supported by ONR and ARL:UT IR&amp;D Program.]

Incomplete acoustic time reversal, frequency shifting, and matched field processing

In a reciprocal time-invariant medium, sound can travel in both directions along acoustic paths. This bi-directionality enables acoustic retrofocusing via time reversal (TR) and acoustic source localization via matched field processing (MFP). Given this common basis, the simplest frequency-domain formulations of acoustic TR and MFP are essentially identical; both involve a quadratic product of forward- and backward-propagating complex fields. For this presentation, all scenarios begin with the acoustic field from a remote source that propagates forward through a potentially-complicated acoustic environment to a transducer array where it is recorded. The difference between TR and MFP then arises because the second backward-propagating (time-reversed) acoustic field may be (i) a genuine field in the actual environment as in acoustic TR, or (ii) a predicted field developed from a model of the environment as in MFP. This presentation describes a third possibility, frequency-difference MFP or incomplete acoustic TR, that combines (i), (ii), and a multiplicative property of harmonic plane waves to produce frequency-downshifting. The resulting unconventional formulation involves a cubic product of complex fields and allows robust reduced-resolution source localization with sparse arrays in complicated uncertain environments. Example results from simulated, laboratory, and ocean propagation data are shown. [Sponsored by ONR, NAVSEA, NSF].

Stabilized leapfrog scheme run backward in time, and the explicit O(Δ t)2 stepwise computation of ill-posed time-reversed 2D Navier–Stokes equations

Richardson's leapfrog scheme is notoriously unconditionally unstable in well-posed, forward, linear dissipative evolution equations. Remarkably, that scheme can be stabilized, marched backward in time, and provide useful reconstructions in an interesting but limited class of ill-posed, time-reversed, 2D incompressible Navier–Stokes initial value problems. Stability is achieved by applying a compensating smoothing operator at each time step to quench the instability. Eventually, this leads to a distortion away from the true solution. This is the stabilization penalty. In many interesting cases, that penalty is sufficiently small to allow for useful results. Effective smoothing operators based on , with real p>2, can be efficiently synthesized using FFT algorithms. Similar stabilizing techniques were successfully applied in several other ill-posed evolution equations. The analysis of numerical stability is restricted to a related linear problem. However, as is found in leapfrog computations of well-posed meteorological and oceanic wave propagation problems, such linear stability is necessary but not sufficient in the presence of nonlinearities. Here, likewise, additional Robert–Asselin–Williams (RAW) time-domain filtering must be used to prevent characteristic leapfrog nonlinear instability unrelated to ill-posedness. Several 2D Navier–Stokes backward reconstruction examples are included, based on the stream function-vorticity formulation, and focusing on pixel images of recognizable objects. Such images, associated with non-smooth underlying intensity data, are used to create severely distorted data at time T>0. Successful backward recovery is shown to be possible at parameter values significantly exceeding expectations.

Characteristics of Low-Frequency Acoustic Wave Propagation in Ice-Covered Shallow Water Environment

Mastering the sound propagation law of low-frequency signals in the Arctic is a major frontier basic research demand to improve the level of detection, communication, and navigation technology. It is of practical significance for long-distance sound propagation and underwater target detection in the Arctic Ocean. Therefore, how to establish an effective model to study the characteristics of the acoustic field in the Arctic area has always been a hot topic in polar acoustic research. Aimed at solving this problem, a mathematical polar acoustic field model with an elastic seafloor is developed based on a range-dependent elastic parabolic equation theory. Moreover, this method is applied to study the characteristics of polar sound propagation for the first attempt. The validity and effectiveness of the method and model are verified by the elastic normal mode method. Simultaneously, the propagation characteristics of low-frequency signals are studied in a polar sound field from three aspects, which are seafloor parameters, sea depth, and ice thickness. The results show that the elastic parabolic equation method can be well utilized to the Arctic low-frequency acoustic field. The analysis of the influence factors of the polar sound field reveals the laws of sound transmission loss of low-frequency signals, which is of great significance to provide information prediction for underwater submarine target detection and target recognition.

Robust long-range source localization in the deep ocean using phase-only matched autoproduct processing.

Passive source localization in the deep ocean using array signal processing techniques is possible using an algorithm similar to matched field processing (MFP) that interrogates a measured frequency-difference autoproduct instead of a measured pressure field [Geroski and Dowling, J. Acoust. Soc. Am. 146, 4727-4739 (2019)]. These results are extended herein to a new MFP-style algorithm, phase-only matched autoproduct processing, that is more robust at source-array ranges as large as 225 km. This new algorithm is herein described and compared to three existing approaches. The performance of all four techniques is evaluated using measured ocean propagation data from the PhilSea10 experiment. These data nominally span a 12-month period; include six source-array ranges from 129 to 450 km; and involve signals with center frequencies between 172.5 and 275 Hz, and bandwidths of 60 to 100 Hz. In all cases, weight vectors are calculated assuming a range-independent environment using a single sound-speed profile measured near the receiving array. The frequency-differencing techniques considered here are capable of localizing all six sources, with varying levels of consistency, using single-digit-Hz difference frequencies. At source-array ranges up to and including 225 km, the new algorithm requires fewer signal samples for success and is more robust to the choice of difference frequencies.

Parabolic equations in motionless and moving media

The narrow-angle parabolic equation (NAPE) provides a robust approach for sound propagation in inhomogeneous media such asthe atmosphere and ocean. Several numerical methods for solving the NAPE in a motionless medium have been developed. The Crank-Nicholson finite-difference method is one of the simplest and readily supports range-dependent environmental processes such as turbulence. The NAPE, boundary condition, and artificial absorbing layer are discretized, and the solution is written in a matrix form. A starting field, which approximates the sound source, is marched forward by solving a matrix equation. Because the matrices involved are triagonal, the solution is highly efficient. For many applications in atmospheric and ocean acoustics, the NAPE needs to be generalized for wide-angle propagation and moving media (winds or currents). Recently derived wide-angle parabolic equations (WAPEs) in moving media are reviewed including the phase errors pertinent to the equations. In the Pade (1,1) and high-frequency approximations, the WAPE in a moving medium with arbitrary Mach numbers is surprisingly simple. It can be implemented numerically with minimal modifications to existing Crank-Nicholson NAPE solvers.

Impact of the April\u2013May SAM on Central Pacific Ocean sea temperature over the following three seasons

Although the impact of the extratropical Pacific signal on the El Niño–Southern Oscillation has attracted increasing concern, the impact of Southern Hemisphere Annular Mode (SAM)-related signals from outside the southern Pacific Basin on the equatorial sea temperature has received less attention. This study explores the lead correlation between the April–May (AM) SAM and central tropical Pacific sea temperature variability over the following three seasons. For the positive AM SAM case, the related simultaneous warm SST anomalies in the southeastern Indian Ocean favor significant regulation of vertical circulation in the Indian Ocean with anomalous ascending motion in the tropics. This can further enhance convection over the Marine Continent, which induces a significant horizontal Kelvin response and regulates the vertical Walker circulation. These two processes both result in the anomalous easterlies east of 130° E in the equatorial Pacific during AM. These easterly anomalies favor oceanic upwelling and eastward propagation of the cold water into the central Pacific. The cold water in turn amplifies the development of the easterly wind and further maintains the cold water into the boreal winter. The results presented here not only provide a possible link between extratropical climate variability in the Indian Ocean and climate variation in the equatorial Pacific, but also shed new light on the short-term prediction of tropical central Pacific sea temperature.

Infrasonic Earthquake Detectability Investigated in Southern Part of Japan, 2019.

The Kochi University of Technology (KUT) Infrasound Sensor Network contains 30 infrasound sensors which are distributed all over Japan especially in Shikoku Island. At all infrasound stations installed with three-axis accelerometers to measure the peak ground acceleration (PGA). Many earthquakes were detected by our system after establishing of the network since 2016. In this study we will focus on all the possibilities for infrasound detection generated from earthquakes using KUT sensor network and International Monitoring system (IMS) stations for the earthquakes which were detected in southern part of Japan during 2019. As for earthquakes with strike-slip mechanisms the P-waves could not be detected by our sensors. In addition, The conversion from seismic to acoustic waves can be happened through the generating of the T-phase from oceanic earthquakes. On 9 May 2019, progressive multi-channel cross correlation (PMCC) method applied infrasound and hydroacoustic waves from two earthquakes happened in west of Kyushu Island as the T-phase was well-recorded at H11N station near Wake Island. Moreover, infrasound propagation modeling is applied to the reconstructed atmosphere profile by Ground to Space Model (AVO-G2S) to confirm the infrasound arrivals, furthermore the 3D ray tracing process and the calculations by using the transmission loss equation with normal modes and parabolic equation methods are investigated. The study confirmed the infrasound generation scenario from the T-phase of oceanic propagation.