Shallow-water Dispersion Research Articles

Minimal model for tidal bore revisited

This develops a recent analysis of gentle undular tidal bores (2018 New J. Phys. 20 053066) and corrects an error. The simplest linear-wave superposition, of monochromatic waves propagating according to the shallow-water dispersion relation, leads to a family of profiles satisfying natural tidal bore boundary conditions, involving initial smoothed steps with different shapes. These profiles can be uniformly approximated to high accuracy in terms of the integral of an Airy function with deformed argument. For the long times corresponding to realistic bores, the profiles condense asymptotically onto the previously obtained integral-Airy function with linear argument: as the bore propagates, it forgets the shape of the initial step. The integral-Airy profile expands slowly, as the cube root of time, rather than advancing rigidly. This ‘minimal model’ leads to simple formulas for the main properties of the profile: amplitude, maximum slope, ‘wavelength’, and steepness; and an assumption about energy loss suggests how the bore weakens as it propagates.

Acoustic wave attenuation and dispersion in shallow water

The propagation of sound in shallow water is studied. Signals are recorded at several distances from the source. The amplitudes of the signals’ spectral components are calculated at these points. The frequency dependence of the attenuation coefficient is found using the maximum likelihood approach.

Localization for broadband source by a single vector sensor in shallow water

The physical meaning of array invariant is the absolute traveling time of different modal from a source to a receiver under the average sound speed. It can be gotten by the derivative of the arriving time against the corresponding cosecant function of elevation angle for each modal, which can be used for the passive source localization. A vector sensor can be seen as a small volumetric array. It has its capability of elevation angle determination to describe the multi-modal propagation and the single-modal dispersion in shallow water, which may imply a chance to get the array invariant for the source localization. Here, we take advantage of the dispersion based short time Fourier transform and warping transform techniques for the time-frequency analysis of vector sensor signals. This technique can improve acoustic normal mode identification and thereby extract the modal data more accurately for array invariant determination. The idea had been effectively validated during the experiment that took place in ...

High-Resolution GNSS-Tracked Drifter for Studying Surface Dispersion in Shallow Water

AbstractThe use of Global Navigation Satellite System (GNSS)-tracked Lagrangian drifters allows more realistic quantification of fluid motion and dispersion coefficients than Eulerian techniques because such drifters are analogs of particles that are relevant to flow field characterization and pollutant dispersion. Using the fast-growing real-time kinematic (RTK) positioning technique derived from GNSS, drifters are developed for high-frequency (10 Hz) sampling with position estimates with centimeter accuracy. The drifters are designed with small size and less direct wind drag to follow the subsurface flow that characterizes dispersion in shallow waters. An analysis of position error from stationary observation indicates that the drifter can efficiently resolve motion up to 1 Hz. The result of the field deployments of the drifter in conjunction with acoustic Eulerian devices shows a higher estimate of the drifter streamwise velocities. Single particle statistical analysis of field deployments in a shallow estuarine zone yielded estimates of dispersion coefficients comparable to those of dye tracer studies. The drifters capture the tidal elevation during field studies in a tidal estuary.

Study of Microwave Backscattering From Two-Dimensional Nonlinear Surfaces of Finite-Depth Seas

This paper presents a study of the microwave backscattering from 2-D time-evolving nonlinear surfaces of a sea with finite depth by using the second-order small-slope approximation. According to the shallow-water dispersion relation, the revised nonlinear hydrodynamic choppy wave model in connection with an experiment-verified sea spectrum for finite-depth water is employed to construct the wave profiles in the finite-depth sea. The numerical results show that the discrepancy between the choppy surfaces of the infinite-depth sea and their finite-depth counterparts for monostatic normalized radar cross section is much smaller than that between the linear surfaces and the nonlinear choppy surfaces. Furthermore, the comparison of the Doppler spectra of the backscattered echoes from the linear and nonlinear choppy sea surfaces shows that the nonlinear hydrodynamic features significantly impact the Doppler spectrum. In particular, the Doppler spectrum for nonlinear finite-depth sea presents much higher second-order peaks and increased spectral amplitudes in the frequency range around the Doppler peak frequency, which reiterates the importance of the role that the nonlinear hydrodynamic effect of waves played in the interpretation of backscattering from finite-depth nearshore seas from the qualitative point of view.

Automatic Detection and Characterization of Dispersive North Atlantic Right Whale Upcalls Recorded in a Shallow-Water Environment Using a Region-Based Active Contour Model

Various automatic detection and characterization techniques have been proposed to implement mitigation measures to protect the endangered North Atlantic Right Whales in their habitats. These species prefer shallow waters during their seasonal migration. Such shallow-water acoustical environments act as a waveguide and cause the monocomponent upcall emitted by the vocalizing whale to become a dispersive multicomponent signal with different time arrivals and relative energy. In this paper, the discrimination between the Right Whale upcalls and background noise has been investigated using the support vector machine classifier. To perform this task, a region-based active contour segmentation method is proposed. In this work, both synthesized data based on typical Right Whale vocalizations and real data recorded in Cape Cod Bay are used to evaluate the proposed method. We show how the shallow-water dispersion effects which cause higher order mode generation affect the parameters used for classification and descriptive statistics. We compare the descriptive statistics of the call duration using both single-mode and multimode approaches. The single-mode analysis was performed by extracting the frequency contour of the first mode.

North Pacific right whale up-call source levels and propagation distance on the southeastern Bering Sea shelf

Call source levels, transmission loss, and ambient noise levels were estimated for North Pacific right whale (Eubalaena japonica) up-calls recorded in the southeastern Bering Sea in autumn of 2000 and 2001. Distances to calling animals, needed to estimate source levels, were based on two independent techniques: (1) arrival-time differences on three or more hydrophones and (2) shallow-water dispersion of normal modes on a single receiver. Average root-mean-square (rms) call source levels estimated by the two techniques were 178 and 176 dB re 1 μPa at 1 m, respectively, over the up-call frequency band, which was determined per call and averaged 90 to 170 Hz. Peak-to-peak source levels were 14 to 22 dB greater than rms levels. Transmission loss was approximately 15∗log(10)(range), intermediate between cylindrical and spherical spreading. Ambient ocean noise within the up-call band varied from 72 to 91 dB re 1 μPa(2)/Hz. Under average noise conditions, call spectrograms were detectable for whales at distances up to 100 km, but propagation and detection distance may vary depending on environmental parameters and anthropogenic noise. Obtaining distances to animals and acoustic detection range is a step toward using long-term passive acoustic recordings to estimate abundance for this critically endangered whale population.

Adaptive finite element method for analysis of pollutant dispersion in shallow water

A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts:(1) computation of the velocity flow field and water surface elevation, and (2) computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy, as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.

Multi-mode models of flow and of solute dispersion in shallow water. Part 3. Horizontal dispersion tensor for velocity

Svendsen & Putrevu (1994) revealed that the much larger off-shore than vertical effective viscosity for longshore currents is the consequence of a shear dispersion mechanism. The multi-mode representation for the flow gives a mathematical framework within which a more general derivation can be made. It is shown that to a first approximation the horizontal shear dispersion tensor for velocity is the same as that for solutes.

Broadband frequency dispersion in shallow water as an active classification technique

Recently, an active broadband dispersion phenomenon was observed empirically in measured data for propagation paths within the mixed layer (ML) [Dien etal. (1994)]. This so-called Wilson Dispersion Phenomena (WDP) is explained simply by noting that high-frequency energy trapped within the ML travels faster than low frequencies that diffractively ‘‘leak’’ out of the ML. Thus WDP is a useful technique for distinguishing between reflectors in the ML and reflectors below the ML. More recently it was shown that the WDP may occur in other shallow-water environments [Davies etal. (1994)]. Several sound-speed profile (SSP) environments are examined, using normal mode theory, for depth dependence of broadband frequency dispersion. A very conservative approach is taken regarding frequency reflectors. Geoacoustic properties of the bottom are not addressed. SSPs for which dispersion depth dependence is observed within the water column for a lossy bottom are labeled useful for active classification. Future research including geoacoustic properties of the sub-bottom may lead to a wider range of SSP and geoacoustic sub-bottom environments which produce dispersion depth dependence. It has been empirically observed that bottom reflectors (the primary false targets) never have significant dispersion and are spread over much longer times than reflectors within the water column. a)Work performed while on temporary leave from Neptune Sciences, Inc., Slidell, LA 70458; b)Currently stationed at Fleet Numerical Oceanographic Ctr., Monterey, CA 93943.

Multi-mode models of flow and of solute dispersion in shallow water. Part 2. Logarithmic velocity profiles

A two-mode model for velocity and solute concentration in shallow-water flows is derived which allows for departures from the logarithmic velocity profile and from vertically well-mixed concentrations. The modelling is tested against exact results for a buoyancy-driven transverse flow and for a modified logarithmic velocity profile.

Multi-mode models of flow and of solute dispersion in shallow water. Part 1. General derivation

Instead of considering just the vertically averaged current and the vertically averaged concentration, a multi-mode model is derived in which more of the vertical structure can be computed directly rather than being lumped into a dispersion coefficient. Test cases, of laminar flows, are used to quantify the accuracy of the lowest non-trivial truncation (two modes) in replicating both the flow and the dispersion process.

Tidally averaged models for dispersion in shallow water

This paper deals with the advection and diffusion of contaminants in tidal waters. The analysis starts with the well‐known vertically integrated advection‐diffusion equation. In order to derive a tidally averaged model to describe the advection and dispersion processes over long periods and to gain insight into the tidally induced dispersion, a new method to average the tide is introduced. Here it is assumed that both the dispersion coefficient and the residual flow are sufficiently small. The averaging procedure is derived by using a random walk model to describe the dispersion process. This random walk model is shown to be exactly consistent with the advection‐diffusion equation. The averaging procedure results in equations for the averaged advective transport as well as equations for the effective dispersion tensor describing the mixing process that occurs within one tidal cycle. By using a numerical model to determine the tidal movement over one tidal cycle, the tidally averaged advective transport and dispersion tensor in each grid point of the model is approximated numerically. In this way a tidally induced dispersion map of the area under study is obtained.

Stochastic modelling of dispersion in shallow water

A random walk model to describe the dispersion of pollutants in shallow water is developed. By deriving the Fokker-Planck equation, the model is shown to be consistent with the two-dimensional advection-diffusion equation with space-varying dispersion coefficient and water depth. To improve the behaviour of the model shortly after the deployment of the pollutant, a random flight model is developed too. It is shown that over long simulation periods, this model is again consistent with the advection-diffusion equation. The various numerical aspects of the implementation of the stochastic models are discussed and finally a realistic application to predict the dispersion of a pollutant in the Eastern Scheldt estuary is described.

An approximate model for nonlinear dispersion in monochromatic wave propagation models

A method is proposed for smoothly matching an approximate, shallow-water dispersion relation to an analytically obtained relation for intermediate and deep water. The method provides a correct limit for increasing water depth in the case of weakly non-linear waves, and provides a smooth prediction of wave parameters for the entire range of water depth. The model is applied to a parabolic equation form of the combined refraction-diffraction model, and numerical results are presented in comparison to published data.