Internal wave excitation from a collapsing mixed region

The collapse of a uniform density fluid (a “mixed region”) into a surrounding ambient fluid with complex stratification is examined by way of laboratory experiments and fully nonlinear numerical simulations. The analysis focuses upon the consequent generation of internal gravity waves and their influence upon the evolution of the collapsing mixed region. In experiments and simulations for which the ambient fluid has uniform density over the vertical extent of the mixed region and is stratified below, we find the mixed region collapses to form an intrusive gravity current and internal waves are excited in the underlying stratified fluid. The amplitude of the waves is weak in the sense that the intrusion is not significantly affected by the waves. However, scaling the results to the surface mixed layer of the ocean we find that the momentum flux associated with the waves can be as large as 1 N/m². In simulations for which the ambient fluid is stratified everywhere, including over the vertical extent of the mixed region, we find that internal waves are excited with such large amplitude that the collapsing mixed region is distorted through strong interactions with the waves.     

Acoustic model-based matched filter processing for fadingtime-dispersive ocean channels: theory and experiment

It is shown that the performance of a conventional matched filter can be improved if the reference (replica) channel compensates for the distortion by the ocean medium. A model-based matched filter is generated by correlating the received signal with a reference channel that consists of the transmitted signal convolved with the impulse response of the medium. The channel impulse responses are predicted with a broadband propagation model using in situ sound speed measured data and archival bottom loss data. The relative performance of conventional and model-based matched filter processing is compared for large time-bandwidth-product linear-frequency-modulated signals propagating in a dispersive waveguide. From ducted propagation measurements conducted in an area west of Sardinia, the model-based matched filter localizes the depths of both the source and receiving array and the range between them. The peak signal-to-noise ratio for the model-based matched filter is always larger than that of the conventional filter     

Real time time-frequency active sonar processing: a SIMD approach

A paradigm for massively parallel processing of matched filters, replica correlators, ambiguity functions, and time-frequency distributions is presented, using a SIMD (single instruction stream, multiple data stream) programming methodology. It is shown that active sonar detection algorithms, as implemented by frequency domain processing, can be a natural match to a SIMD methodology, meeting the extensive computational needs of enhanced active sonar systems. The decomposition process is presented, and examples are given of the output of the computer program CMASP (Connection Machine Ambiguity Surface Processor). CMASP can provide real-time simultaneous multiple-beam, Doppler, and waveform replica correlations. Synthetic data are processed, and the corresponding CMASP outputs are displayed as three-dimensional ambiguity surfaces on networked graphic workstations. Because of efficient problem decomposition, other time-frequency processing can be exploited. Specifically, real-time instantaneous-like time-frequency distributions have been realized in which the data set is presented and processed as time-varying spectral representations     

Internal wave dispersions in density-stratified deep oceans with a thermocline

As to two typical Väisälä frequency profiles in deep oceans, one in the Arctic Ocean and one in the Atlantic, the approximate analytical method ofHyun (1976) is used to calculate internal wave dispersion relations. The method is shown to have good agreement with the matrix numerical method. By making calculations for an exemplary Väisälä frequency profile with a thermocline, an assessment is made of the inaccuracies in the dispersion curves obtained by the ordinary WKB method which does not take into account the turning point singularities.     

A nonlinear wave profile correction of the diffraction of a wave by a long breakwater: Fixed point approach

The authors of the present paper have suggested an iterative scheme to calculate the nonlinear wave profiles [Jang and Kwon, 2005. Application of nonlinear iteration scheme to the nonlinear water wave problem: Stokes wave. Ocean Engineering 32, 1862–1872]. The scheme was shown to be good for estimating nonlinear wave profiles. In the study, the iterative scheme is applied to the wave-diffraction problem by a long breakwater to calculate a diffracted wave by the breakwater. The iterative solution of diffraction was compared with the linear solution of Sommerfeld, 1896. [Mathematische Theoried der Diffraction. Mathematical Annals 47, 317–374]. For a small wave slope, the two solutions were in good agreement. However, the scheme enabled us to observe the nonlinear behaviors of a beating phenomenon and of wave profile such as Stokes’ wave for a relatively large wave slope: as the wave slope becomes larger, we can examine the nonlinear wave characteristics of the actual shapes of waves, i.e., the crests are steeper and the troughs are flatter.     

On non-linear wave interaction with cylindrical bodies: a vortex sheet approach

An alternative, relatively straightforward, method is presented for calculating non-linear, two-dimensional wave interaction with submerged bodies. The free surface is represented by a vortex sheet and the body surface by a source sheet in a time-stepping procedure with the limitation that overtopping may not occur. Errors inherent in the method are assessed. For starting flow over a circular cylinder with diameter up to at least half a wavelength, the surface profiles local to the cylinder closely approximate those for longer times after only one period. By this time forces, for waves of even moderate steepness, have settled down to values predicted by analytical linear theory. A good approximation to effects associated with wave trains of infinite extent may thus be obtained by simulating a fairly limited space (several wavelengths).     

Fifth generation digital sonar signal processing

This paper discusses the evolutionary development, which has taken place over the last decade, in digital sonar systems architecture with the application of first, second, and third generation computers as system controllers for sonar systems. It is the opinion of the authors that, with the arrival of microprocessors, the system controller tasks in real time digital sonars will diminish. We present, as the "fourth generation," the present systems which still have a relatively large CPU, assisted by an array of microprocessors under their control for several subtasks which can be handled, more efficiently, locally in the systems. The "fifth generation" concept is postulated as a further development of this concept. A distributed processing scheme is presented in which the processing elements are actually highly functionally distributed themselves at the lowest level of architecture; consequently, the user views them as uniprocessors within the tightly coupled network. This approach should result in relatively high throughput utilizing a fairly small repertoire of modular hardware components and requiring minimal software effort by implementing, via firmware, very high level macros. This concept allows adaptive system architecture for the various advanced sonar data processing requirements for multielement linear, spatial, or blanket type array systems postulated for the future.     

Uncertainty tolerance in underwater acoustic signal processing

Because of the difficulties in accurately characterizing the statistical behavior of underwater acoustic channels, tolerance to uncertain statistical modeling is an important property for underwater acoustic signal processing procedures to possess. This paper provides an overview of a number of techniques developed in recent years that can be applied to provide uncertainty tolerance in underwater signal processing applications. In addition to a discussion of general concepts of uncertainty tolerance, specific methods for attaining tolerance to uncertainty in temporal/spatial statistics for procedures such as Wiener and matched filtering, time-delay estimation, sonar system design, and signal prediction are reviewed. Tolerance to uncertainty in amplitude statistics is also a key issue in underwater channels, and techniques for achieving this goal are discussed in the contexts of signal estimation, identification, and detection procedures.     

Digital signal processing for precision wide-swath bathymetry

A mathematical model is formulated which accurately represents the envelope function of bottom return signals received from a number of spatial directions comprising a wide swath. The bottom return signals are processed utilizing a digital nonrecursive matched filter whose coefficients are tapered using a Tukey window. High-speed convolution employing the fast Fourier transform is examined for implementation of the digital matched filtering operation. Computer simulation of the signal processing system indicates that, even in the presence of considerable background and fluctuation noises, the processor provides an output signal having a well-defined peak. The error in time of arrival is found to be less than 3 ms, corresponding to an error in depth of less than 0.1 percent, for an average signal-to-noise ratio of 15 dB and a vertical ocean depth of 12 000 ft (3.7 km). These performance figures apply to the most difficult case of mapping at angles ofpm 45degoff vertical.     

Chaotic radar signal processing over the sea

It is demonstrated that the random nature of sea clutter may be explained as a chaotic phenomenon. For different sets of real sea clutter data, a correlation dimension analysis is used to show that sea clutter can be embedded in a finite-dimensional space. The result of correlation dimension analysis is used to construct a neural network predictor for reconstructing the dynamics of sea clutter. The deterministic model so obtained is shown to be capable of predicting the evolution of sea clutter. The predictive analysis is also used to analyze the dimension of sea clutter. Using the neural network as an approximation of the underlying dynamics of sea clutter, a dynamic-based detection technique is introduced and applied to the problem of detecting growlers (small fragments of icebergs) in sea clutter. The performance of this method is shown to be superior to that of a conventional detector for the real data sets used here     

Internal wave band kinetic energy production: flat vs. sloping bottom

Velocity and temperature measurements obtained with acoustic Doppler current profilers and thermistor strings are used to evaluate the production of internal wave band kinetic energy mainly in the frequency band σ>15 cpd. Results from a flat 19 m deep, vigorous tidal environment in a shelf sea are compared with energy production in a bottom boundary layer above a continental slope. In the tidal environment, maximum production occurs in the near-bottom and near-surface layers. A distinct mid-depth maximum in KE production occurs during a period when wind speeds exceed 10 m s⁻¹ and significant wave height ∼2 m. At the same time, no significant changes in the along-shore current speed take place but the cross-shore current, generated by strong stratification, is weakened. This suggests a direct energy input from the wind via surface waves into the water column turbulence. Maximum kinetic energy production in the frequency band σ>1.9 cpd, thus including the semidiurnal tide, occurs at mid-depth when strong stratification is present. The overall magnitude of internal wave band kinetic energy production agrees well with independent dissipation estimates obtained from microstructure profilers. Above the sloping bottom, KE production is somewhat larger than observed in the shallow tidal environment, despite rms currents being ∼50% smaller and wind effects being small. Above the sloping bottom KE shear production was comparable to buoyancy production. The latter was negligible at the shelf sea site.     

Internal inlet for wave generation and absorption treatment

A new method of implementing, in two-dimensional (2-D) Navier–Stokes equations, a numerical internal wave generation in the finite volume formulation is developed. To our knowledge, the originality of this model is on the specification of an internal inlet velocity defined as a source line for the generation of linear and non-linear waves. The use of a single cell to represent the source line and its transformation to an internal boundary condition proved to be an interesting alternative to the common procedure of adding a mass source term to the continuity equation within a multi-cell rectangular region. Given the reduction of the source domain to a one-dimensional region, this simple new type of source introduced less perturbation than the 2-D source type. This model was successfully implemented in the PHOENICS code (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series). In addition, the volume of fluid (VOF) fraction was used to describe the free surface displacements. A friction force term was added to the momentum transport equation in the vertical direction, in order to enhance wave damping, within relatively limited number of cells representing the sponge layers at the open boundaries. For monochromatic wave, propagating on constant water depth, numerical and analytical results showed good agreements for free surface profiles and vertical distribution of velocity components. For solitary wave simulation, the wave shape and velocity were preserved; while, small discrepancy in the tailing edge of the free surface profiles was observed. The suitability of this new numerical wave generation model for a two source lines extension was investigated and proven to be innovative. The comparisons between numerical, analytical and experimental results showed that the height of the merging waves was correctly reproduced and that the reflected waves do not interact with the source lines.     

Transient discrimination using a subspace method [acoustic array signal processing]

This paper describes a method using a subspace algorithm that can be used to discriminate between signals. Discrimination is necessary to ensure that the same transient from different data records is used in processing. The subspace discrimination algorithm was tested against synthetic transients and found to discriminate well at high signal-to-noise ratios (SNRs).     

Real- and synthetic-array signal processing of buried targets

Results from two field experiments aimed at investigating the detection and classification of buried targets are presented. In both experiments a 2-16-kHz parametric source was used. In the first experiment, the source was used in combination with a 12-m horizontal line array and in the second with a 1.4-m vertical line array which was displaced horizontally along an underwater rail to form a 10 m /spl times/ 1.4 m two-dimensional synthetic aperture sonar (SAS). To increase the SAS integration time, the parametric source was electronically scanned in azimuth during the displacement along the rail, as in spotlight mode. It is shown that both arrays allow important signal-to-reverberation gains, enhancing the detection of sub-bottom echoes. A new, environmentally adaptive, matched filter which further improves the signal to reverberation ratio while allowing discrimination between proud and buried targets is presented and validated experimentally. The use of resonant scattering for target classification of buried objects is discussed, in the particular case of spherical shells.     

Internal wave spectrum in shallow water: measurement and comparisonwith the Garrett-Munk model

The covariance matrix of sound-speed variations is determined from yo-yo CTD data collected during the SWARM 95 experiment at a fixed station. The data covered approximately 2 h and were collected during a period when nonlinear solitary internal waves were absent or negligible. The method of empirical orthogonal functions (EOF) is applied to the sound-speed covariance matrix assuming that the internal wave modes are uncorrelated. The first five eigenvectors are found to agree well with the theoretically modeled eigenfunctions based on the measured buoyancy frequency and the internal wave eigenmode equation. The mode amplitudes for the first five modes are estimated from the corresponding eigenvalues. They agree with the Garrett-Munk model if j*=1 is used instead of j*=3. A second method is used to deduce the mode amplitudes and mode frequency spectra by projecting the sound-speed variation (as a function of time) onto the theoretical mode depth functions. The mode amplitudes estimated with this method are in agreement with the EOF results. A modified Garrett-Munk model is proposed to fit the frequency spectrum of linear internal waves in shallow water     

Surface manifestations of internal waves investigated by a subsurface buoyant jet: Part 2. Internal wave field

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, a major simulation of internal wave actuation by buoyant turbulent jets generated by wastewater flows from underwater collector diffusers in conditions of temperature stratification with deep and shallow thermocline has been performed. Using a modification of the particle tracing velocimetry (PTV) method in the stratification mode with shallow thermocline, the velocities of currents generated by internal waves at the surface of the water area are measured. A theoretical model is developed describing the fields of internal waves in the presence of jet stream. Dispersion relations and structures of lower (first and second) modes of internal waves in the stratified basin for different rates of liquid outflow from the collector model are obtained. The experimentally measured field of isothermal shifts with respect to the system of characteristic modes of internal waves is decomposed. A mixed regime of internal wave actuation with the simultaneous existence of the first and second modes is observed. The characteristics of perturbations in the liquid column and on its surface are compared. This analysis allows us to prove that the velocity fields on the surface are indeed surface manifestations of internal waves.     

Internal wave generation in an improved two-dimensional Boussinesq model

A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model.     

Internal wave generation in an improved two-dimensional Boussinesq model

A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model.     

On a near-optimal control approach for a wave energy converter in irregular waves

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers–Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal (one being odd and other even), full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this difficulty and the non-causality of the exciting force impulse response function, this paper investigates the use of propagating-wave surface elevation up-wave of the device to synthesize the necessary forces. Long-crested waves are assumed, and the approach is based on the formulations of Naito and Nakamura [2] and Falnes [22]. A predominantly heaving submerged device comprised of three vertically stacked discs driving a linear power take-off is studied. The overall formulation leads to smooth control that is near-optimal, given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. Absorbed power performance with the near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results for wave spectra over a range of energy periods and significant wave heights are compared for the three situations studied. While practical implementation presents engineering challenges, in terms of time-averaged absorbed power, unconstrained near-optimal control is found to perform significantly better than single-frequency tuning in the spectra with longer energy periods (>10 s for the present device), and somewhat better in the spectra with shorter energy periods (here ≤10 s).