Measurements Of Internal Waves Research Articles

On coherently processing multiple arrays in underwater environments with spatial coherence losses from random medium effects and sensor position uncertainties

Under ideal circumstances coherently beamforming multiple distributed arrays should provide improvements over the standard approach of processing the arrays individually and combining them incoherently. These include improved directivity and higher gain. However, two major challenges when coherently processing spatially separated arrays in a real ocean are dealing with coherence losses or wave front distortions caused by random medium effects like internal waves and uncertainties in sensor locations. Some of the consequences are degraded beampatterns and poorer array directivity. In this paper, we perform a simulation-based study utilizing numerical propagation models along with theory examining the effects of wave front distortions induced by random medium effects like internal waves and sensor position uncertainties on coherently beamforming distributed arrays in representative ocean waveguides. Realistic realizations of wave front distortions are generated from actual internal wave measurements and models. The sensitivities of coherent processing to these effects are characterized by resultant beampatterns and losses in array directivity along with a quantification of the tolerances.

Calculation of internal-wave-driven instability and vortex shedding along a flat bottom

The instability and vortex shedding in the bottom boundary layer caused by internal solitary waves of depression propagating along a shallow pycnocline of a fluid are computed by finite-volume code in two dimensions. The calculated transition to instability agrees very well with laboratory experiments (Carret al.,Phys. Fluids, vol. 20, issue 6, 2008, 06603) but disagrees with existing computations that give a very conservative instability threshold. The instability boundary expressed by the amplitude depends on the depth$d$of the pycnocline divided by the water depth$H$, and decays by a factor of 2.2 when$d/H$is 0.21, and by a factor of 1.6 when$d/H$is 0.16, and the stratification Reynolds number increases by a factor of 32. The instability occurs at moderate amplitude at large scale. The calculated oscillatory bed shear stress is strong in the wave phase and increases with the scale. Its non-dimensional magnitude at stratification Reynolds number 650 000 is comparable to the turbulent stress that can be extracted from field measurements of internal solitary waves of similar nonlinearity, moving along a pycnocline of similar relative depth.

Variational mode decomposition for estimating critical reflected internal wave in stratified fluid

The shear resulting from internal wave reflections can play a crucial role in the transport and resuspension of sediments in oceanic conditions. In particular, when these waves undergo a \textit{critical reflection} phenomenon, the reflected wave can produce a very large shear. Separating the reflected wave from the incident wave is a technical challenge since the two waves share the same temporal frequency. In our study, we present a series of experimental measurements of internal waves in \textit{critical reflection} configuration and we analyze them using the 2D-VMD-prox decomposition method. This decomposition method was adapted to specifically decompose waves in an internal wave critical reflection, showing an improvement in its performance with respect to preexisting internal wave decomposition methods. Being able to confidently isolate the reflected wave allowed us to compare our results to a viscous and non-linear model for critical reflection, that correctly describes the dependence of the shear rate produced in the boundary as a function of the experimental parameters.

Tidal Energy Flows between the Midriff Islands in the Gulf of California

The Gulf of California has many regions of potential tidal-stream energy that have been identified and characterized using in-situ measurements and numerical ocean models. The Midriff Islands region has received particular attention due to its increased current speeds and high kinetic energy. This increase in energy can be seen in the formation of internal wave packets propagating for several hundred kilometers. Here we present a brief description of internal wave measurements travel towards the Northern Gulf and explore energy generation sites. In this paper we characterize the tidal inflow and outflow that passes throughout the Midriff Islands in the central part of the Gulf. We use a three-dimensional numerical ocean model that adequately reproduces the tidal flow and the increase in speed and kinetic energy between the islands. The current flow structure shows the highest velocity cores near the shore and far from the bottom. During the rising tide, the maximum current flow (~0.6 ms−1) was found between Turón Island and San Lorenzo Island, from the surface to 200 m depth. When the currents flowed out of the Gulf, during the falling tide, the maximum negative current (−0.8 ms−1) was found between Tiburon Island and Turón Island, from near the surface to 80 m depth. Although there are favorable conditions for power generation potential by tidal flows, the vertical variability of the current must be considered for field development and equipment installation sites.

Generation of second-mode internal solitary waves during winter in the northern South China Sea

Field measurements of second-mode internal solitary waves (mode-2 ISWs) during the winter on the upper continental slope of the northern South China Sea were reported in Yang et al. (2009), but their generation mechanism remains elusive. We investigated this issue with a multi-modal evolution model and theoretical analysis, which suggest that the observed mode-2 ISWs were generated by a shoaling mode-2 semidiurnal internal tide (IT) that emanated from the Luzon Strait. The results show that two groups of mode-2 ISWs usually appear within one semidiurnal tidal period, successively riding on expanded and subsequently compressed pycnoclines. The number of wave groups largely depends on the amplitudes of the ITs; that is, a larger IT produces larger mode-2 ISWs. Furthermore, intermodal coupling dominates the evolution of a mode-1 IT, highlighting the importance of considering mode scattering in the propagation of low-mode ITs.

Проблемы и возможности измерений параметров внутренних волн в океане методом оптиколокации

Проблемы и возможности измерений параметров внутренних волн в океане методом оптиколокации

Internal wave pressure, velocity, and energy flux from density perturbations

Determination of energy transport is crucial for understanding the energy budget and fluid circulation in density varying fluids such as the ocean and the atmosphere. However, it is rarely possible to determine the energy flux field $\mathbf{J} = p \mathbf{u}$, which requires simultaneous measurements of the pressure and velocity perturbation fields, $p$ and $\mathbf{u}$. We present a method for obtaining the instantaneous $\mathbf{J}(x,z,t)$ from density perturbations alone: a Green's function-based calculation yields $p$, and $\mathbf{u}$ is obtained by integrating the continuity equation and the incompressibility condition. We validate our method with results from Navier-Stokes simulations: the Green's function method is applied to the density perturbation field from the simulations, and the result for $\mathbf{J}$ is found to agree typically to within $1\%$ with $\mathbf{J}$ computed directly using $p$ and $ \mathbf{u}$ from the Navier-Stokes simulation. We also apply the Green's function method to density perturbation data from laboratory schlieren measurements of internal waves in a stratified fluid, and the result for $\mathbf{J}$ agrees to within $6\%$ with results from Navier-Stokes simulations. Our method for determining the instantaneous velocity, pressure, and energy flux fields applies to any system described by a linear approximation of the density perturbation field, e.g., to small amplitude lee waves and propagating vertical modes. The method can be applied using our Matlab graphical user interface EnergyFlux.

Coherence measurements of acoustic normal modes during one month of internal wave events on the New Jersey continental shelf

During the Shallow Water Acoustic Experiment 2006 (SW06) conducted on the New Jersey continental shelf, the three-dimensional (3D) temperature field for one month of internal wave (IW) events has been reconstructed by Badiey et al. [J. Acoust. Soc. Am. El. 134(5), 4035 (2013)]. The aforementioned IW events, with the angle between the acoustic track and the IW front varying from -8° to 83°, were measured while simultaneously acoustic signals were transmitted from fixed sources at an along-shelf distance of about 20 km with frequencies at 87.5–112.5 Hz (m-sequence), 175–225 Hz (m-sequence), 270–330 Hz (chirp), and 470–530 Hz (chirp), respectively. The acoustic signals were recorded by an L-shaped hydrophone array moored inside the area with IW measurements. The main goal of this paper is to analyze the coherence of acoustic normal modes accompany with the simultaneously measured IW events. The coherence of acoustic normal modes decomposed from the measured acoustic field is obtained as a function of frequency and IW parameters, such as the IW propagation direction, amplitude, coherence length, etc. The relationship between the modal coherence and IW parameters is discussed. [Work supported by ONR322OA.]

Internal wave‐driven transport of fluid away from the boundary of a lake

A field experiment was conducted to study transport of fluid from the boundary to the interior of a lake. Tracking of a tracer injected into the metalimnion was combined with measurements of meteorological forcing, internal waves, and temperature microstructure. Seiches of vertical mode 2 and horizontal modes 1 and 2 were initiated after a wind event, and the tracer moved 950 m into the interior after 29.2 h. Four potential mechanisms for spreading of the tracer from the boundary to the interior were considered: intrusions from boundary mixing, horizontal dispersion, advection by seiches, and advection and dispersion driven by internal waves. Some evidence of boundary mixing was observed 0.5 h before the dye injection, when the speed of seiche‐driven currents was large, but a model of an intrusion driven by steady input overpredicted the propagation distance by a factor of about two. A one‐dimensional model with only dispersion yielded a dispersion coefficient of 0.8 m2 s−1, and a one‐dimensional model with only advection caused by internal waves predicted the position of the peak concentration and a change in longitudinal variance that was 60% of the measured change. Estimates of dispersion caused by the interaction of vertical diffusion with velocity gradients in the internal wave field are large enough to explain the rest of the spreading and suggest that the transport can be modeled as wave‐driven advection and dispersion.

Nonsteady dynamics of turbulent axisymmetric jets in stratified fluid: Part 1. Experimental study

The nonsteady dynamics of turbulent axially symmetrical jets in stratified fluid with a great density gradient (pycnocline) is studied in laboratory experiments in the large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences (IAP RAS) simulating wastewater flows from underwater collectors in coastal cities. An underwater survey of jets in the pycnocline region has been carried out along with synchronous measurements of internal waves. It is shown that a jet quasiperiodically oscillates in a vertical plane, thus effectively generating internal waves when interacting with the pycnocline. It is ascertained that the axially symmetrical mode of jet oscillations is a source of internal waves.

Internal wave measurements on the Cycladic Plateau of the Aegean Sea

The internal wave climate in the southern Aegean Sea is examined with an array of two bottom‐mounted acoustic Doppler current profilers and three profiling moorings deployed on the northern continental slope of the Cretan Sea for 3 months. Frequency spectra indicate an extremely weak internal wave continuum, about 4–10 times weaker than the Garrett‐Munk and Levine reference levels. Spectra are instead dominated by semidiurnal internal tides and near‐inertial waves, which are examined in detail by bandpass filtering. In the semidiurnal band, a barotropic tidal flow of ≈2 cm s−1 is observed, with a pronounced spring/neap modulation in phase with the lunar fortnightly cycle. One to two days following several of these spring tide periods, a distinct internal tide featuring 10–20 m vertical displacements and 15–20 cm s−1baroclinic velocities is detectable propagating upward and to the southeast. Time‐mean energy increases a factor of 2–5 within about 100 m from the bottom, implying generation and/or scattering from the bottom, whose slope is nearly critical to semidiurnal internal waves over much of the array. Several strong, downward propagating near‐inertial events are also seen, each of which occurs following a period of work done by the wind on the mixed layer as estimated from a nearby surface mooring. The high‐frequency internal wave continuum is more temporally constant but increases substantially toward the end of the deployment. Significant but unexplained differences in kinetic energy occur between successive spring tide periods in the case of the internal tides and between successive wind events in the case of the near‐inertial signals. Substantial variability is observed in the low‐frequency flows, which likely contributes to the time variability of the internal wave signals.

Rapid swing and spin of [deep] taut-wire-moored instruments

Abstract Rapid ‘swing’, compass variations O(10°) in O(10 s), and ‘spin’, complete rotations around the vertical axis within a few minutes, are a concern of acoustic current meters moored in-line. Observations are used from fast sampling, at once per 1 and 30 s, instrumentation on deep-ocean moorings mainly outside surface wave and bottom boundary influences. Such instruments do not require a vane common to some historic mechanical current meters and they are often moored in a much easier to handle sub-surface buoy or mounting rack, without vanes. In their mountings they are nearly symmetric, so that they can spin freely in (turbulent; shear) flows. A comparison is made between noise levels of such free spinning instrumentation with those of instruments mounted in a fixed bottom-frame and with those of instruments equipped with a vane to one side. Typical spinning has a single rotation varying between 40 and 200 s. Spinning is shown to be highly binary: on or off. Its effects are found negligible on estimates of ocean currents, provided compass updates are adequate as in existing instrumentation. Acoustic noise is O(10) times larger than noise due to spinning. Some effects of spinning are noticed in the acoustic echo amplitude showing higher noise at frequencies >100 cpd, cycles per day. The character of this noise changes dramatically due to spinning. However, it is mainly in the ocean turbulence range and does not affect measurements of internal waves or periodic zooplankton motions.

Horizontal reflection of a low-frequency sound signal from a moving nonlinear internal wave front.

Simultaneous measurements of acoustical and internal waves are reported while an internal wave approaches an acoustic track during the SW06 experiment. The incoming internal wave packet acts as a moving layer reflecting and refracting acoustic waves in the horizontal plane. The mechanism of this interaction is shown in received acoustic data on a vertical hydrophone array using a modal approach. It is shown that the wave front of internal waves behaves as selective filter, depending on the mode number and frequency of the broadband signal. In other words the reflection coefficient in horizontal plane depends on mode number and frequency. Experimental data analysis shows good agreement with the theory. [Work supported by ONR 321OA.]

Acoustical Measurement of Nonlinear Internal Waves Using the Inverted Echo Sounder

Abstract The performance of pressure sensor–equipped inverted echo sounders for monitoring nonlinear internal waves is examined. The inverted echo sounder measures the round-trip acoustic travel time from the sea floor to the sea surface and thus acquires vertically integrated information on the thermal structure, from which the first baroclinic mode of thermocline motion may be inferred. This application of the technology differs from previous uses in that the wave period (∼30 min) is short, requiring a more rapid transmission rate and a different approach to the analysis. Sources of error affecting instrument performance include tidal effects, barotropic adjustment to internal waves, ambient acoustic noise, and sea surface roughness. The latter two effects are explored with a simulation that includes surface wave reconstruction, acoustic scattering based on the Kirchhoff approximation, wind-generated noise, sound propagation, and the instrument’s signal processing circuitry. Bias is introduced as a function of wind speed, but the simulation provides a basis for bias correction. The assumption that the waves do not significantly affect the mean stratification allows for a focus on the dynamic response. Model calculations are compared with observations in the South China Sea by using nearby temperature measurements to provide a test of instrument performance. After applying corrections for ambient noise and surface roughness effects, the inverted echo sounder exhibits an RMS variability of approximately 4 m in the estimated depth of the eigenfunction maximum in the wind speed range 0 ≤ U10 ≤ 10 m s−1. This uncertainty may be compared with isopycnal excursions for nonlinear internal waves of 100 m, showing that the observational approach is effective for measurements of nonlinear internal waves in this environment.

Schlieren measurements of internal waves in non-Boussinesq fluids

Previous experiments that have examined the generation of internal gravity waves by a monochromatic source have been restricted to small amplitude forcing in Boussinesq stratified fluids. Here we present measurements of internal waves generated by a circular cylinder oscillating at large amplitude in a non-Boussinesq fluid. The ‘synthetic schlieren’ optical measurement technique (Sutherland et al. in J Fluid Mech 390:93–126, 1999) is extended to stratifications in which the index of refraction of the fluid may vary nonlinearly with density. The method is applied to examine disturbances in approximately uniformly stratified ambient fluids consisting either of sodium chloride (NaCl) or sodium iodide (NaI) solutions whose concentrations increase to near-saturation at the bottom of the tank. In particular, we report upon the first extensive measurements of the optical properties of NaI solutions as they depend upon concentration and density. Applying the results to experiments, we find that large amplitude forcing generates a patch of oscillatory turbulence surrounding the cylinder, thereby increasing the effective cylinder size and decreasing the amplitude of the waves in comparison with the predictions of linear theory. We parameterize the influence of the turbulent boundary layer in terms of an effective cylinder radius and forcing amplitude.

Seafloor Pressure Measurements of Nonlinear Internal Waves

Abstract Highly resolved pressure measurements on the seafloor over New Jersey’s continental shelf reveal the pressure signature of nonlinear internal waves of depression as negative pressure perturbations. The sign of the perturbation is determined by the dominance of the internal hydrostatic pressure (p0Wh) due to isopycnal displacement over the contributions of external hydrostatic pressure (ρ0gηH; ηH is surface displacement) and nonhydrostatic pressure (p0nh), each of opposite sign to p0Wh. This measurement represents experimental confirmation of the wave-induced pressure signal inferred in a previous study by Moum and Smyth.

Internal-wave radiation and optical measurements in stratified fluids

In many problems of considerable geophysical and industrial interest, fluid flows are characterized by the presence of a stable vertical density gradient. Under suitable conditions such fluids can support internal waves. In many aspects internal waves are similar to surface waves. Owing to small density difference across the fluid depth the effective gravity governing the dynamics of internal waves is typically by two or three orders of magnitude smaller than the terrestrial gravity. In a continuously stratified fluid the strength of gravity and viscous effects depends on the vertical density gradient, fluid viscosity, and characteristics of a wave-emitting disturbance. In the present report we focus our attention on experiments with internal waves generated by circular and rectilinear oscillations of cylinders in a uniformly stratified fluid. Quantitative measurements of internal waves are performed with the help of ‘synthetic’ schlieren technique based on computer evaluation of optical distortions in stratified fluids. The effects of the type and amplitude of oscillations on the generation of linear and nonlinear density-gradient disturbances are discussed.

Oceanic Isopycnal Slope Spectra. Part I: Internal Waves

Abstract Horizontal tow measurements of internal waves are rare and have been largely supplanted in recent decades by vertical profile measurements. Here, estimates of isotherm displacements and turbulence dissipation rate from a towed vehicle deployed near Hawaii are presented. The displacement data are interpreted in terms of horizontal wavenumber spectra of isopycnal slope. The spectra span scales from 5 km to 0.1 m, encompassing both internal waves and turbulence. The turbulence subrange is identified using a standard turbulence fit, and the rest of the motions are deemed to be internal waves. The remaining subrange has a slightly red slope (ϕ ∼ k−1/2x) and vertical coherences compatible with internal waves, in agreement with previous towed measurements. However, spectral amplitudes in the internal wave subrange exhibit surprisingly little variation despite a four-order-of-magnitude change in turbulence dissipation rate observed at the site. The shape and amplitude of the horizontal spectra are shown to be consistent with observations and models of vertical internal wave spectra that consist of two subranges: a “linear” subrange (ϕ ∼ k0z) and a red “saturated” subrange (ϕ ∼ k−1z). These two subranges are blurred in the transformation to horizontal spectra, yielding slopes close to those observed. The saturated subrange does not admit amplitude variations in the spectra yet is an important component of the measured horizontal spectra, explaining the poor correspondence with the dissipation rate.

Acoustic Visualization of Nonlinear Internal Gravity Waves Using an Improved High Frequency Sonar System

High frequency sonar systems have been used by the Naval Research Laboratory to study nonlinear internal gravity waves and define the fine structure of ocean temperature and salinity layers that are found in coastal waters, usually within 130 meters of the surface. Of particular interest is the fine structure of these waves, which are being investigated using high sensitivity sonar systems that provide 1 m horizontal resolution and less than 8 cm vertical resolution. This article describes the integration of commercial and custom-designed components, including a recently patented transmitter-receiver switch. The significance of this T-R switch is that it improves the sensitivity of short-range sonar systems, enables a more refined measurement of nonlinear internal gravity waves, and could have broad industry applications.

Visualization and measurement of internal waves by ‘synthetic schlieren’. Part 1. Vertically oscillating cylinder

We present measurements of the density and velocity fields produced when an oscillating circular cylinder excites internal gravity waves in a stratified fluid. These measurements are obtained using a novel, non-intrusive optical technique suitable for determining the density fluctuation field in temporally evolving flows which are nominally two-dimensional. Although using the same basic principles as conventional methods, the technique uses digital image processing in lieu of large and expensive parabolic mirrors, thus allowing more flexibility and providing high sensitivity: perturbations of the order of 1% of the ambient density gradient may be detected. From the density gradient field and its time derivative it is possible to construct the perturbation fields of density and horizontal and vertical velocity. Thus, in principle, momentum and energy fluxes can be determined.In this paper we examine the structure and amplitude of internal gravity waves generated by a cylinder oscillating vertically at different frequencies and amplitudes, paying particular attention to the role of viscosity in determining the evolution of the waves. In qualitative agreement with theory, it is found that wave motions characterized by a bimodal displacement distribution close to the source are attenuated by viscosity and eventually undergo a transition to a unimodal displacement distribution further from the source. Close quantitative agreement is found when comparing our results with the theoretical ones of Hurley & Keady (1997). This demonstrates that the new experimental technique is capable of making accurate measurements and also lends support to analytic theories. However, theory predicts that the wave beams are narrower than observed, and the amplitude is significantly under-predicted for low-frequency waves. The discrepancy occurs in part because the theory neglects the presence of the viscous boundary layers surrounding the cylinder, and because it does not take into account the effects of wave attenuation resulting from nonlinear wave–wave interactions between the upward and downward propagating waves near the source.