Internal Wave Packets Research Articles

Large-eddy simulation of the generation and propagation of internal solitary waves

A modified large-eddy simulation model, the dynamic coherent eddy model (DCEM) is employed to simulate the generation and propagation of internal solitary waves (ISWs) of both depression and elevation type, with wave amplitudes ranging from small, medium to large scales. The simulation results agree well with the existing experimental data. The generation process of ISWs is successfully captured by the DCEM method. Shear instabilities and diapycnal mixing in the initial wave generation phase are observed. The dissipation rate is not equal at different locations of an ISW. ISW-induced velocity field is analyzed in the present study. The structure of the bottom boundary layer (BBL) of internal wave packets is found to be different from that of a single ISW. A reverse boundary jet instead of a separation bubble exists behind the leading internal wave while separation bubbles appear in other parts of the wave-induced velocity field. The boundary jet flow resulting from the adverse pressure gradients has distinctive dynamics compared with free shear jets.

Anelastic internal wave reflection and transmission in uniform retrograde shear

We perform fully nonlinear simulations in two dimensions of a horizontally periodic, vertically localized, anelastic internal wavepacket in order to examine the effects of weak and strong nonlinearity upon wavepackets approaching a reflection level in uniform retrograde shear. Transmission, reflection, and momentum deposition are measured in terms of the horizontal momentum associated with the wave-induced mean flow. These are determined in part as they depend upon the initial wavenumber vector, \documentclass[12pt]{minimal}\begin{document}$\vec{k}=(k,m)$\end{document}k⃗=(k,m), which determines the modulational stability (if |m/k| ≳ 0.7) or instability (if |m/k| ≲ 0.7) of moderately large amplitude quasi-monochromatic internal wavepackets. Whether modulationally stable or unstable, the evolution of the wavepacket is determined by the height of the reflection level predicted by linear theory, zr, relative to the height, zΔ, at which weak nonlinearity becomes significant, and the height, \documentclass[12pt]{minimal}\begin{document}$z_b>z_\Delta$\end{document}zb>zΔ, at which linear theory predicts anelastic waves first overturn in the absence of shear. If \documentclass[12pt]{minimal}\begin{document}$z_r<z_\Delta$\end{document}zr<zΔ, the amplitude remains sufficiently small and the waves reflect as predicted by linear theory. If zr is moderately larger than \documentclass[12pt]{minimal}\begin{document}$z_\Delta$\end{document}zΔ, a fraction of the momentum associated with the wavepackets transmits past the reflection level. This is because the positive shear associated with the wave-induced mean flow can partially shield the wavepacket from the influence of the negative background shear enhancing its transmission. The effect is enhanced for weakly nonlinear modulational unstable wavepackets that narrow and grow in amplitude faster than the anelastic growth rate. However, as nonlinear effects become more pronounced, a significant fraction of the momentum associated with the wavepacket is irreversibly deposited to the background below the reflection level. This is particularly the case for modulationally unstable wavepackets, whose enhanced amplitude growth leads to overturning below the predicted breaking level. Because the growth in the amplitude envelope of modulationally stable wavepackets is retarded by weakly nonlinear effects, reflection is enhanced and transmission retarded relative to their modulationally unstable counterparts. Applications to mountain wave propagation through the stratosphere in the winter hemisphere are discussed.

The evolution of a stratified turbulent cloud

AbstractLocalized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.

Internal wave radiation by a turbulent fountain in a stratified fluid

Large eddy simulation is applied to model a fountain in a density-stratified fluid. The fountain is formed, as a vertical turbulent jet penetrates through a pycnocline. The jet flow is initiated by the formulation of a boundary condition in the form of an upward neutral-buoyancy fluid flow with the Gaussian axisymmetric mean-velocity profile and a given fluctuation level. It is shown that at a Froude number Fr higher than a certain critical value the fountain executes self-oscillations accompanied by internal wave generation within the pycnocline. The predominant self-oscillation mode is axisymmetric, when the fountain top periodically breaks down generating internal wave packets traveling toward the periphery of the computation domain. The characteristic frequency of the internal waves coincides with that of the fountain top oscillations and monotonically decreases with increase in Fr. The Fr-dependence of the fountain top oscillation amplitude obtained in the numerical solution is in good agreement with the predictions of the theoretical Landau model for the instability mode in the soft self-excitation regime.

Current field features and propagation characteristics of suspected internal solitary wave packet

The observational data of acoustic Doppler current profiler (ADCP) indicates that a suspected internal solitary wave packet (ISWP) consists of two depression waves in the northern South China Sea (SCS). This paper analyzes the current field features and propagation characteristics of the front and rear waves, calculates their propagation phase speeds and direction angels respectively, and demonstrates that the generation site of the suspected ISWP is Luzon Strait (LS).The our result shows that for the front wave, the height is 96m, the time period is 16min, the propagation phase speed is 1.04ms−1, the direction angel is 283.4°, and the wavelength is 1.0km; for the rear wave, the height is 80m, the time period is 14min, the propagation phase speed is 0.89ms−1, the direction angel is 299°, and the wavelength is 0.74km. The maximum horizontal velocity of the front wave is 1.1ms−1 in depth 106m below the sea surface, and the maximum shear is 0.030s−1 in the wave trough; the maximum horizontal velocity of the rear wave is 0.84ms−1 at the same depth and the maximum shear is 0.020s−1 in the wave trough as well. According to the data and theoretical analysis there is an interaction between the front and rear waves 17km to the direction of LS, showing that they were not generated during the same time interval. In this paper, our results may provide understanding the physical features and propagation characteristics of sequential internal solitary waves and their relationships.

Energy fluctuations of high-frequency sound signals in a shallow water in the presence of nonlinear internal waves

The paper presents an analysis of energy fluctuations of high-frequency (2–4.5 kHz) sound signals propagating in a shallow water in the presence of nonlinear (soliton-like) internal waves (2006 Shallow Water experiment, US Atlantic shelf). Signals were received by three single hydrophones in different directions at distances of ∼4, ∼12, and ∼5 km from the source. The angle between the first two acoustic tracks was ∼15°. The third track was almost an extension of the first and was on the other side of the source. A relatively short (one to two solitons) nonlinear internal wave packet first moved approximately along the first two tracks and then along the third track. It is demonstrated that in the presence of solitons on the track in the frequency spectrum of energy fluctuations, there is an isolated frequency that depends, in particular, on the angle between the soliton front and the acoustic track. The experimental results agree well with the theory previously proposed by the authors, where the occurrence mechanism of fluctuations is explained using the ray approach.

Time-varying three-dimensional mapping of internal waves during the Shallow Water 2006 experiment

Formation and propagation of internal waves have recently become of interest to ocean acousticians, since the propagation of internal waves in shallow water waveguide plays an important role in intensity fluctuations of acoustic signals [J. Acoust. Soc. Am. 112(2), 747–760 (2007)]. Modeling the acoustic field in these regions requires detailed knowledge of sound speed and its spatial and temporal variability resulting from propagating internal waves. Although satellite imagery can provide snapshots of the surface impressions of the internal waves, due to low sampling in time (limited images in each orbit) other techniques to obtain the time varying, three-dimensional (3D) internal wave field are desirable. An example to obtain a time-varying, 3D internal wave field is presented in this paper. The internal wave fine structure is reconstructed using simultaneous measurement of temperature data using thermistor arrays and the surface impressions of a moving internal wave packet using a ship’s radar during the Shallow Water 2006 experiment (SW06). The parameters of the internal wave train, such as wave speed, propagation direction, and amplitude of the first wave front, are determined. The resulting temperature field induced by the internal waves is used as environmental input to a 3D acoustic model to study the effects of internal wave on acoustic propagation. [Work supported by ONR322OA.]

Airborne lidar detection and characterization of internal waves in a shallow fjord

A dual-polarization lidar and photography are used to sense internal waves in West Sound, Orcas Island, Washington, from a small aircraft. The airborne lidar detected a thin plankton layer at the bottom of the upper layer of the water, and this signal provides the depth of the upper layer, amplitude of the internal waves, and the propagation speed. The lidar is most effective when the polarization filter on the receiver is orthogonal to the transmitted light, but this does not depend significantly on whether the transmitted light is linearly or circularly polarized. The depolarization is greater with circular polarization, and our results are consistent with a single parameter Mueller scattering matrix. Photographs of the surface manifestation of the internal waves clearly show the propagation direction and width of the phase fronts of the internal waves, even though the contrast is low (2%). Combined with the lidar profile, the total energy of the internal wave packet was estimated to be 9 MJ.

A stochastic response surface formulation for the description of acoustic propagation through an uncertain internal wave field

A modeling and simulation study is performed in a littoral ocean waveguide subject to uncertainty in four quantities: source depth, tidal forcing, initial thermocline structure, and sediment sound speed. In this partially known shelf-break environment, tidal forcing over a density-stratified water column produces internal tides and solitary wave packets. The resulting uncertainty in the space-time oceanographic field is mapped into the sound speed distribution which, in turn, introduces uncertainty into the acoustic wave field. The latter is treated as a stochastic field whose intensity is described by a polynomial chaos expansion. The expansion coefficients are estimated through constrained multivariate linear regression, and an analysis of the chaos coefficients provides insight into the relative contribution of the uncertain acoustic and oceanographic quantities. Histograms of acoustic intensity are estimated and compared to a reference solution obtained through Latin Hypercube sampling. A sensitivity analysis is performed to illustrate the relative importance of the four contributions of incomplete information about the environment. The simulation methodology represents an end-to-end analysis approach including both oceanographic and acoustic field uncertainty where the latter is quantified using stochastic basis expansions in the form of a polynomial chaos representation.

Transport theory applied to shallow water acoustics: The relative importance of surface scattering and linear internal waves

Acoustic fields in shallow water have a statistical nature due to complex, time-evolving sound speed fields and scattering from rough boundaries. A coupled-mode transport theory [Creamer (1996), Colosi and Morozov (2009)] allows for the prediction of acoustic field second moments like mean intensity and coherence. This was previously applied to study low frequency acoustic fluctuations in an environment typical of that of the Shallow Water 2006 (SW06) experiment on the New Jersey Continental shelf. Here the propagation was found to be strongly adiabatic and random sound speed fluctuations from internal waves radically altered acoustic interactions with intense nonlinear internal wave packets. Here, we extend the SW06 study to examine the ability of transport equations to describe high frequency (>1 kHz) sound in shallow water. Mode coupling rates from internal waves are expected to be larger, and scattering effects from rough surfaces need treatment. The aforementioned transport theory is merged with the rough surface scattering transport theory of Thorsos et al (2009). Oceanographic and sea surface measurements are used to constrain the internal wave and sea surface models. The relative importance of linear internal waves and surface scattering effects are studied using transport theory and Monte Carlo simulations.

On the mechanism of A-type and B-type internal solitary wave generation in the northern South China Sea

Internal solitary waves (ISWs) in the northern South China Sea (SCS) are investigated using historical observational data, linear theory, global inverse tidal model, and a fully nonlinear nonhydrostatic numerical model. It was found on the basis of mooring data that the appearance of ISWs in the northern SCS is strongly correlated with the maximum of semidiurnal barotropic tidal forcing in the Luzon Strait (LS), but not with the largest peaks of diurnal tidal currents. The role of the latter lies in the modulation of the baroclinic tidal signal in such a way that the diurnal intermittency of ISW characteristics known as A-type waves (large-amplitude rank-ordered ISW packets) and B-type waves (single weak ISWs) is introduced into the internal wave fields.Both A- and B-waves were reproduced in a series of numerical experiments. It was found that due to the neap-spring variability of the tidal forcing, a permanent transition of A-type waves into B-type waves and vice versa takes place. This effect is treated in terms of a multi-harmonic approach. It is assumed that the internal wave field in the SCS is a sum of progressive semidiurnal and diurnal internal tidal waves radiated from the LS. Their superposition in space creates an alternation of large and small troughs. In the course of nonlinear steepening and ultimate disintegration the large and small troughs give rise to type A and type B internal wave packets, respectively. The neap-spring variability of tidal forcing alters the specific contribution of diurnal and semidiurnal constituents and leads to the wave transition from one type to another.

Regular and chaotic dynamics of a fountain in a stratified fluid

In the present paper, we study by direct numerical simulation (DNS) and theoretical analysis, the dynamics of a fountain penetrating a pycnocline (a sharp density interface) in a density-stratified fluid. A circular, laminar jet flow of neutral buoyancy is considered, which propagates vertically upwards towards the pycnocline level, penetrates a distance into the layer of lighter fluid, and further stagnates and flows down under gravity around the up-flowing core thus creating a fountain. The DNS results show that if the Froude number (Fr) is small enough, the fountain top remains axisymmetric and steady. However, if Fr is increased, the fountain top becomes unsteady and oscillates in a circular flapping (CF) mode, whereby it retains its shape and moves periodically around the jet central axis. If Fr is increased further, the fountain top rises and collapses chaotically in a bobbing oscillation mode (or B-mode). The development of these two modes is accompanied by the generation of different patterns of internal waves (IW) in the pycnocline. The CF-mode generates spiral internal waves, whereas the B-mode generates IW packets with a complex spatial distribution. The dependence of the amplitude of the fountain-top oscillations on Fr is well described by a Landau-type two-mode-competition model.

The island‐scale internal wave climate of Moorea, French Polynesia

Analysis of five‐year records of temperatures and currents collected at Moorea reveal strong internal wave activity at predominantly semi‐diurnal frequencies impacting reef slopes at depths ≥30 m around the entire island. Temperature changes of 1.5°C to 3°C are accompanied by surges of upward and onshore flow and vertical shear in onshore currents. Superimposed on annual temperature changes of approximately 3°C, internal wave activity is high from Oct–May and markedly lower from Jun–Sep. The offshore pycnocline is broadly distributed with continuous stratification to at least 500 m depth, and a subsurface fluorescence maximum above the strong nutricline at approximately 200 m. Minimum buoyancy periods range from 4.8 to 6 min, with the maximum density gradient occurring at 50 to 60 m depth in summer and deepening to approximately 150 to 200 m in winter. The bottom slope angle around all of Moorea is super‐critical relative to the vertical stratification angle suggesting that energy propagating into shallow water is only a portion of total incident internal wave energy. Vertical gradient Richardson numbers indicate dominance by density stability relative to current shear with relatively limited diapycnal mixing. Coherence and lagged cross‐correlation of semi‐diurnal temperature variation indicate complex patterns of inter‐site arrival of internal waves and no clear coherence or lagged correlation relationships among island sides. Semi‐diurnal and high frequency internal wave packets likely arrive on Moorea from a combination of local and distant sources and may have important impacts for nutrient and particle fluxes in deep reef environments.

Spatial-Temporal Distribution and Characteristics of Internal Waves in the Lombok Strait Area Studied by Alos-Palsar Images

Numerous packets of internal waves were revealed in Advanced Land Observing Satellite Phased Array L-band Synthetic Aperture Radar (ALOSPALSAR) images of the Lombok Strait area, and high-resolution and quick look images were used for their detection and analysis. The parameters of internal waves, such as the number of waves in a packet, crest length, and propagation velocity were estimated from the images. This paper describes the use of PALSAR imagery for internal wave frequency detection and presents the results of a survey that detected 90 internal wave occurrences with ScanSAR and Fine Mode PALSAR imagery over the period May 2006 to April 2011. The paper also discusses the spatial and temporal distribution of internal wave occurrences in the Lombok Strait area.

On‐shelf transport of slope water lenses within the seasonal pycnocline

We show that discrete lenses of anomalously high‐salinity water, originating from the shelf edge and trapped within the seasonal pycnocline, are advected 100 km or more onto the Celtic Sea continental shelf. We propose that the lenses are created by increased diapycnal mixing at the shelf edge associated with breaking high‐frequency internal wave packets. Quasi‐synoptic hydrography sections show the lenses to be 3–5 km wide, their temporal persistence confirmed by moored instrumentation and a series of CTD casts. Estimates of the propagation speed of these features (∼0.020 m s−1) compare favorably with the magnitude of observed residual currents. Residual current variability within the pycnocline is dominated by vertical structures most consistent with the second baroclinic mode. The residual flow is therefore thought to be predominantly driven by non‐linear second mode internal tidal waves. These are observations of a shelf edge exchange process not previously identified.

Frequency dependent beating patterns and amplitude increase during the approach of an internal wave packet

A frequency-dependent beating pattern in the spectrogram of broadband signals transmitted during the approach of an internal wave packet to an acoustic propagating path is reported. An analytical expression relating the acoustic signal measurements and environmental parameters under certain conditions is obtained. Three-dimensional parabolic equation modeling results compare well with Shallow Water 2006 experiment data.

Anelastic Internal Wave Packet Evolution and Stability

Abstract As upward-propagating anelastic internal gravity wave packets grow in amplitude, nonlinear effects develop as a result of interactions with the horizontal mean flow that they induce. This qualitatively alters the structure of the wave packet. The weakly nonlinear dynamics are well captured by the nonlinear Schrödinger equation, which is derived here for anelastic waves. In particular, this predicts that strongly nonhydrostatic waves are modulationally unstable and so the wave packet narrows and grows more rapidly in amplitude than the exponential anelastic growth rate. More hydrostatic waves are modulationally stable and so their amplitude grows less rapidly. The marginal case between stability and instability occurs for waves propagating at the fastest vertical group velocity. Extrapolating these results to waves propagating to higher altitudes (hence attaining larger amplitudes), it is anticipated that modulationally unstable waves should break at lower altitudes and modulationally stable waves should break at higher altitudes than predicted by linear theory. This prediction is borne out by fully nonlinear numerical simulations of the anelastic equations. A range of simulations is performed to quantify where overturning actually occurs.

Propagation speeds of strongly nonlinear near-surface internal waves in the Strait of Georgia

[1] A novel aerial observational method for studying internal features in the coastal ocean is developed and tested in a study of large nonlinear internal solitary-like waves. Photogrammetrically rectified oblique photo images from a circling aircraft are used to track a number of internal wave packets for periods of up to one hour in the Strait of Georgia, British Columbia, Canada. Combining these sequences with coincident water column data allows us to obtain a more complete view of the spatial structure of internal waves. Highly accurate measurements of wave propagation speeds and directions are possible. The applicability of various weakly nonlinear theories in modeling propagation of the observed large-amplitude waves is tested. The measured wave speeds enable us to differentiate between classic internal wave models. The linear, KdV (Korteweg-de Vries), and BO (Benjamin-Ono) models are applied with and without background shear. After background shear effects are included, it is found that a continuously stratified BO equation can predict propagation speeds within observational error, and that this is not true for other theories. The technique may be useful in future studies of oblique internal wave interactions.

Research Spotlight: Observing nonlinear internal waves over New Jersey's continental shelf

Nonlinear internal waves, which occur below the ocean's surface, can influence coastal environments, for instance, through increased turbulent mixing that affects fluxes of nutrients and heat.The details of how these waves are generated are not well understood. Shroyer et al. used ship and mooring data collected off the coast of New Jersey during August 2006 to describe the nonlinear internal wavefield and background oceanographic conditions. They found that during most of that month, nonlinear internal wave packets occurred irregularly and had displacements of about 8 meters, but during 17–21 August the nonlinear internal waves were more closely phased with the surface tide and were almost twice as large, with displacements around 15 meters, despite being coincident with the neap tide. The study provides significant new details on the evolution and variability of nonlinear internal waves. (Journal of Geophysical Research‐Oceans, doi:10.1029/2010JC006332, 2011)

Current and Density Observations of Packets of Nonlinear Internal Waves on the Outer New Jersey Shelf

AbstractClosely spaced observations of nonlinear internal waves (NLIWs) were made on the outer continental shelf off New Jersey in June 2009. Nearly full water column measurements of current velocity were made with four acoustic Doppler current profilers (ADCPs) that were moored about 5 km apart on the bottom along a line approximately normal to the bathymetry between water depths of 67 and 92 m. Density profiles were obtained from two vertical strings of temperature and conductivity sensors that were deployed near each of the interior ADCP moorings. In addition, a towed ScanFish provided profiles and fixed-level records of temperature and salinity through several NLIW packets near the moorings. Several case studies were selected to describe the propagation of the NLIWs. One to three solitary waves of depression were observed in five selected packets. There were also occurrences of multiple-phase dispersive wave packets. The average propagation speed corrected for advection of the observed waves was 0.51 ...