Internal Solitary Waves Of Depression Research Articles

Transformation of internal solitary waves at the edge of ice cover

Abstract. Internal wave-driven mixing is an important factor in the balance of heat and salt fluxes in the polar regions of the ocean. Transformation of internal waves at the edge of the ice cover can enhance the mixing and melting of ice in the Arctic Ocean and Antarctica. In the polar oceans, internal solitary waves (ISWs) are generated by various sources, including tidal currents over bottom topography, the interaction of ice keels with tides, time-varying winds, vortices, and lee waves. In this study, a numerical investigation of the transformation of ISWs propagating from open water in the stratified sea under the edge of the ice cover is carried out to compare the depression ISW transformation and loss of energy on smooth ice surfaces, including those on the ice shelf and glacier outlets, with the processes beneath the ridged underside of the ice. They were carried out using a non-hydrostatic model that is based on the Reynolds-averaged Navier–Stokes equations in the Boussinesq approximation for a continuously stratified fluid. The Smagorinsky turbulence model extended for stratified fluid was used to describe the small-scale turbulent mixing explicitly. Two series of numerical experiments were carried out in an idealized 2D setup. The first series aimed to study the processes of the ISWs of depression transformation under an ice cover of constant submerged ice thickness. Energy loss was estimated based on a budget of depth-integrated pseudoenergy before and after the wave transformation. The transformation of ISWs of depressions is controlled by the blocking parameter β, which is the ratio of the minimum thickness of the upper layer under the ice cover to the incident wave amplitude. The energy loss was relatively small for large positive and large negative values of β. The maximal value of energy loss was about 38 %, and it was reached at β≈0 for ISWs. In the second series of experiments, a number of keels were located on the underside of the constant-thickness ice layer. The ISW transformation under ridged ice also depends on the blocking parameter β. For large keels (β<0), more than 40 % of energy is lost on the first keel, while for relatively small keels (β>0.3), the losses on the first keel are less than 6 %. Energy losses due to all keels depend on the distance between them, which is characterized by the parameter μ, i.e. the ratio of keel depth to the distance between keels. In turn, for a finite length of the ice layer, the distance between keels depends on the keel quantity.

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.

A study of the interaction between depression internal solitary waves and submerged floating tunnels in stratified fluids

Internal wave is a wave phenomenon that traverses almost the depth of the ocean, posing safety challenges and threats to any underwater structure, including the submerged floating tunnel (SFT). Based on the Navier-Stokes (NS) equations and the density transport equation, a numerical model for analyzing the nonlinear interaction between depression internal solitary waves (ISWs) and SFTs in stratified fluids is proposed. After verification with theoretical and experimental results, the hydrodynamic model is utilized to simulate the prototype ISW–SFT interaction under three conditions, i.e., fixed SFT, unconstrained SFT, and constrained SFT. The variation of wave and velocity fields around the SFT in the interaction is simulated, which leads to the wave forces on the SFT as well as the induced motion responses. The simulated results show the wave forces, including horizontal force, vertical force, and moment, are closely correlated with the submergence, wave amplitude and density ratio. When the SFT is unconstrained, the sway and heave displacements are extremely large, while the roll angle is relatively small. When the SFT is constrained by mooring line, it is found the motion displacements are much smaller than the unconstrained condition, inferring the high efficiency of mooring line constraint. However, as motion displacements in the constrained condition are close to the allowable deflection limit of floating bridges for reliability and serviceability, the motion responses should be carefully considered, especially when the SFT encounters internal soliton trains, which may lead to the probability of fatigue failure.

Numerical modeling of energy dissipation of internal solitary waves encountering step topography

In this study, we conducted simulation experiments using a large-eddy simulation method to examine the interaction of internal solitary waves (ISWs) with step topography. We investigated the propagation, transmission, reflection, and breaking of depression ISWs. The features of ISW depend on the geometrical parameters of the step topography that define the initial setting. The relationships between the ISWs geometric and energy loss features as well as the initial setting parameters were analyzed; related empirical relations were developed. Following the analysis of the vortex changes during the process of wave-topography interaction, the different breaking processes and their development rules were discussed. The results showed that, as the obstacle height increased, the degree of energy conversion during the interaction increased. There is no explicit relationship between the loss of energy and energy conversion during the interaction of an ISW with an obstacle. The maximum wave energy loss obtained by eliminating the effect of the tailed wave generated during wave generation and considering the energy conversion is approximately 5%–10% lower than that obtained with traditional methods. Additionally, the mode-2 ISW was detected during the wave-topography interaction, and its velocity profiles in the vertical direction were analyzed, which may be one of the reasons for the accelerated energy dissipation in the system.

Estimate of energy loss from internal solitary waves breaking on slopes

Abstract. Internal solitary waves (ISWs) emerge in the ocean and seas in various forms and break on the shelf zones in a variety of ways. This results in intensive mixing that affects processes such as biological productivity and sediment transport. As ISWs of depression propagate in a two-layer ocean, from the deep part onto a shelf, two mechanisms are significant: (1) the breaking of internal waves over bottom topography when fluid velocities exceed the wave phase speed that causes overturning of the rear face of the wave, and (2) the changing of polarity at the turning point where the depths of the upper and lower layers are equal. We assume that the parameters that describe the process of the interaction of ISWs in a two-layer fluid with an idealized shelf-slope topography are (1) the nondimensional wave amplitude, normalized on the upper-layer thickness; (2) the ratio of the height of the bottom layer on the shelf to the incident wave amplitude; and (3) the angle of the bottom inclination. Based on a proposed three-dimensional classification diagram, four types of wave propagation over the slopes are distinguished: the ISW propagates over the slope without changing polarity and wave breaking, the ISW changes polarity over the slope without wave breaking, the ISW breaks over the slope without changing polarity, and the ISW both breaks and changes polarity over the slope. The energy loss during ISW transformation over slopes with various angles was estimated using the results of 85 numerical experiments. “Hot spots” of high levels of energy loss were highlighted for an idealized bottom configuration that mimics the continental shelf in the Lufeng region in the South China Sea.

Three-dimensional perspective on a convective instability and transition to turbulence in an internal solitary wave of depression shoaling over gentle slopes

Three-dimensional perspective on a convective instability and transition to turbulence in an internal solitary wave of depression shoaling over gentle slopes

Observations of Internal Structure Changes in Shoaling Internal Solitary Waves Based on Seismic Oceanography Method

High spatial resolution and deep detection depths of seismic reflection surveying are conducive to studying the fine structure of the internal solitary wave. However, seismic images are instantaneous, which are not conducive to observing kinematic processes of the internal solitary waves. We improved the scheme of seismic data processing and used common-offset gathers to continuously image the same location. In this way, we can observe internal fine structure changes during the movement of the internal solitary waves, especially the part in contact with the seafloor. We observed a first-mode depression internal solitary wave on the continental slope near the Dongsha Atoll of the South China Sea and short-term shoaling processes of the internal solitary wave by using our improved method. We found that the change in shape of waveform varies at different depths. We separately analyzed the evolution of the six waveforms at different depths. The results showed that the waveform in deep water deforms before that in shallow water and the waveform in shallow water deforms to a greater degree. We measured four parameters of the six waveforms during the shoaling including phase velocity, amplitude, wavelength, and slopes of leading and trailing edge. The phase velocity and amplitudes of waveforms in shallow water increase, the wavelengths decrease, and the slopes of trailing edge gradually become larger than that of the leading edge, while the amplitudes of the deep water waveforms do not change significantly and the phase velocities decrease. Our results are consistent with previous studies made by numerical simulations, which suggest the effectiveness of the new processing scheme. This improved scheme cannot only study the internal solitary waves shoaling, but also has great potential in the study of other ocean dynamics.

Numerical Solution of Ostrovsky Equation over Variable Topography Passes through Critical Point Using Pseudospectral Method

Internal solitary waves have been documented in several parts of the world. This paper intends to look at the effects of the variable topography and rotation on the evolution of the internal waves of depression. Here, the wave is considered to be propagating in a two-layer fluid system with the background topography is assumed to be rapidly and slowly varying. Therefore, the appropriate mathematical model to describe this situation is the variable-coefficient Ostrovsky equation. In particular, the study is interested in the transition of the internal solitary wave of depression when there is a polarity change under the influence of background rotation. The numerical results using the Pseudospectral method show that, over time, the internal solitary wave of elevation transforms into the internal solitary wave of depression as it propagates down a decreasing slope and changes its polarity. However, if the background rotation is considered, the internal solitary waves decompose and form a wave packet and its envelope amplitude decreases slowly due to the decreasing bottom surface. The numerical solutions show that the combination effect of variable topography and rotation when passing through the critical point affected the features and speed of the travelling solitary waves.

Forces on a semi-submersible in internal solitary waves with different propagation directions

Experiments were conducted to study the forces acting on a semi-submersible platform induced by internal solitary waves (ISWs) with different propagation directions. The ISW propagation directions range from 0 deg to 180 deg at the interval of every 30 deg. A series of depression ISWs were generated by a laboratory piston-type wave-maker in a two-layer fluid system. Conductivity probes are used to obtain the ISW profiles at the interface of the two-layer fluid. Experimental results show that the force peak on both columns and pontoons part induced by ISWs increases linearly with wave amplitude under all the propagation directions. The force peak is also influenced significantly by propagation direction. The inline force peak on the pontoons part reaches the maximum in the 90 deg direction, while that of the columns part is the largest in the 30 deg direction at the same wave amplitude. The transverse force on pontoons part is almost zero in the 0 deg and 90 deg direction. The force peaks of 30 deg and 150 deg have no obvious difference because of the symmetrical semi-submersible, so are 60 deg and 120 deg. Besides, effects of propagation direction on the vertical force peak are negligible.

Formation of Recirculating Cores in Convectively Breaking Internal Solitary Waves of Depression Shoaling over Gentle Slopes in the South China Sea

AbstractThe formation of a recirculating subsurface core in an internal solitary wave (ISW) of depression, shoaling over realistic bathymetry, is explored through fully nonlinear and nonhydrostatic two-dimensional simulations. The computational approach is based on a high-resolution/accuracy deformed spectral multidomain penalty-method flow solver, which employs the recorded bathymetry, background current, and stratification profile in the South China Sea. The flow solver is initialized using a solution of the fully nonlinear Dubreil–Jacotin–Long equation. During shoaling, convective breaking precedes core formation as the rear steepens and the trough decelerates, allowing heavier fluid to plunge forward, forming a trapped core. This core-formation mechanism is attributed to a stretching of a near-surface background vorticity layer. Since the sign of the vorticity is opposite to that generated by the propagating wave, only subsurface recirculating cores can form. The onset of convective breaking is visualized, and the sensitivity of the core properties to changes in the initial wave, near-surface background shear, and bottom slope is quantified. The magnitude of the near-surface vorticity determines the size of the convective-breaking region, and the rapid increase of local bathymetric slope accelerates core formation. If the amplitude of the initial wave is increased, the subsequent convective-breaking region increases in size. The simulations are guided by field data and capture the development of the recirculating subsurface core. The analyzed parameter space constitutes a baseline for future three-dimensional simulations focused on characterizing the turbulent flow engulfed within the convectively unstable ISW.

Numerical study on the transformation of an internal solitary wave propagating across a vertical cylinder

A finite volume method based 3D Cartesian grids is developed to study the effect of cylinder diameter on the evolution of a depression internal solitary wave (ISW) with different initial wave amplitudes across a vertical cylinder. This method solves the Navier–Stokes equations using an Improved Delayed Detached Eddy Simulation turbulence model. Numerical results reveal that the significant symmetric vortex shedding on the front and rear side of the cylinder during the wave-obstacle interaction, especially at the large diameter. Moreover, the vortex shedding affects the variations of the horizontal force on different depths. Results also show transmitted wave amplitude and total net horizontal force increase with initial wave amplitude and the diameter of the cylinder, in which the former is less significant than the latter, while the converse is true for the run-up height along the cylinder. In addition, the total horizontal forces on the cylinder reverse direction from compression to tension in the upper layer and conversely it is also true in the lower layer during the propagation of a depression ISW.

Continental slope-confined canyons in the Pearl River Mouth Basin in the South China Sea dominated by erosion, 2004–2018

Repeat multibeam bathymetric surveys conducted in 2004, 2005 and 2018 show that seven slope-confined canyons on the continental slope of the Pearl River Mouth Basin, South China Sea, were dominated by large volume, widespread erosion. Erosion volumes were up to 3.4 times greater than deposition volumes. Erosion-dominated areas of the canyons are up to 2.3 times greater than areas dominated by deposition. Average rates of erosion (ranging from 0.7 to 0.8 m/yr) were greater than average rates of deposition (ranging from 0.5 to 0.8 m/yr). In plan view, the erosion-dominated zones exhibit two characteristic shapes: (1) linear, found mainly in upper canyon reaches, distributed predominantly along canyon axes and at the base of eastern canyon walls, and; (2) blocky, found mainly in lower canyon reaches, widely distributed along the steep canyon walls and on lower-canyon interfluves. The deposition-dominated zones are scattered along canyon floors and walls. Seismic reflection data show lateral shifts of canyon fill deposits through time, indicative of longer-term eastward canyon migration. The linear erosion-dominated zones may be attributed to erosive turbidity currents triggered by energetic internal solitary waves shoaling on the shelf. The eastward canyon shifts were likely induced by rapid near-bed eastward currents generated mainly by westward propagating powerful internal solitary waves of depression. The widespread erosion in the deeper canyon areas and interfluves is likely a consequence of slope instabilities associated with the presence of gas hydrates. This study indicates that active sedimentary processes can occur in slope-confined canyons even during sea level highstands. Local, site-specific oceanographic and geological features (e.g., internal solitary waves, gas hydrates) can significantly increase sedimentary activity in and around submarine canyons.

Scalar transport by propagation of an internal solitary wave over a slope-shelf

Internal solitary waves (ISWs) of depression are commonly found in the coastal environment and are believed to re-suspend sediments in coastal regions where the waves break. In this research, the direct numerical simulation is used to study the scalar transport induced by the ISWs of depression propagating over a slope-shelf topography. The scalar in this paper is considered to represent the concentrations of very fine suspended solids or pollutants. Vortices are observed from the numerical results at the bottom boundary layer on the slope during the ISW shoaling process, resulting in a scalar transport. All incident ISWs of depression are observed to produce a waveform inversion on the shelf. The scalar transport from a slope to a shelf is the consequence of the combined vortices at the bottom boundary layer and the overturning of the ISWs of depression, and the latter was commonly ignored in previous studies. This study shows that the ISW-induced scalar transport consists of the following four stages: the slip transport, the wash transport, the vortex transport, and the secondary transport. A dimensionless time scales of the four stages are calculated, and the beginning times of the wash transport and the secondary transport are found to be uncorrelated with the slope gradients, taking values of 1.26, 4, respectively.

Experimental study of forces on a multi-column floating platform in internal solitary waves

Experiments were conducted to study the forces exerted by internal solitary waves (ISWs) on a floating platform. Depression ISWs were generated by a piston-type wave maker in a density stratified two-layer fluid in a 30-m-long wave flume. Experimental ISWs were compared with ISW theoretical models in terms of frequency-amplitude relationships. The forces and moments on the multi-column floating platform model were measured. Based on the experimental results, the empirical coefficients Cm and Cd are obtained as a function of KC, Reynolds number and the layer depth h1/h. The force prediction based on Morison’s equation and pressure integral were also performed, and the calculated results are well consistent with the measurements. Besides, the forces and moments increase linearly with the wave amplitude, and the maximums of the horizontal forces and moments increase with the layer depth h1/h decreasing.

Polarity Variations of Internal Solitary Waves over the Continental Shelf of the Northern South China Sea: Impacts of Seasonal Stratification, Mesoscale Eddies, and Internal Tides

AbstractSpatiotemporal variations in internal solitary wave (ISW) polarity over the continental shelf of the northern South China Sea (SCS) were examined based on mooring-array observations from October 2013 to June 2014. Depression ISWs were observed at the easternmost mooring, where the water depth is 323 m. Then, they evolved into elevation ISWs at the westernmost mooring, with a depth of 149 m. At the central mooring, with a depth of 250 m, the ISWs generally appeared as depression waves in autumn and spring but were elevation waves in winter. Seasonal variations in stratification caused this seasonality in polarity. On the intraseasonal time scales, anticyclonic eddies can modulate ISW polarity at the central mooring by deepening the thermocline depth for periods of approximately 8 days. During some days in autumn and spring, depression ISWs and ISWs in the process of changing polarity from depression to elevation appeared at time intervals of 10–12 h because of the thermocline deepening caused by internal tides. Isotherm anomalies associated with eddies and internal tides have a more significant contribution to determining the polarity of ISWs than do the background currents. The observational results reported here highlight the impact of multiscale processes on the evolution of ISWs.

Laboratory investigation on internal solitary waves interacting with a uniform slope

Internal solitary waves (ISWs) propagating in a two layer stratified fluid system are studied by laboratory experiments through the standard lock-release method. We investigated the generation, propagation, and breaking phases of large amplitude internal solitary waves of depression, propagating horizontally in a wave tank. ISWs main features depend on the geometrical parameters that define the initial experimental setting. Relations between ISWs geometric and kinematic features and the initial setting parameters are analyzed and empirical relations are developed. The approach of the ISWs towards a uniform slope is investigated. Depending on both wave properties and slopes values, different physical processes characterize the shoaling phase, causing different breaker type. Following a qualitatively analysis of the different breaking mechanisms, collapsing-plunging breakers show the larger contribution in terms of mixing. The characteristics of the breaking events affecting internal wave packets propagating towards the North of the Messina Strait (Mediterranean Sea) are discussed. Additional laboratory experiments are performed to investigate how the pycnocline thickness is affected by the breaking of plunging ISWs. The consequent increase of the pycnocline thickness results to be nonlinearly related with the Iribarren number.

Numerical study on evolution of an internal solitary wave across an idealized shelf with different front slopes

Numerical simulations are performed to investigate the influence of variable front slopes on flow evolution and waveform inversion of a depression ISW (internal solitary wave) over an idealized shelf with variable front slopes. A finite volume based on Cartesian grid method is adopted to solve the Reynolds averaged Navier-Stokes equations using a k-ε model for the turbulent closure. Numerical results exhibit the variations of several pertinent properties of the flow field, in the case with or without waveform inversion on the horizontal plateau of an obstacle. The clockwise vortex is stronger than the counterclockwise one, almost throughout the wave-obstacle interaction. Analysis of the turbulent energy budget reveals that the turbulent production term in the governing equations dominates the wave evolution during a wave-obstacle interaction; otherwise the buoyancy production term and the dissipation term due to viscosity within turbulent eddies play a major role in energy dissipation. In addition, the front slope affects mainly the process and reflection of the wave evolution but has less influence than other physical parameters. Moreover, total wave energy of the leading crest is smaller than that of the leading trough even in the cases with waveform inversion on the plateau.

Shoaling of the internal solitary waves over the continental shelf of the northern South China Sea

The activities of internal solitary waves (ISWs) over the continental shelf of the northern South China Sea (SCS) are of high complexity. In this study, we investigated the spatial-temporal characteristics of the shoaling ISWs over the northern SCS continental shelf using the satellite images and the results of numerical simulation. The examination of the ISW signals in the satellite optical images revealed the existence of three types of ISWs in the region north to the Dongsha Island, namely, mode-1 depression ISW, mode-1 elevation ISW, and mode-2 convex ISW. The geographical distributions of these ISWs were derived from the satellite images. Numerical results exhibited the process of polarity conversion of ISWs, by which mode-1 elevation waves were transformed from the shoaling mode-1 depression waves. The mode-2 convex ISWs generally followed the mode-1 depression ISWs. The numerical results suggested that the interaction of the mode-1 depression ISWs with the up-slope topography locally generated mode-2 ISWs, and such waves of high vertical mode dissipated rapidly during the inshore propagation.

Experimental investigation of sediment resuspension beneath internal solitary waves of depression

AbstractInternal solitary waves (ISWs) of depression are common features of coastal environments and believed to resuspend sediments where they shoal. In this study, the sediment resupension process associated with ISWs propagating over a flat bed was investigated in the laboratory. The first‐ever profile measurements of the three‐dimensional instantaneous velocity field beneath the ISWs revealed that resuspension occurs during burst like vertical velocity events, which lift sediments into the water column, in the adverse pressure gradient region beneath the trailing part of the wave. Resuspension was not observed when the wave‐induced viscous bed stress was maximal directly beneath the ISW trough. Prediction of wave‐induced resuspension was, therefore, unsuccessful using a traditional viscous bed stress‐based Shields diagram. A parameterization for ISW‐induced resuspension is proposed as a function of the maximum instantaneous vertical velocity in the bursts . Here we have replaced the viscous bed stress with , where is the instantaneous resuspending bed stress and is the near‐bed fluid density. From these results, it is possible for field‐oceanographers to predict the occurrence of ISW‐induced resuspension from the bulk wave and stratifications characteristics in a two‐layer stratification. Further research is required to extend the parameterization to larger Reynolds numbers at field‐scale.

A spectral quadrilateral multidomain penalty method model for high Reynolds number incompressible stratified flows

SUMMARYA two‐dimensional quadrilateral spectral multidomain penalty method (SMPM) model has been developed for the simulation of high Reynolds number incompressible stratified flows. The implementation of higher‐order quadrilateral subdomains renders this model a nontrivial extension of a one‐dimensional subdomain SMPM model built for the simulation of the same type of flows in vertically nonperiodic domains (Diamessis et al., J. Comp. Phys, 202:298‐322, 2005). The nontrivial aspects of this extension consist of the implementation of subdomain corners, the penalty formulation of the pressure Poisson equation (PPE), and, most importantly, the treatment of specific challenges that arise in the iterative solution of the SMPM‐discretized PPE. The two primary challenges within the framework of the iterative solution of the PPE are its regularization to ensure the consistency of the associated linear system of equations and the design of an appropriate two‐level preconditioner. A qualitative and quantitative assessment of the accuracy, efficiency, and stability of the quadrilateral SMPM solver is provided through its application to the standard benchmarks of the Taylor vortex, lid‐driven cavity, and double shear layer. The capacity of the flow solver for the study of environmental stratified flow processes is shown through the simulation of long‐distance propagation of an internal solitary wave of depression in a manner that is free of numerical dispersion and dissipation. The methods and results presented in this paper make it a point of reference for future studies oriented toward the reliable application of the quadrilateral SMPM model to more complex environmental stratified flow process studies. Copyright © 2014 John Wiley & Sons, Ltd.