Interaction Of Internal Waves Research Articles

Eddy–Internal Wave Interactions: Stimulated Cascades in Cross-Scale Kinetic Energy and Enstrophy Fluxes

Abstract The interactions between oceanic mesoscale eddies, submesoscale currents, and internal gravity waves (IWs) are investigated in submesoscale-resolving realistic simulations in the North Atlantic Ocean. Using a novel analysis framework that couples the coarse-graining method in space with temporal filtering and a Helmholtz decomposition, we quantify the effects of the interactions on the cross-scale kinetic energy (KE) and enstrophy fluxes. By systematically comparing solutions with and without IW forcing, we show that externally forced IWs stimulate a reduction in the KE inverse cascade associated with mesoscale rotational motions and an enhancement in the KE forward cascade associated with divergent submesoscale currents, i.e., a “stimulated cascade” process. The corresponding IW effects on the enstrophy fluxes are seasonally dependent, with a stimulated reduction (enhancement) in the forward enstrophy cascade during summer (winter). Direct KE and enstrophy transfers from currents to IWs are also found, albeit with weaker magnitudes compared with the stimulated cascades. We further find that the forward KE and enstrophy fluxes associated with IW motions are almost entirely driven by the scattering of the waves by the rotational eddy field, rather than by wave–wave interactions. This process is investigated in detail in a companion manuscript. Finally, we demonstrate that the stimulated cascades are spatially localized in coherent structures. Specifically, the magnitude and direction of the bidirectional KE fluxes at submesoscales are highly correlated with, and inversely proportional to, divergence-dominated circulations, and the inverse KE fluxes at mesoscales are highly correlated with strain-dominated circulations. The predominantly forward enstrophy fluxes in both seasons are also correlated with strain-dominated flow structures.

Evolution of Internal Gravity Waves in a Mesoscale Eddy Simulated Using a Novel Model

Abstract We investigate the effect of wave–eddy interaction and dissipation of internal gravity waves propagating in a coherent mesoscale eddy simulated using a novel numerical model called the Internal Wave Energy Model based on the six-dimensional radiative transfer equation. We use an idealized mean flow structure and stratification, motivated by observations of a coherent eddy in the Canary Current System. In a spindown simulation using the Garret–Munk model spectrum as initial conditions, we find that wave energy decreases at the eddy rim. Lateral shear leads to wave energy gain due to a developing horizontal anisotropy outside the eddy and at the rim, while vertical shear leads to wave energy loss which is enhanced at the eddy rim. Wave energy loss by wave dissipation due to vertical shear dominates over horizontal shear. Our results show similar behavior of the internal gravity wave in a cyclonic as well as an anticyclonic eddy. Wave dissipation by vertical wave refraction occurs predominantly at the eddy rim near the surface, where related vertical diffusivities range from to . Significance Statement Using a novel model and observations from the Canary Current System of a coherent eddy of 100-km diameter, we explore the interaction between a realistic internal gravity wave field and this eddy. We study wave refraction and energy transfers between the waves and the eddy induced by the eddy’s lateral and vertical shear. Waves lose energy at the eddy rim by vertical shear and gain outside of the eddy rim by horizontal shear. We find large vertical wave refraction by vertical shear at the eddy rim, where waves break and mix density, which can have wide ranging effects on the ocean’s circulation. These results are important for understanding the ocean’s mixing and energy cycle and to develop eddy and wave parameterizations.

Eddy–Internal Wave Interactions and Their Contribution to Cross-Scale Energy Fluxes: A Case Study in the California Current

Abstract Oceanic mixing, mostly driven by the breaking of internal waves at small scales in the ocean interior, is of major importance for ocean circulation and the ocean response to future climate scenarios. Understanding how internal waves transfer their energy to smaller scales from their generation to their dissipation is therefore an important step for improving the representation of ocean mixing in climate models. In this study, the processes leading to cross-scale energy fluxes in the internal wave field are quantified using an original decomposition approach in a realistic numerical simulation of the California Current. We quantify the relative contribution of eddy–internal wave interactions and wave–wave interactions to these fluxes and show that eddy–internal wave interactions are more efficient than wave–wave interactions in the formation of the internal wave continuum spectrum. Carrying out twin numerical simulations, where we successively activate or deactivate one of the main internal wave forcing, we also show that eddy–near-inertial internal wave interactions are more efficient in the cross-scale energy transfer than eddy–tidal internal wave interactions. This results in the dissipation being dominated by the near-inertial internal waves over tidal internal waves. A companion study focuses on the role of stimulated cascade on the energy and enstrophy fluxes.

Oceanic internal solitary wave interactions via the KP equation in a three-layer fluid with shear flow

Oceanic internal solitary wave interactions via the KP equation in a three-layer fluid with shear flow

Dynamical analysis of (4 + 1)-dimensional Davey Srewartson Kadomtsev Petviashvili equation by employing Lie symmetry approach

In this study, (4+1)-dimensional Davey Srewartson Kadomtsev Petviashvili equation is investigated, which can be employed to depict internal wave interactions encompassing both elastic and non-elastic behaviors. Initially, the translational symmetries of the equation are identified by employing Lie symmetry method. Then, by utilizing these symmetries, the discussed model is translated into an ordinary differential equation. The new auxiliary equation approach is then employed to obtain precise solutions, and the results are visually represented. Afterward, the dynamical behavior of the equation is analyzed from multiple perspectives, including bifurcation, chaos, and sensitivity analysis. Bifurcation is conducted at fixed points, while an external force is applied to the dynamical system, leading to the discovery of chaotic behavior using various tools such as 3D and 2D phase plots, time series plots, Poincaré maps, and multistability analysis. Furthermore, sensitive nature of the model is examined at different initial values, revealing the significant sensitivity of the proposed model, where even small changes in the initial conditions result in notable variations. At the end, conclusion is presented.

Diapycnal Mixing and Double Diffusion over the Continental Slope in the Northern Sea of Japan in the Warm Half-Year

This study investigates double diffusion processes responsible for diapycnal mixing in the Primorye current in the northern Sea of Japan. The results of processing and analysis of a long time series of data from regular Aqualog-profiler measurements of thermohaline characteristics and current velocity over the continental slope between the horizons of 60 and 420 m from April to October 2015. Using the Osborne-Cox parameterization (1972) and Gregg’s (1989) parameterization, we estimated heat and salt diffusivities, as well as the buoyancy flux. To reveal the processes of double diffusion, the Turner angle was estimated. We estimated contributions of diffusive convection and salt fingers into the buoyancy flux. Due to double diffusion, the intense vertical mixing covered the layer from 80 to 170 m. From mid-spring to early May, diffusive convection penetrated to a horizon of 250 m, and then a process like salt fingers played a leading role. Shear instability caused by the weakly nonlinear interaction of internal waves prevailed in the underlying layers.

Observations of Internal Wave Interactions in a Southern Ocean Standing Meander

Abstract We characterize the internal wave field at a standing meander of the Antarctic Circumpolar Current (ACC) where strong winds, bathymetry, and a strong eddy field combine to form a dynamic environment for the generation and dissipation of internal waves. We use Electromagnetic Autonomous Profiling Explorer float data spanning 0–1600 m depth collected from a meander near the Macquarie Ridge, south of Australia. Of the 112 internal waves identified, 69% are associated with upward energy propagation. Most of the upward propagating waves (35%) are found near the Polar Front and are likely generated by mean flow–topography interactions. Generation by wind forcing at the sea surface is likely responsible for more than 40% of the downward propagating waves. Our results highlight advection of the waves and wave–mean flow interactions within the ACC as the dominant processes affecting the wave dynamics. The larger dissipation time scales of the waves compared to advection suggests they are likely to dissipate away from the generation site. We find that about 79% (66%) of the waves in cyclonic eddies (the Subantarctic Front) are influenced by horizontal strain, whereas 92% of the waves in the slower Polar Front are influenced by the relative vorticity of the background flow. There is energy exchange between internal waves and the mean flow, in both directions. The mean energy transfer (1.4 ± 1.0 × 10−11 m2 s−3) is from the mean flow to the waves in all dynamic regions except in anticyclonic eddies. The strongest energy exchange (5.0 ± 3.7 × 10−11 m2 s−3) is associated with waves in cyclonic eddies.

Oblique interactions of internal solitary waves in the lower atmosphere

Internal solitary waves frequently occur in the atmosphere. On rare occasions, they create the awe-inspiring spectacle known, for example, as the Morning Glory Clouds, a spectacular roll cloud, or series of roll clouds predictably appearing in the southern part of the Gulf of Carpentaria. Nevertheless, solitary wave–wave interactions have rarely been studied and documented; thus, we here focus on the long-time evolution of the superposition of two solitons featuring an X-shape and, more complicated, the interactions between three solitons initially posing as a Y-shape. To better understand the underlying dynamics of these phenomena, we derive a bidirectional and isotropic theoretical equation in a two-layer fluid system with variable bottom topography. This is accomplished by using its Hamiltonian structure and the Taylor expansion of the Dirichlet–Neumann operator for the potential theory. Essentially, the derived equation is an extension of the widely recognized Benjamin–Ono equation at two horizontal dimensions, and thereby, it possesses plane soliton solutions propagating in any horizontal direction. It is noted that the initial angles play an essential role in the oblique wave–wave interactions, manifested as the determination of waveforms, amplitudes, and the emergence of the Mach stem. In addition, the wave evolution is slightly modulated by the topographic effects, partly due to invoking the assumption of small topography.

Interaction of mode-one internal solitary waves of opposite polarity in double-pycnocline stratifications

Numerical simulations of the interaction of internal solitary waves (ISWs) of opposite polarity are conducted by solving the incompressible Euler equations under the Boussinesq approximation. A double-pycnocline stratification is used. A method to determine when ISWs of both polarities exist is also presented. The simulations confirm previous work that the interaction of waves of the same polarity are soliton-like; however, here it is shown that when a fast ISW with the same polarity as a Korteweg–de Vries (KdV) solitary wave catches up and interacts with a slower ISW of opposite polarity, the interaction can be far from soliton-like. The energy in the fast KdV-polarity wave can increase by more than a factor of 5 while the energy in the slower negative-KdV-polarity wave can decrease by 50 %. Large trailing wave trains may be generated and in some cases multiple ISWs with KdV polarity may be formed by the interaction.

Numerical study of the interaction between an internal solitary wave and a submerged extended cylinder using OpenFOAM

To investigate the impacts of cylinder extended length, rotation angle and wave incidence angle on hydrodynamic characteristics, the numerical simulation of an internal solitary wave (ISW) interaction with a submerged extended cylinder is conducted by using OpenFOAM. The accordance between the experimental data and numerical simulation forces on the isolated cylinder shows that the OpenFOAM-based numerical model can deal with the ISW-submerged cylinder interaction. The distributions of forces, maximum dynamic pressure forces and flow field around the submerged extended cylinder are discussed to reveal the hydrodynamic characteristics of submerged cylinder under the ISW action. The horizontal forces on an extended cylinder are found to change from increasing to decreasing with the increase in extended length when the extended length is 2.5 times the cylinder diameter. The forces on the cylinder are sensitive to the change in the rotation angle. Both the horizontal loads and the evolution of the wave profile are easily affected by the change in incidence angle. The vortices shedding around the cylinder varies with the change of wave incidence angle. Investigation of the ISW and a submerged cylinder interactions can help to understand the mechanism of structural damage in internal wave ocean environment.

Triadic resonant instability in confined and unconfined axisymmetric geometries

We present an investigation of the resonance conditions governing triad interactions of cylindrical internal waves, i.e. Kelvin modes, described by Bessel functions. Our analytical study, supported by experimental measurements, is performed both in confined and unconfined axisymmetric domains. We are interested in two conceptual questions: can we find resonance conditions for a triad of Kelvin modes? What is the impact of the boundary conditions on such resonances? In both the confined and unconfined cases, we show that sub-harmonics can be spontaneously generated from a primary wave field if they satisfy at least a resonance condition on their frequencies of the form $\omega _0 = \pm \omega _1 \pm \omega _2$ . We demonstrate that the resulting triad is also spatially resonant, but that the resonance in the radial direction may not be exact in confined geometries due to the prevalence of boundary conditions – a key difference compared with Cartesian plane waves.

Investigation of the interaction of internal solitary waves with the slope-shelf topography

In this paper, internal solitary waves (ISWs) propagating over shelf topographies are studied based on numerical experiments conducted according to the lock-release method. The wave generation, propagation, and interactions with slope-shelf topography are investigated in a wave tank. The primary features of the propagation of ISWs on the slope are assessed. Shear and advection instabilities are observed in the current simulations in some cases with 1.29 < Bs < 1.75 (Bs is defined as the ratio of layer water depth on the shelf to the ISW amplitude). The induced density flow contributes to the growth of potential energy by dilution and stripping, primarily through its head, which is one of the factors used to enhance the mixing efficiency. In addition, the obtained results are compared with those of previous experiments conducted by other researchers, while considering the differences in local topography. The comparison reveals that local topography is a reason for the experimental differences of some research studies. ISW breaking on a slope is strongly influenced by the initial flow field of the slope, which may lead to differences in the prediction of the breaking point by using boundary layer separation as a criterion. As the incident wave amplitude increases, the location of the breaking point shifts downward and its magnitude gradually decreases.

KmT, Kilometer-long mooring of high-resolution Temperature measurements results overview

The global oceans show extensive bottom topography above which intensive turbulent mixing is generated by breaking internal waves. Growing evidence suggests that the mixing is sufficient to maintain the ocean’s stable vertical density stratification, thereby preventing the deep-ocean from becoming a stagnant pool of cold water. Observational details of the extent of turbulent mixing away from topography are still scarce however. In this paper, results are presented from 760 high-resolution temperature sensors that were moored between 8 and 1146.5 m above a 2380-m deep sloping seafloor of Mount Josephine NE-Atlantic for 4 months. The local seafloor-slope is supercritical for semidiurnal internal tides under average stratification. The purpose of the > 1-km-long densely instrumented mooring is to provide insight in the variability of coherent scales, and in the connection between seamount-slope and mixing-effects up to 7-km horizontally into the ocean-interior. Largest four-month mean turbulence values are found near the seafloor, decreasing to half an order of magnitude lower values at 500 m above, and remaining steady-high further up. Local increases of mean turbulence values are observed in bands of 100–200 m thickness. Larger internal wave breaking occurs during baroclinic spring tide, which also affects internal waves and turbulent overturning in the interior. Spectrally, a turbulence inertial subrange dominates part of the internal wave band continuum near the seafloor. Coupling between interior- and near-seafloor-mixing is not only via previously suggested isopycnal transport of mixed waters, but also via strong internal wave interactions. Seamount-flow contributes to absolute vorticity so that blue-shifted near-inertial motions interact with internal tides.

Mutual enhancement of wind- and tide-induced near-inertial internal waves in Luzon Strait

Abstract Tide-induced near-inertial internal waves (NIWs) are generated by tide-topography interaction and are energized by internal tides through triadic resonant interaction of internal waves. They are located above topography and could be in close contact with wind-induced NIWs when the topography is a tall ridge, like in the Luzon Strait of the northern South China Sea (SCS). A natural question arises as to whether there is significant interaction between wind- and tide-induced NIWs. By using moored velocity observations, satellite-tracked surface drifter dataset, and idealized numerical simulations, we find that in the presence of tide-induced NIWs, the wind can inject slightly more near-inertial energy (NIE), while in the presence of wind-induced NIWs, significantly more tidal energy is transferred to NIWs. Thus, wind- and tide-induced NIWs can mutually enhance each other, producing more NIE than a linear superposition of that generated by wind and tide forcing alone. Increasing wind intensity and tidal excursion lead to saturation of NIE enhancement, while a taller ridge leads to stronger enhancement. The high mixed-layer NIE near Luzon Strait is mostly generated by the wind, while the mutual enhancement between wind- and tide-induced NIWs can further enhance this pattern. The interaction between wind- and tide-induced NIWs leads to an enhancement of 25% more NIE. If tide-induced NIWs are neglected, as is usually the case in the estimation of NIE, the total NIE will be underestimated by almost 50%. This might imply that tide-induced NIWs are important for the energetics of NIWs in Luzon Strait.

Turbulent Mixing Variability in an Energetic Standing Meander of the Southern Ocean

Abstract This study presents novel observational estimates of turbulent dissipation and mixing in a standing meander between the Southeast Indian Ridge and the Macquarie Ridge in the Southern Ocean. By applying a finescale parameterization on the temperature, salinity, and velocity profiles collected from Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats in the upper 1600 m, we estimated the intensity and spatial distribution of dissipation rate and diapycnal mixing along the float tracks and investigated the sources. The indirect estimates indicate strong spatial and temporal variability of turbulent mixing varying from O(10−6) to O(10−3) m2 s−1 in the upper 1600 m. Elevated turbulent mixing is mostly associated with the Subantarctic Front (SAF) and mesoscale eddies. In the upper 500 m, enhanced mixing is associated with downward-propagating wind-generated near-inertial waves as well as the interaction between cyclonic eddies and upward-propagating internal waves. In the study region, the local topography does not play a role in turbulent mixing in the upper part of the water column, which has similar values in profiles over rough and smooth topography. However, both remotely generated internal tides and lee waves could contribute to the upward-propagating energy. Our results point strongly to the generation of turbulent mixing through the interaction of internal waves and the intense mesoscale eddy field.

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.

A Characteristics Set Computation Model for Internal Wavenumber Spectra and Its Validation with MODIS Retrieved Parameters in the Sulu Sea and Celebes Sea

The quasi-linear or nonlinear interactions among different ocean motions dominate the system internal structure and appearance feature presented in spatial and temporal evolution. However, deficiency of the characteristics set computation model for internal wavenumber spectra proves to be a serious barrier to derive interaction mechanisms of internal waves with large or small scale ocean motions. In this study, a characteristics set computation model for internal wavenumber spectra is proposed for complicated offshore environments. The refraction of current shear instability, bottom topography and the reflection at surface and bottom are attentively considered in the complicated characteristics inlaid scheme. Model results are validated with MODIS retrieved internal wave parameters in the Sulu Sea and Celebes Sea. This original characteristics set computation model for internal wavenumber spectra can be used widely and can further improve the understandings of generation, dissipation, nonlinear wave-wave interaction and mixing process of internal waves.

Variability of Internal Wave Strain Over the Western Boundary Region in the North Atlantic

Based on the CTD profiles and mooring measurements of the Line W program in the North Atlantic about 35°N/70°W, we investigated the spatial variability of internal wave-induced strain variance along the Line W section and the associated reasons. The results showed that the internal wave strain variance over the slope could be up to five times larger than that in the interior. We have validated that internal tides and near-inertial waves were not the crucial processes for causing this variability. Meanwhile, we found that the high-frequency internal waves generated by the interaction of anticyclonic eddy and low-frequency internal waves may be a potential cause of strain enhancement. This study implies a potential route of mesoscale eddies to enhance the strain variance induced by internal waves.

Numerical investigation of an internal solitary wave interaction with tandem horizontal cylinders

To investigate the effect of the position (L) and centre-to-centre (D) distance of tandem cylinders on hydrodynamic characteristics, an internal solitary wave (ISW) propagation over the tandem horizontal cylinders is simulated based on OpenFOAM. The agreement between the numerical simulation results of the force on single cylinder and experimental data indicates that the numerical model employed can well simulate the interaction between ISW and cylinder. The hydrodynamic characteristics including the force, maximum dynamic pressure and vorticity around the tandem two cylinders are revealed. The distribution of maximum forces on each cylinder located at different L is not sensitive to the change of D. Both the intensity and distribution of maximum dynamic pressures and vortices around two cylinders are easily affected by the variations of L and D. The maximum dynamic pressures around cylinder 1 are greater than those around cylinder 2. Based on the regression analysis, a formula of force variation range ratio of the tandem two cylinders is established. Once the extreme values of the forces on the single cylinder have been obtained, it is possible to calculate the range variation of forces on each of the tandem two cylinders under the same simulation condition.

Generation of internal waves in a two-layered stratified system with a free surface by coupled mass sources

The generation of internal waves (IWs) is of fundamental concern in numerical studies on the IWs and particularly their interaction with the currents and structure topography. In this study, a coupled mass sources (CMS) approach is proposed to generate IWs in a two-layer stratified system considering the free-surface effect. The numerical verifications are performed in the NEWTANK model solving full Navier-Stokes equations. The multi-layered VOF (ML-VOF) method is employed to track the movement of the interface and free surface simultaneously. The verifications indicate that the CMS method is capable of generating internal solitary waves (ISWs) with weak and strong nonlinearity under the free surface. The prescribed ISW can be generated at the very beginning with no obvious trailing waves compared with the commonly used gravity-collapse method. Furthermore, the free-surface soliton aroused at the top of ISW is consistent with the theoretical solution. The verifications also demonstrate that the CMS method is competent to generate ideal internal periodic waves (IPWs) in both Boussinesq and non-Boussinesq conditions considering the free-surface effect. Finally, the internal wave interaction with the currents simulated by the CMS method is discussed to demonstrate the advantages of this approach.