Generation Of Internal Waves Research Articles

On the Large-x Asymptotic of the Classical Solutions to the Non-Linear Benjamin Equation in Fractional Sobolev Spaces

In this work, we study the large-x asymptotic of classical solutions to the non-linear Benjamin equation modeling propagation of small amplitude internal waves in a two fluid system. In our analysis, we extend known Hs-well-posedness results to the case of the variable-weight Sobolev spaces. The spaces provide a direct control over the asymptotics of classical solutions and their weak derivatives, and permit us to compute the bulk large-x asymptotic of classical solutions explicitly in terms of input data. The asymptotic formula provides a precise description of the qualitative behaviour of classical solutions in weighted spaces and yields a number of weighted persistence and continuation results automatically.

Mechanisms of Reappeared Period Shifts of Internal Solitary Waves Based on Mooring Array Observations in the Northern South China Sea

AbstractMooring observations have revealed that the daily reappeared time (DRt) of internal solitary waves (ISWs) in the northern South China Sea (SCS) manifests systematic shifts. This study aims to reveal the dynamic mechanisms behind this phenomenon using the theory of modulation of shear flow to the internal tide wave (IT) propagation. Approximate solutions for the frequency modulation function (FMF) and the amplitude modulation function (AMF) of ITs are derived and validated by the mooring array measurements on the northern SCS continental shelf in 2019 and 2020. Namely, the mechanisms of the ISW reappeared period shift (RPS derived from DRt) and amplitude variation are attributed to the modulation of low‐frequency flow with a period of about 7 days to ITs. The FMF is induced by the vorticity of the low‐frequency flow (FS1) and the Doppler shift (FS2). Thus, the sign of the FMF value may be positive (blue shift) and negative (red shift), depending on the algebraic summation of the two terms. The FS2 derived from mooring observed velocities confirms the modulation effects of mean current on the frequency shift and the amplitude variation of ITs and ISWs.

Estimating the In Situ Stratification via Remotely Sensed Internal Wave Speeds

Abstract This work tests a methodology for estimating the ocean stratification gradient using remotely sensed, high temporal and spatial resolution field measurements of internal wave propagation speeds. The internal wave (IW) speeds were calculated from IW tracks observed using a shore-based, X-band marine radar deployed at a field site on the south-central coast of California. An inverse model, based on the work of Kar and Guha, utilizes the linear internal wave dispersion relation, assuming a constant vertical density gradient is the basis for the inverse model. This allows the vertical gradient of density to be expressed as a function of the internal wave phase speed, local water depth, and a background average density. The inputs to the algorithm are the known cross-shore bathymetry, the background ocean density, and the remotely sensed cross-shore profiles of IW speed. The estimated density gradients are then compared to the synchronously measured vertical density profiles collected from an in situ instrument array. The results show a very good agreement offshore in deeper water (∼50–30 m) but more significant discrepancies in shallow water (20–10 m) closer to shore. In addition, a sensitivity analysis is conducted that relates errors in measured speeds to errors in the estimated density gradients. Significance Statement The propagation speed of ocean internal waves inherently depends on the vertical structure of the water density, which is termed stratification. In this work, we evaluate and test with real field observations a technique to infer the ocean density stratification from internal wave propagation speeds collected from remote sensing images. Such methods offer a way to monitor ocean stratification without the need for extensive in situ measurements.

Features of Earth’s lower ionosphere during solar eclipse and sunset and sunrise hours according to measurements by the API method near Nizhny Novgorod

We present the results of experimental studies into the response of Earth’s lower ionosphere to a partial solar eclipse. The studies have been carried out using the method of resonant scattering of radio waves by artificial periodic irregularities (APIs) in ionospheric plasma. The irregularities were created in the field of a standing wave when a powerful radio wave, generated by radiation to the zenith by transmitters of the mid-latitude heating facility SURA, was reflected from the ionosphere. During location of a periodic structure by probe radio waves when the Wolf—Bragg backscattering condition was met, a scattered signal was received and its amplitude and phase were measured. After the end of the impact on the ionosphere, the irregularities gradually disappeared (relaxed). We have examined variations in characteristics of scattered signals. During the eclipse, the scattered signal amplitude increased by 30–40 dB, and the relaxation time increased 1.5–2.0 times. In some cases, stratification of the signal amplitude in the D-region was observed due to stratification of the electron density profile. By analyzing altitude profiles of relaxation time, we obtained neutral component temperature and density, height of the turbopause, and turbulent velocity. The velocity of vertical regular motion of plasma at each height was measured from the time variation in the scattered signal phase. From the results of measurements of scattered signal characteristics during four partial eclipses, we have obtained that the neutral component temperature decreases, on average, 50–70 K. Variations in the temperature, vertical plasma velocity, and turbopause level exhibited deep quasi-periodic variations with periods from 15 min to several hours, typical of internal gravity wave propagation. The vertical temperature and velocity profiles showed changes with altitude on scales ranging from 5 to 30 km. Comparison between the results of studies of the lower ionosphere during sunrise-sunset hours has revealed that its response during a partial eclipse and the transition to the night regime is identical. According to the measurements by the partial reflection method, during the August 01, 2008 eclipse there was a decrease in the electron density in the D-region 3–5 times. We have concluded that during an eclipse there was a significant change in both the ionized and neutral components of the atmosphere in the lower ionosphere.

Особенности нижней ионосферы Земли во время затмений Солнца и в заходно-восходные часы по измерениям методом ИПН вблизи Нижнего Новгорода

We present the results of experimental studies into the response of Earth’s lower ionosphere to a partial solar eclipse. The studies have been carried out using the method of resonant scattering of radio waves by artificial periodic irregularities (APIs) in ionospheric plasma. The irregularities were created in the field of a standing wave when a powerful radio wave, generated by radiation to the zenith by transmitters of the mid-latitude SURA heating facility, was reflected from the ionosphere. During the eclipse, the scattered signal amplitude increased by 30–40 dB, and the relaxation time increased 1.5–2.0 times. In some cases, stratification of the signal amplitude in the D-region was observed due to stratification of the electron density profile. By analyzing altitude profiles of relaxation time, we obtained neutral component temperature and density, height of the turbopause, and turbulent velocity. The velocity of vertical regular motion of plasma at each height was measured from the time variation in the scattered signal phase. From the results of measurements of scattered signal characteristics during four partial eclipses, we have obtained that the neutral component temperature decreases, on average, 50–70 K. Variations in the temperature, vertical plasma velocity, and turbopause level exhibited deep quasi-periodic variations with periods from 15 min to several hours, typical of internal gravity wave propagation. The vertical temperature and velocity profiles showed changes with altitude on scales ranging from 5 to 30 km. Comparison between the results of studies of the lower ionosphere during sunrise-sunset hours has revealed that its response during a partial eclipse and the transition to the night regime is identical. According to the measurements by the partial reflection method, during the August 01, 2008 eclipse there was a decrease in the electron density in the D-region 3–5 times. We have concluded that during an eclipse there was a significant change in both the ionized and neutral components of the atmosphere in the lower ionosphere.

Инструментальные наблюдения и статистический анализ вертикальных профилей температуры в юго-западной части залива Петра Великого Японского моря

The study is based on data from four moorings stretched out in the north-northwest – south-southeast direction across the isobaths in the southwestern Peter the Great Bay, the Sea of Japan, on 3–14 October, 2022. For this purpose, timeseries of vertical profiles of temperature and its gradient were expanded into empirical orthogonal functions; timescales were estimated using wavelet transform. In all cases, the leading mode captures vertical stratification variability related to the thermocline shoaling or deepening, manifesting itself by concerted oscillations of temperature and its vertical gradient, which occurred on the near-inertial, semi-diurnal and two-diurnal timescales. The near-inertial oscillations were the most intense during most of the time, while the semi-diurnal ones were the most intense on the fourth and fifth days. From the joint wavelet spectra it was found that temperature anomalies moved towards the shallower area and the speed was estimated as equal to 0.44–0.55 and 0.95–1.11 m/s for the near-inertial and semi-diurnal timescales, respectively. The speed on the two-diurnal timescale differs by an order of magnitude between the pairs of two deeper and two shallower moorings, equaling to 1.17 and 0.15 m/s, respectively. The results were interpreted as related to the near-inertial and semi-diurnal internal wave propagation from the continental slope towards the inner shelf and two-diurnal timescale was speculated to be a difference between them caused by non-linearity.

Experimental and numerical study on damage behavior of air-backed steel-concrete-steel composite panels subjected to underwater contact explosion

The damage behavior and explosion resistance of air-backed steel-concrete-steel (SCS) composite panels subjected to underwater contact explosions were investigated experimentally and numerically. Firstly, the underwater explosion experiments of the SCS panels were conducted using the novel test setup, and the final damage morphology and residual deflection of these panels were obtained. Secondly, the corresponding finite element model was established in LS-DYNA and validated against the test results, based on the refined numerical modelling, the damage process of the SCS composite panel under 200 g underwater contact explosion was reproduced. After that, the damage mechanism of the SCS panels was revealed through the analysis of internal energy absorption and stress wave propagation inside the SCS panels. Subsequently, the damage behavior of the SCS panels when subjected to underwater and air contact explosions was compared. Finally, a series of parametric analysis were performed to explore the effects of the material strength and structural form on the explosion resistance of SCS panels. Both the experimental and numerical results indicate that the SCS panels suffered global damage. The core concrete absorbed more than 80 % of the explosion energy and the restraint of the steel plates effectively reduced the spalling damage of the core concrete. The SCS composite panel makes full use of the advantages of concrete and steel panels, resulting in superior underwater explosion resistance.

Modulation of the internal wave regime over a tropical seamount ecosystem by basin-scale oceanographic processes

Shallow seamounts are becoming increasingly recognised as key habitats for conservation due to their role as biological refuges, particularly throughout oligotrophic oceans. Traditionally, Taylor caps have been invoked as the mechanism driving biomass aggregation over seamounts but emerging evidence based on higher resolution measurements highlights the importance of internal waves (IW) to the local ecosystem. These waves can flush the benthic habitat with cool water from depth and impact on nutrient supply over short time scales through turbulent mixing that may also influence fish behaviour. They are dependent on the regional stratification, however, and thus influenced by planetary-scale variability in oceanographic conditions. We present here detailed observations of the internal wave regime over a shallow seamount, called Sandes, in the central Indian Ocean throughout different phases of the Indian Ocean Dipole (IOD) that modulated the regional stratification. A deep thermocline, caused by the 2019 IOD event precluded internal wave activity over the summit, whereas a thermocline collocated with the summit during 2020 when the IOD reversed polarity resulted in a 30 m amplitude internal tide signal (t ∼ 12.5 h). A shallow thermocline, observed during 2022, resulted in propagation of IWs over the summit with less visible internal tide. Harmonic analysis shows the presence of high frequency waves (t ∼ 15 min) on both flanks of the seamount during 2020 & 2022, which are likely a result of local shear instability, whereas 2019 shows an asymmetric response, potentially due to the strong background current and suppression of the thermocline beneath the depth of the summit. The potential importance of the waves over the summit to the local ecosystem may be attributed to the elevated turbulence measured at the thermocline during internal wave propagation, with ε > 10-5 W kg-1 routinely observed. Our results highlight the ability of thermocline depth to act as a gating condition for internal wave evolution over the summit. These results show that, whilst the water column exhibits variability at short spatiotemporal scales compared to the frequently cited Taylor cap dynamics, it is also regulated by the wider basin scale processes. Thus, a more integrated approach is needed when assessing these dynamic and environmentally critical habitats to include the effects of physical oceanographic controls across multiple spatiotemporal scales.

Nonreflecting Propagation of Internal Waves in an Exchange Flow of a Shallow Two-Layer Medium in a Channel with a Variable Cross Section

Nonreflecting Propagation of Internal Waves in an Exchange Flow of a Shallow Two-Layer Medium in a Channel with a Variable Cross Section

Effects of stratification on overshooting and waves atop the convective core of M⊙ main-sequence stars

ABSTRACT As a massive star evolves along the main sequence, its core contracts, leaving behind a stable stratification in helium. We simulate two-dimensional convection in the core at three different stages of evolution of a $5\,\mathrm{ M}_{\odot }$ star, with three different stratifications in helium atop the core. We study the propagation of internal gravity waves in the stably stratified envelope, along with the overshooting length of convective plumes above the convective boundary. We find that the stratification in helium in evolved stars hinders radial motions and effectively shields the radiative envelope against plume penetration. This prevents convective overshooting from being an efficient mixing process in the radiative envelope. In addition, internal gravity waves are less excited in evolved models compared to the zero-age-main-sequence model, and are also more damped in the stratified region above the core. As a result, the wave power is several orders of magnitude lower in mid- and terminal-main-sequence models compared to zero-age-main-sequence stars.

Large-amplitude internal waves and turbulent mixing in three-layer flows under a rigid lid

We consider a nonlinear long-wave Boussinesq-type model describing the propagation of breaking internal solitary waves in a three-layer flow between two rigid boundaries. The Green–Naghdi-type equations govern the fluid flow in the top and bottom homogeneous layers. In the intermediate hydrostatic layer, the fluid is non-homogeneous, and its flow is described by the depth-averaged shallow water equations for shear flows. The velocity shear in the outer layers can lead to the development of the Kelvin–Helmholtz instability and turbulent mixing. To take this into account, we propose a simple law of vertical mixing, which governs the interaction of these layers. Stationary solutions and non-stationary calculations show the effect of mixing (or breaking) for waves of sufficiently large amplitude. We construct steady-state soliton-like solutions of the three-layer model adjacent to a given constant flow. The obtained theoretical profiles of breaking solitary waves are consistent with laboratory experiments.

Characteristics of internal waves in the Bali Sea from Sentinel-1A data and ocean modeling

Abstract Internal waves (IWs) that propagate into the Bali Sea are supposed to originate from the generating sill area in the southern part of the Lombok Strait. This study aims to investigate surface features and mechanism of IWs formation and propagation into the Bali Sea. The datasets are acquired from the Sentinel-1A imageries and CROCO model simulation. The results showed that solitary wave packets are spread over two areas: near Lombok Strait as generating area, and in the western and northern parts of the Bali Sea as propagating area. The length of IWs crests increased as they moved into the propagation area. The model showed that mixed semidiurnal tidal currents near the sill flow northward (southward) alternately during the flood (ebb) tidal period, resulting in the pycnocline deepening down to ~400 m near the northern sill area during the flood tide. Furthermore, the model demonstrated an alternating upward and downward movement of vertical currents components, associated with propagation of IWs’ crests and troughs along IWs pathway.

The modified cubic Benjamin–Ono equation describing internal solitary waves in the deep ocean and its related properties

In this article, we investigate the propagation of internal solitary waves in deep ocean. Based on the principles of nonlinear theory, perturbation expansion, and multi-scale analysis, a time-dependent modified cubic Benjamin–Ono (mCBO) equation is derived to describe internal solitary waves in the deep ocean with stronger nonlinearity. When the dispersive term ∂3f∂X3 vanishes, the mCBO equation transforms into the cubic BO equation. Similarly, when the dispersive term ∂3f∂X3 becomes zero and the nonlinear term ∂f3∂X degenerates into ∂f2∂X, the mCBO equation reduces to the BO equation. Furthermore, if the integral term ∂2∂X2ℵ(f) disappears, it simplifies to the mKdV equation. To gain deeper insight into the characteristics of solitary waves, conservation of mass and momentum associated with them are discussed. By employing Hirota's bilinear method, we obtain soliton solutions for the mCBO equation and subsequently investigate interactions between two solitary waves with different directions, leading to the occurrence of important events such as rogue waves and Mach reflections. Additionally, we explore how certain parameters influence Mach stem while drawing meaningful conclusions. Our discoveries reveal the complex dynamics of internal solitary waves within the deep ocean and contribute to a broader understanding of nonlinear wave phenomena.

Internal waves generated from asymmetric topographies

Previous experimental and theoretical research on tidally generated internal waves over oceanic topography has often used symmetric topographic profiles. However, due to the complex nature of real ocean topography, the effect of asymmetry cannot be overlooked. Studies have shown that topographic complexities, including asymmetry, can have a significant impact on internal wave generation, but topographic asymmetry has not yet been explored in a systematic manner. This work presents a comparison of tidally generated internal waves from nine different two-dimensional asymmetric topographies, consisting of a steeper Gaussian curve on one side, and a wider Gaussian curve on the other. The amplitude of the wider curve varies from 60% of the steeper curve to its equivalent. Two oscillation frequencies are tested. Kinetic energy density in tidally generated internal waves on each side of the topography is compared qualitatively and quantitatively, in both physical and Fourier space. When compared to similar symmetric topographies, waves generated by the asymmetric topographies varied distinctly in both magnitude and wavenumber distribution of kinetic energy density. Waves on the relatively steep side of the topography contain up to 50% more kinetic energy than on the wider side. However, there is very little kinetic energy at the higher wavenumbers associated with the steeper topography. Instead, the internal wavefield is dominated by lower wavenumbers, 50%–90% of the kinetic energy density is contained in wavelengths corresponding to the wider side of the topography. Decreasing the amplitude of the wider curve does not make an appreciable difference in the kinetic energy density spectrum. Thus, the differences quantified here are due solely to changing slope and show the effect which relatively slight asymmetry has on internal wave generation.

Generation of diurnal internal solitary waves (ISW-D) in the Sulu Sea: From geostationary orbit satellites and numerical simulations

Our recent study reported the existence of internal solitary waves with the diurnal tidal cycle (ISW-D) in the Sulu Sea, however, the three-dimensional characteristics and generation mechanism of ISW-D are still unclear (Huang et al., 2023). In this work, the spatial–temporal characteristics, generation mechanism and propagating process of ISW-D in the Sulu Sea are first preliminary investigated based on high-temporal-resolution Geostationary Orbiting Satellite (GOS) images and high-spatial-resolution two-dimensional numerical model (MITgcm). GOS images from 2018-2022 are retrieved and a total of 13 pairs of ISW-D packets are found. ISW-D occur at spring tide during May–August, with an average interpacket distance of 198 km and a phase speed of 2.30 m/s. To further knowledge of the generation mechanism and propagation process of ISW-D, the non-linear and non-hydrostatic numerical simulations are conducted. The comparison of ISW-D parameters with GOS images proves the validity of numerical simulations. The results of numerical simulations and theoretical parameters indicate that ISW-D are generated at the sill near Pearl Bank by internal tide release mechanism. Moreover, three sensitivity experiments are designed to investigate the effects of tidal force and seawater stratification on the generation and propagation of ISW-D. The results reveal that the ISW-D is generated by diurnal tides with stronger intensity than semidiurnal tides. Seawater stratification does not influence the generation of ISW-D but modulates the propagation process. Phase speeds from GOS images and theoretical model show a positive correlation between the phase speeds of ISW-D and the intensity of seawater stratification.

Application of fluctuations in the sound field in inversion of internal solitary wave phase speed

Internal solitary waves propagation perturbing the sound velocity field, causes fluctuations in the sound field. This paper proposes to process the sound pressure data by the Product of the Slope and the even square of the Difference between two points of the acoustic parameter-time curve (PSD). The PSD processed data are processed to time-frequency analysis to extract the frequencies of the fluctuations in sound field. In this paper, numerical simulations and laboratory experiments are carried out on the process of internal solitary wave propagation in the sound field, and the characteristics of the sound field perturbation by internal solitary waves of different amplitudes are investigated. Results are both showing that the method can extract the dominant frequency of fluctuations in the sound field caused by internal solitary waves in real conditions. The method can be applied to the inversion of internal solitary wave phase speed which related to other parameters such as amplitude and characteristic width by theory. It is anticipated that this method can help realize the monitoring of internal solitary waves using acoustic paths.

Weakly nonlinear models of stochastic wave propagation in two-layer hydrodynamic systems

The paper discusses three-dimensional models of the propagation of stochastic internal waves in hydrodynamic systems: ’half-space - half-space’, ’half-space - layer with rigid lid’, and ’layer with solid bottom - layer with rigid lid’. In constructing the models, the layers are considered to be ideal fluids separated by a contact surface. The main objective of the modeling is to obtain a dynamic equation for the stochastic amplitude of surface waves. A comparative analysis of the obtained results has been conducted. In order to control the contribution of nonlinear terms, a dimensionless non-numerical parameter has been introduced. The models are distinguished by boundary conditions that determine the general form of solutions. As a result, a dynamic equation for the stochastic amplitude of internal waves has been derived. After ensemble averaging of the amplitudes, the dynamic equation is formulated in integral form using Fourier-Stieltjes integrals. The dynamic equation reveals two-wave and three-wave interactions, as well as the contribution of dispersion to wave dynamics. An investigation of the boundary case of the transition of internal waves in the ’half-space - half-space’ system to surface waves in the absence of an upper liquid layer confirms the validity of the results.

Studying the Internal Wave Generation Mechanism in the Northern South China Sea Using Numerical Simulation, Synthetic Aperture Radar, and In Situ Measurements

The internal waves in the South China Sea are highly correlated with the tidal currents in the Luzon Strait, which makes it possible to establish an internal wave prediction model based on internal wave kinematics. However, the kinematic model requires the input of the exact location and time of the initial internal wave for which the generation mechanism of internal waves in the northern South China Sea must be well understood. By analyzing the internal wave field in the northern South China Sea (SCS) simulated using the MIT General Circulation Model (MITgcm) and observations from satellite synthetic aperture radar (SAR) and mooring temperature–salinity–depth (TSD) chains, the source regions and propagation initiation times of internal waves are identified for three typical tidal phases, i.e., the diurnal-tide-dominated phase (DTP), transition tide phase (TTP), and semidiurnal-tide-dominated phase (STP). The generation procedures of Type A and Type B internal waves are discussed in detail with those data. The present study reveals that Type A and Type B waves are generated at the eastern and western ridges, respectively, and both commence their westward propagation at the peak of the eastward tidal flow. The dynamics of lee waves and the resonance effect with double ridges constitute the generation mechanisms of internal waves in the northern SCS. Combined with varying configurations of tidal conditions, topography, and stratification, the generation procedures of Type A and Type B waves in the DTP, TTP, and STP are elucidated with the generation mechanism in a unified and self-consistent way. In short, during DTP, weaker A waves alternate with weaker B waves each day; during TTP, strong A waves and strong B waves appear alternately every day; and there are two weak A waves per day during the STP. The generation mechanism can help in developing future empirical models for generating internal waves using tidal currents, topography, and stratification without requiring complex fluid dynamics calculations.

Observation of vertical coupling during a major sudden stratospheric warming by ICON and GOLD: a case study of the 2020/2021 warming event

The response of the thermospheric daytime longitudinally averaged zonal and meridional winds and neutral temperature to the 2020/2021 major sudden stratospheric warming (SSW) is studied at low-to middle latitudes (0◦ - 40◦N) using observations by NASA’s ICON and GOLD satellites. The major SSW commenced on 1 January 2021 and lasted for several days. Results are compared with the non-SSW winter of 2019/2020 and pre-SSW period of December 2020. Major changes in winds and temperature are observed during the SSW. The northward and westward winds are enhanced in the thermosphere especially above ∼140 km during the warming event, while temperature around 150 km drops up to 50 K compared to the pre-SSW phase. Changes in the zonal and meridional winds are likely caused by the SSW-induced changes in the propagation and dissipation conditions of internal atmospheric waves. Changes in the horizontal circulation during the SSW can generate upwelling at low-latitudes, which can contribute to the adiabatic cooling of the low-latitude thermosphere. The observed changes during the major SSW are a manifestation of long-range vertical coupling in the atmosphere.

Kelvin Wave Propagation over a Sloping Interface and Relationships with El Niño Southern Oscillation

Internal Kelvin Wave (KW) propagation is studied about variations in the sea surface temperature anomaly (SSTA) over the tropical Pacific. Temperature and Salinity (TS) observations have been used to define the vertical structure of the ocean about the propagation properties of KWs. Changes in the vertical structure of the water column determine consistent zonal variations in the wave velocity, with values varying, roughly, from 1.8 to 2.6 m/s. The authors document that KWs are formed regularly at the western boundary of the tropical Pacific, but, in these cases, never overcome the dateline. Occasionally, KWs are generated in the region comprised between 170oE and 170oW, and, on all these occasions, a positive phase of the El Niño Southern Oscillation (El Niño) event is recorded. A model, named Sloping Interface Model (SIM), is proposed to relate changes in the pycnocline depth, associated with transiting KWs, and SST anomaly variations. In the SIM, whose equations are consistent with the Recharge/Discharge paradigm, the ocean is described as a two-layer system and the climatological state, represented by a sloping pycnocline, is maintained by a constant easterly wind stress. Using the SIM and coherently with the Recharge/Discharge paradigm, the authors show that changes in the averaged SSTA over El Niño 3, 3.4 and 4 regions are nearly perfectly correlated to pycnocline displacements due to transiting KWs.