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An exceptionally strong westward propagating quasi‐6‐day wave (Q6DW) with zonal wavenumber 1 in connection with the rare 2019 Southern Hemispheric Sudden Stratospheric Warming (SSW) is observed by two meteor radars at 30°S and is found to modulate and interact with the diurnal tide and gravity waves (GWs). The diurnal tide is amplified every 6 days and a prominent 21 hr child wave attributed to Q6DW‐diurnal tide nonlinear interaction occurs. Q6DW modulation on GWs is confirmed as the 4–5 day periodicity in GW variances. Simultaneously, the Q6DW appears to shift its period toward the periodicity of the modulated GW variances. Enhancement is also observed in the first results of meteor radar observed Q6DW Eliassen‐Palm flux, which may facilitate the global perturbation and persistence of this Q6DW. We conclude that the observed SSW triggered Q6DW‐tide and Q6DW‐GW interactions play an important role in coupling the lower atmospheric forcings to ionospheric variabilities. Plain Language Summary: Our work provides observational evidence for the 6‐day planetary wave‐tide and 6‐day planetary wave‐gravity wave interactions at the Earth's mesosphere and lower thermosphere. The results strongly support the theory that wave‐wave interactions are the primary mechanism coupling planetary waves to ionospheric variability and provide an additional mechanism as the 6‐day wave modulation on the gravity waves. We utilize measurements from two meteor radars to diagnose planetary wave characteristics and identify wave‐wave interactions, and compute the first‐time meteor radar observed Eliassen‐Palm flux. Enhancement is observed in the Eliassen‐Palm flux of 6‐day wave following the SSW maximum phase, which demonstrates that energy of the 6‐day wave is enhanced and therefore, facilitates the global perturbation and persistence of the 6‐day wave for an extended time period. While meteor radar observations are widely used to investigate planetary waves and tides, high meteor detection rate is required for further studying temperature perturbations and small scale waves (e.g., gravity waves). Thus, this work also highlights the capability of a modern multi‐static meteor radar system, Chilean Observation Network De meteOr Radars, in resolving oscillations of small spatial scales over a broad range of periods, and for calculating Eliassen‐Palm flux of planetary waves. Key Points: A dominating W1 Q6DW is observed at 30°S and its Eliassen‐Palm flux is enhanced during the 2019 SH SSWQ6DW amplifies the diurnal tide every 6 days and a strong 21 hr child wave is observedQ6DW modulates the gravity wave variances and its frequency appears to shift accordingly [ABSTRACT FROM AUTHOR]

A second-order numerical wave-maker is realized by combining the paddle wave-maker theory proposed by Schäffer for physical experiments with the Fluent software. The numerical results from the paddle wave-maker method are compared with the results from the modified mass source wave-maker method, the theoretical solutions, and the physical experimental data. The numerical model based on the paddle wave-maker method is verified, and the applicable scopes of the two wave-maker methods are discussed. The paddle wave-maker method is not suitable for bichromatic wave combinations that include shallow-water waves. However, within their common applicable range, the numerical results from the paddle wave-maker method are better than those from the modified mass source wave-maker method, at least for the grid divisions adopted in this study. The effects of the incident wave parameters on the nonlinear wave-wave interaction are also analyzed. [ABSTRACT FROM AUTHOR]

Abstract It is now established that the primary microseism, the secondary microseisms, and the hum are the three main components of seismic noise in the frequency band from about 0.003 Hz to 1.0 Hz. Monthly averages of seismic noise are dominated by these signals in seismic noise. There are, however, some temporary additional signals in the same frequency band, such as signals from tropical cyclones (hurricanes and typhoons) in the ocean and on land, stormquakes, weather bombs, tornadoes, and wind-related atmospheric pressure loading. We review these effects, lasting only from a few hours to a week but are significant signals. We also attempt to classify all seismic noise. We point out that there are two broad types of seismic noise, the propagating seismic waves and the quasi-static deformations. The latter type is observed only for surface pressure changes at close distances. It has been known since about 1970 but has not been emphasized in recent literature. Recent data based on co-located pressure and seismic instruments clearly show its existence. Because the number of phenomena in the first type is large, we propose to classify all seismic noise into three categories: (1) propagating seismic waves from ocean sources, (2) propagating seismic waves from on-land sources, and (3) quasi-static deformation at ocean bottom and on land. The microseisms and the hum are in the first category although there are differences in the detailed processes of their excitation mechanisms. We will also classify temporary signals by these categories.

In a SAR image acquired by the ERS-2 satellite, crossed "X-shape" internal solitary waves (ISWs) south to Dongsha Island are found to be a wave–wave interaction composed of five solitons: two head waves, two tail waves, and the overlapped part. To explain this remote sensing phenomenon, based on a high-resolution three-dimensional MIT general circulation model (MITgcm) using realistic topography and tidal forcing, the "X-shape" internal waves are reproduced at the same location. The development processes of the waves indicate that the "X-shape" ISWs are two waves diffracted from one internal wave southeast to Dongsha Island. During the propagation, the amplitude of their overlapped part of the "X-shape" ISWs becomes significantly larger than the sum of the amplitudes of both head waves, which proves that nonlinear wave–wave interaction has occurred. Based on wave–wave interaction theory, the theoretical maximum value of the amplitude of the overlapped part at the initial moment is calculated as 14.12 m, which is in good agreement with the model results of 14 m. Meanwhile, the variation of the theoretical amplitude of the overlapped part is basically consistent with that of the modeled one, confirming the occurrence of the wave–wave interaction. Besides, when the waves propagate over varying water depths, the type of the wave–wave interaction can change rather than being fixed from the start. [ABSTRACT FROM AUTHOR]

It is now established that the primary microseism, the secondary microseisms, and the hum are the three main components of seismic noise in the frequency band from about 0.003 Hz to 1.0 Hz. Monthly averages of seismic noise are dominated by these signals in seismic noise. There are, however, some temporary additional signals in the same frequency band, such as signals from tropical cyclones (hurricanes and typhoons) in the ocean and on land, stormquakes, weather bombs, tornadoes, and wind-related atmospheric pressure loading. We review these effects, lasting only from a few hours to a week but are significant signals. We also attempt to classify all seismic noise. We point out that there are two broad types of seismic noise, the propagating seismic waves and the quasi-static deformations. The latter type is observed only for surface pressure changes at close distances. It has been known since about 1970 but has not been emphasized in recent literature. Recent data based on co-located pressure and seismic instruments clearly show its existence. Because the number of phenomena in the first type is large, we propose to classify all seismic noise into three categories: (1) propagating seismic waves from ocean sources, (2) propagating seismic waves from on-land sources, and (3) quasi-static deformation at ocean bottom and on land. The microseisms and the hum are in the first category although there are differences in the detailed processes of their excitation mechanisms. We will also classify temporary signals by these categories. [ABSTRACT FROM AUTHOR]

The stability of waves in deep water has classically been approached via linear stability analysis, with various model equations, such as the nonlinear Schrödinger equation, serving as points of departure. Some of the most well-studied instabilities involve the interaction of four waves – so called Type I instabilities – or five waves – Type II instabilities. A unified description of four and five wave interaction can be provided by the reduced Hamiltonian derived by Krasitskii (1994). Exploiting additional conservation laws, the discretised Hamiltonian may be used to shed light on these four and five wave instabilities without restrictions on spectral bandwidth. We derive equivalent autonomous, planar dynamical systems which allow for straightforward insight into the emergence of instability and the long time dynamics. They also yield new steady-state solutions, as well as discrete breathers associated with heteroclinic orbits in the phase space. [ABSTRACT FROM AUTHOR]

Internal solitary waves (ISWs) are nonlinear fluctuations in nature that could cause significant interactions between seawater and the seabed. ISWs have been proven to be an adequate cause of sediment resuspension in shallow and deep-sea environments. In the South China Sea, ISWs have the largest amplitude globally and directly interact with the seabed near the Dongsha slope in the northern South China Sea. We analyzed the water profile and high-resolution multibeam bathymetric data near the Dongsha slope and revealed that submarine trenches have a significant impact on the sediment resuspension by ISWs. Moreover, ISWs in the zone of the wave-wave interaction enhanced sediment mixing and resuspension. The concentration of the suspended particulate matter inside submarine trenches was significantly higher than that outside them. The concentration of the suspended particulate matter near the bottoms of trenches could be double that outside them and formed a vast bottom nepheloid layer. Trenches could increase the concentration of the suspended particulate matter in the entire water column, and a water column with a high concentration of the suspended particulate matter was formed above the trench. ISWs in the wave-wave interaction zone near Dongsha could induce twice the concentration of the bottom nepheloid layer than those in other areas. The sediment resuspension caused by ISWs is a widespread occurrence all around the world. The findings of this study can offer new insights into the influence of submarine trench and wave-wave interaction on sediment resuspension and help in geohazard assessment. [ABSTRACT FROM AUTHOR]

This work presents a theoretical discussion and experimental results about the directional bound waves generated by second-order nonlinear interaction between two noncollinear wave trains. Research focus is set on presence, characteristics, and effects of the angle difference between the primary wave trains on the generation of super- and subharmonic bound wave components as well as propagation direction, orbital velocity, and the resulting radiation stress field. An analytical model is derived, and computations thereof conducted for different conditions of wave height, period, and depth. Laboratory tests, systematically conducted in a wave basin, confirm computational results from analytical formulation and indicate that (i) the magnitude of all second-order properties (setup and setdown of the mean water level, orbital velocities) are strongly dependent on the individual combination of periods and directions of the primary wave trains, (ii) the direction of the bound wave differs from those of the primary waves, and (iii) the radiation stress components show a spatial and temporal oscillatory pattern outside the surf zone. [ABSTRACT FROM AUTHOR]

Internal solitary wave (ISW) occurs in the stratified ocean can cause severe damage on the structures. Moreover, the interaction between these waves can noticeably influence the characteristics of their propagation. This study investigates the frontal collision process between two elevation-type ISWs using a numerical model of wave-wave interaction in stratified fluids, based on the multi-domain boundary element method (MDBEM). The analysis of collision characteristics, such as maximum runup, residence time, and phase shifting, is conducted based on the calculation results. It is observed that the maximum runup during the collision of two waves exceeds the linear superposition of initial amplitudes due to nonlinear effects. The role of nonlinear effects becomes more prominent with increasing initial amplitudes. As the initial wave amplitudes increase, the residence time of ISWs during collision decreases. The residence of ISWs leads to phase shifting, which becomes apparent after the collision. The final constant value of phase shifting increases with the initial wave amplitude, and the rate of increase is slower for larger initial amplitudes. Additionally, phase shifting is more obvious when there is a larger depth ratio of the upper and lower-layer fluids. [ABSTRACT FROM AUTHOR]

Here we have investigated the possibility of an inertio-acoustic wave-mode to be unstable with regards to gravity mode perturbations through non-linear triad interactions in the context of a shallow non-hydrostatic model. We have considered highly truncated Galerkin expansions of the perturbations around a resting, hydrostatic and isothermal background state in terms of the eigensolutions of the linear problem. For a single interacting wave triplet, we have shown that an acoustic mode cannot amplify a pair of inertio-gravity perturbations due to the high mismatch among the eigenfrequencies of the three interacting wave-modes, which requires an unrealistically high amplitude of the acoustic mode in order for pump wave instability to occur. In contrast, it has been demonstrated by analysing the dynamics of two triads coupled by a single mode that a non-hydrostatic gravity wave-mode participating in a nearly resonant interaction with two acoustic modes can be unstable to small amplitude perturbations associated with a pair of two hydrostatically balanced inertio-gravity wave-modes. This linear instability yields significant inter-triad energy exchanges if the nonlinearity associated with the second triplet containing the two hydrostatically balanced inertio-gravity modes is restored. Therefore, this inter-triad energy exchanges lead the acoustic modes to yield significant energy modulations in hydrostatic inertio-gravity wave modes. Consequently, our theory suggests that acoustic waves might play an important role in the transient phase of the three-dimensional adjustment process of the atmosphere to both hydrostatic and geostrophic balances.

The nature and origins of longitudinal density structures in Mars’ thermosphere between 100 and 120 km altitude, and −30° and −75° latitude around winter solstice (Ls = 70–122°), as measured by the accelerometer on the ExoMars Trace Gas Orbiter (TGO) Mission, are investigated. The methodology consists of deducing the responsible waves by comparing the observed longitude versus local time phase progressions of the structures with those of probable candidate waves in the Mars Climate Database (MCD) climatology. The observed wave‐1, wave‐2, and wave‐3 structures are interpreted as originating mainly from SPW1; (SPW2, S0, DE1); and (SPW3, DE2), respectively, where SPWm denotes a stationary planetary wave with zonal wavenumber s = m, S0 is the zonally symmetric semidiurnal tide, and DE1(DE2) are the eastward‐propagating diurnal tides with s = −1(−2). All of these waves exist in the MCD with amplitudes as large as those observed, although not wholly in the narrow height‐latitude regime accessed by TGO. This disparity between the MCD and TGO amplitude structures is hypothesized to result from the extreme intrusion of the polar‐region eastward winter jet into the thermosphere in the MCD. The winter polar jet blocks poleward expansion of DE1 and DE2 beyond −30° latitude, and also impacts the structures of SPW2, S0 and SPW3 that arise from in situ nonlinear interaction between DE1 and DE2, respectively, with the diurnal migrating tide (DW1).Key Points: Longitudinal density structures measured by Mars TGO accelerometer are interpreted with insights provided by Mars Climate Database (MCD)Stationary planetary waves, some excited by in situ wave‐wave interactions, play a prominent role in explaining the density structuresThe MCD‐TGO comparison suggests that the intensity and vertical‐latitudinal extent of the winter polar jet may be overestimated in the MCD [ABSTRACT FROM AUTHOR]

Here we have investigated the possibility of an inertio-acoustic wave-mode to be unstable with regards to gravity mode perturbations through non-linear triad interactions in the context of a shallow non-hydrostatic model. We have considered highly truncated Galerkin expansions of the perturbations around a resting, hydrostatic and isothermal background state in terms of the eigensolutions of the linear problem. For a single interacting wave triplet, we have shown that an acoustic mode cannot amplify a pair of inertio-gravity perturbations due to the high mismatch among the eigenfrequencies of the three interacting wave-modes, which requires an unrealistically high amplitude of the acoustic mode in order for pump wave instability to occur. In contrast, it has been demonstrated by analysing the dynamics of two triads coupled by a single mode that a non-hydrostatic gravity wave-mode participating in a nearly resonant interaction with two acoustic modes can be unstable to small amplitude perturbations associated with a pair of two hydrostatically balanced inertio-gravity wave-modes. This linear instability yields significant inter-triad energy exchanges if the nonlinearity associated with the second triplet containing the two hydrostatically balanced inertio-gravity modes is restored. Therefore, this inter-triad energy exchanges lead the acoustic modes to yield significant energy modulations in hydrostatic inertio-gravity wave modes. Consequently, our theory suggests that acoustic waves might play an important role in the transient phase of the three-dimensional adjustment process of the atmosphere to both hydrostatic and geostrophic balances. [ABSTRACT FROM AUTHOR]

Electron cyclotron harmonic (ECH) waves play an important role in the magnetosphere‐ionosphere coupling. They are usually considered to be generated by the Bernstein‐mode instability with electron loss cone distributions. By analyzing the Van Allen Probes wave data, we present the direct evidence of the nonlinear interactions between ECH waves in the magnetosphere. Substorm‐injected electrons excite primary ECH waves in a series of structureless bands between multiples of the electron gyrofrequency. Nonlinear interactions between the primary ECH waves produce secondary waves at sum‐ and difference‐frequencies of the primary waves. Our results suggest that the nonlinear wave‐wave interactions can redistribute the primary ECH wave energy over a broader frequency range and hence potentially affect the magnetospheric electrons over a broader range of pitch angles and energies. Plain Language Summary: Electron cyclotron harmonic (ECH) waves significantly contribute to the magnetosphere‐ionosphere coupling via resonating with hot electrons. The resonance effect strongly depends on the wave frequency distributions. Both theoretical studies and laboratory experiments made the point that nonlinear wave‐wave interactions can contribute to the frequency spectrum broadening of ECH waves. However, whether such nonlinear interactions occur in the magnetospheric plasma environment remains to be investigated. In this letter, we present, for the first time, the direct evidence of the nonlinear interactions between magnetospheric ECH waves. The nonlinear wave‐wave interactions redistribute the primary ECH wave energy over a broader frequency range. Hence, these waves are expected to have the ability to resonate with the electrons over a broader range of pitch angles and energies. Key Points: We present the direct evidence of the nonlinear interactions between electron cyclotron harmonic (ECH) waves in the magnetospherePrimary ECH waves are generated by the Bernstein‐mode instability of substorm‐injected electronsSum‐ and difference‐frequency interactions between the primary ECH waves can redistribute wave energy over a broader frequency range [ABSTRACT FROM AUTHOR]

By adopting a 2D time-dependent wave code, we investigate how mode-converted waves at the Ion-Ion Hybrid (IIH) resonance and compressional waves propagate in 2D density structures with a wide range of field-aligned wavenumbers to background magnetic fields. The simulation results show that the mode-converted waves have continuous bands across the field line consistent with previous numerical studies. These waves also have harmonic structures in frequency domain and are localized in the field-aligned heavy ion density well. Our results thus emphasize the importance of a field-aligned heavy ion density structure for ultra-low frequency wave propagation, and suggest that IIH waves can be localized in different locations along the field line.

Abstract: Oblique whistler mode waves have been suggested to play an important role in radiation belt electron dynamics. Recently, X. Fu et al. (2017, https://doi.org/10.1002/2017GL074411) proposed that highly oblique lower band whistler waves could be generated by nonlinear three‐wave resonance. Here we present the first observational evidence of such process, using Van Allen Probes data, where an oblique lower band chorus wave is generated by two quasi‐parallel waves through nonlinear three‐wave interaction. The wave resonance condition is satisfied even in the presence of frequency chirping of one of the pump waves. Different from the simulation results of X. Fu et al. (2017), simultaneous particle data do not show a plateau in the electron distribution, which could be due to the very weak intensity of the generated waves. These results should help to better understand the generation of oblique waves in the inner magnetosphere and their relative roles in energetic electron dynamics. [ABSTRACT FROM AUTHOR]

Magnetic power spectrum and formation of coherent structures have been investigated in the present work applicable to Van Allen radiation belt. The nonlinear interaction of high frequency oblique whistler wave and low frequency magnetosonic wave has been investigated. Simulation was performed of the coupled equation of these two waves. The nonlinear interaction of these waves leads to the formation of the localized structures. These resulting localized structures are of complex nature. The associated magnetic power spectrum has also been studied. Dispersive nonlinear processes account for the high frequency part of the spectrum. The resulting magnetic power spectrum shows a scaling of $k^{ - 4.5}$ . The energy transfer process from injection scales to smaller scales is explained by the results. [ABSTRACT FROM AUTHOR]

ABSTRACT The interannual variability of Indian summer monsoon rainfall ( ISMR) is largely dictated by the continental tropical convergence zone ( CTCZ), characterized by the frequent cyclogenetic tendency associated with the transitory low pressure systems ( LPS(s) or monsoon transients) such as lows, depressions, cyclonic storms etc. A good monsoon is characterized by more intense and sustainable transients having longer westward propagation in comparison with the LPS(s) during weak monsoon. Now the questions arise from the energetics aspects - how does the energy favour the CTCZ to be more cyclogenetic during the good monsoon years? From where the monsoon transients are gaining energy to intensify and to sustain for longer durations during good monsoons compared with those in weak monsoons? The non-linear scale interactions may possibly be the dynamical reason for the intensification and maintenance of LPS(s), but, the quantification of non-linear interactions among the seasonal mean, low frequency oscillations, and synoptic scales are not revealed so far in previous studies. First time, the scale interactive energy exchanges in frequency domain have been explored to unravel the causes of weak LPS(s) during droughts vis-à-vis good monsoon years. It may be inferred from this study that the seasonal mean may play a crucial role for the generation of low and high frequency oscillations through mean-wave interaction whereas the wave-wave interactions have a significant contribution in intensification as well as the maintenance of monsoon transients. The dominant transfer of kinetic energy from the low frequency oscillations to synoptic scale observed over the large region of CTCZ favours the synoptic systems to intensify, survive for longer duration over that region before dissipation causing CTCZ to be more cyclogenetic during the good monsoon period with respect to those in weak monsoons attributing to the rainfall variability over the Indian landmass in contrasting monsoon seasons. [ABSTRACT FROM AUTHOR]

Modeling natural roll waves in unstable open channel flows where Froude number has not been well understood. In this investigation, some evolution properties of natural roll waves are numerically disclosed, with the intention to advance the development of modeling unstable open channel flows. To simulate natural roll waves, the diffusive Saint-Venant equations are solved using a high-resolution scheme based on the finite-volume formulation. The numerical solutions of detailed wave-wave interaction processes, including wave overtaking, absorption, and spawning, are displayed. Wave overtaking and absorption result in the coalescence of multiple waves; wave spawning results in the birth of new waves. The spatial evolution of roll waves always undergoes initial, transition, and final phases. The three phases constitute a generality for roll-wave evolutions. Finally, the spectral analysis along channel reveals that both the wave period and nonperiodicity increase from upstream to downstream channel locations. [ABSTRACT FROM AUTHOR]

Abstract: Characteristics of the quasi-two-day wave (QTDW) have been investigated during late summer of 2005, 2006 and 2007 using meteor wind observations over Santa Maria (29.7°S, 53.7°W), Brazil. Significant inter-annual variability is evident in the derived wave parameters. Maximum wave amplitude is found to be 18 and 42m/s for zonal and meridional wind, respectively. Mean vertical wavelength shows the values of ∼62 and 74km for zonal and meridional components, respectively. In general high QTDW amplitude is observed when diurnal tide amplitude is lower suggesting strong wave-tide interaction and enhancement of the QTDW at the expense of the diurnal tide energy. Furthermore, the amplitude of the QTDW reveals a clear modulation of 7–8 days periodicity suggesting nonlinear interaction among planetary waves and a probable reason for the observed QTDW variability. Comparison of the present site with the other two Brazilian low latitude sites reveals overall latitudinal invariance except during a few local and/or transient events. There is an indication of wave ducting in the mesosphere and lower thermosphere through which the QTDW can extend latitudinally. Although the response of the QTDW to the mean background wind sometimes exhibits meridional (northward) acceleration, there is no evident signature in the zonal background wind. Both mechanisms suggested so far for exciting the QTDW, i.e. (i) baroclinic/barotropic instability and (ii) Rossby-gravity normal modes are found to be consistent with the present findings. [Copyright &y& Elsevier]

Abstract: This paper presents the global spatial (latitude and altitude) structure and temporal variability of the ∼23-day ionospheric zonally symmetric (s =0) planetary wave (PW) seen in the Northern winter of 2008/2009 (October 2008–March 2009). It is shown that these ∼23-day ionospheric oscillations are forced from PWs propagating from below. The COSMIC ionospheric parameters foF2 and hmF2 and electron density at fixed altitudes and the SABER temperatures were utilized in order to define the waves which are present simultaneously in the atmosphere and ionosphere. The long-period PWs from the two data sets have been extracted through the same data analysis method. The similarity between the lower thermospheric ∼23-day (s =0) temperature PW and its ionospheric electron density response provides valuable and strong experimental evidence for confirming the paradigm of atmosphere–ionosphere coupling. [Copyright &y& Elsevier]

Based on the atmospheric circulation data provided by ECMWF and the sea surface temperature data by NOAA, we studied the mechanism for the impact of sea surface temperature anomaly on the ridgeline surface of western Pacific using an improved high truncated spectral model. Our results show that the wave-wave interaction and the wave-mean flow interactions are weaker in the inner dynamic process of atmospheric circulation, when atmospheric circulation is forced by the sea surface temperature of El Niño pattern. With the external thermal forcing changed from winter to summer pattern, the range of ridgeline surface of western Pacific moving northward is smaller, which causes the ridgeline surface of western Pacific on south of normal. On the contrary, the wave-wave interaction and the wave-mean flow interaction are stronger, when atmospheric circulation is forced by the sea surface temperature of La Niña pattern. With the external thermal forcing turning from winter to summer pattern, the ridgeline surface of western Pacific shifts northward about 19 latitude degrees, which conduces the ridgeline surface of western Pacific on north of normal. After moving to certain latitude, the ridgeline surface of western Pacific oscillates with the most obvious 30–60 d period and the 4°–7° amplitude. It is one of the important reasons for the interannual variation of ridgeline surface of Western Pacific that the atmospheric inner dynamical process forced out by different sea surface temperature anomaly pattern is different. [ABSTRACT FROM AUTHOR]

Abstract: This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments. [Copyright &y& Elsevier]

Abstract: Data of neutral meridional wind obtained by the meteor radar at Esrange and data of temperature and pressure measured by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument on board the Thermosphere–Ionosphere–Mesosphere Energetics and Dynamics (TIMED) spacecraft were studied with respect to a day-to-day atmospheric variability with periods ranging from 1.5 to 5 days. The detailed analysis was carried out for February 2004. Perturbations of the atmospheric parameters at the examined periods appeared mainly as eastward-propagating waves of zonal wavenumbers 1 and 2. We suggested that these waves excited by the jet instability on both flanks of the polar-night jet in the upper stratosphere and mesosphere interact nonlinearly with each other, and this interaction generates secondary waves. The radar observed both primary and secondary waves at mesospheric heights. The data analysis supports this suggestion. Under conditions of weaker instability observed in February 2003 the perturbations of atmospheric parameters of periods ranging from 1.5 to 5 days had smaller amplitudes at heights of the mesosphere than those in February 2004. It was found that the Eliassen-Palm fluxes calculated for the waves generated by the jet instability were mainly downward directed. This result suggests a possible dynamical influence of the mesospheric layers on the lower atmospheric levels. [Copyright &y& Elsevier]

Abstract: In this paper, a superposition of two periodic wave profiles in a finite water depth was investigated. This paper is focused on the improvement of a wave profile on the linear superposition of two waves. This improvement was realized by introducing an iterative method, which was based on a fixed point approach. Application of the fixed point approach to the wave superposition made it possible to obtain a wave profile of wave–wave interaction. The improved result of the wave profile was in good agreement with that of the nonlinear perturbation solution of the second order. It was interesting that the improved result revealed the higher-order nonlinear frequencies for two interacting Stokes waves while Dalzell''s solution by a perturbation method could not predict them. [Copyright &y& Elsevier]

Based on the potential flow theory of water waves, the interaction mechanism between the free-surface and internal waves generated by a moving point source in the lower layer of a two-layer fluid was studied. By virtue of the method of Green's function, the properties of the divergence field at the free surface were obtained, which plays an important role in the SAR (Synthetic Aperture Radar) image. It is shown that the coupling interaction between the surface-wave mode and internal-wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr2. The theoretical analysis is qualitatively consistent with the experimental results presented by Ma Hui-yang. [ABSTRACT FROM AUTHOR]

This paper investigates nonlinear wave–wave interactions in a system that describes a modified decay instability and consists of three Langmuir and one ion-sound waves. As a means to establish that the underlying dynamics exists in a 3D space and that it is of the Lorenz-type, both continuous and discrete-time multivariable global models were obtained from data. These data were obtained from a 10D dynamical system that describes the modified decay instability obtained from Zakharov’s equations which characterise Langmuir turbulence. This 10D model is equivariant under a continuous rotation symmetry and a discrete order-2 rotation symmetry. When the continuous rotation symmetry is modded out, that is, when the dynamics are represented with the continuous rotation symmetry removed under a local diffeomorphism, it is shown that a 3D system may describe the underlying dynamics. For certain parameter values, the models, obtained using global modelling techniques from three time series from the 10D dynamics with the continuous rotation symmetry modded out, generate attractors which are topologically equivalent. These models can be simulated easily and, due to their simplicity, are amenable for analysis of the original dynamics after symmetries have been modded out. Moreover, it is shown that all of these attractors are topologically equivalent to an attractor generated by the well-known Lorenz system. [Copyright &y& Elsevier]

A generalization of the Woodward''s theorem is applied to the case of random signals jointly modulated in amplitude and frequency. This yields the signal spectrum and a rather robust estimate of the bispectrum. Furthermore, higher order statistics that quantify the amount of energy in the signal due to nonlinearities, e.g., wave–wave interaction in the case of water waves, can be inferred. Considering laboratory wind generated water waves, comparisons between the presented generalization and more standard techniques allow to extract the spectral energy due to nonlinear wave–wave interactions. It is shown that our analysis extends the domain of standard spectral estimation techniques from narrow-band to broad-band processes. To cite this article: T. Elfouhaily et al., C. R. Mecanique 331 (2003). [Copyright &y& Elsevier]

The vertical and horizontal propagation of internal gravity waves forced by a local thermal source at the lower boundary is examined using the irrotational two-dimensional model developed by Zhang et al. (1995). The source generates waves with the same absolute frequency 1/15 d but different wavenumber. Internal gravity waves with wide spreading frequencies and wavenumbers appear due to wave-wave interactions. The foreced waves 1W (westward-propagating with wavenumber 1) and 1E (eastward-propagating with wavenumber 1), whose absolute phase speeds are 31 m s, are predominant. Other forced waves with smaller phase speeds are relatively weaker. These waves interact with the zonal mean flow, causing the flow to alternate with easterly and westerly with a 32-month period. The absolute maximum wind speeds of easterly and westerly are 35 m s which is larger than the largest phase speed of forced waves. The forced waves 1E and 1W may accelerate easterly and westerly up to ±31 m s, respectively. The excessive accelerations are due to the self-acceleration of waves 1E and 1W or newly generated high frequency waves 1E and 1W. The horizontal propagation of the waves are mainly affected by the forcing and wave-flow interactions which lead to fast-slow variations of wave phase speed and amplitude. [ABSTRACT FROM AUTHOR]

Physical oceanography is increasingly relying on satellite remote sensing to survey the perpetually undersampled ocean, whereas the latest Synthetic Aperture Radars (SARs) are moving forward to provide a more continuous monitoring of the ocean. In this study we use a collection of SAR images to document the two-dimensional horizontal structure of Internal Solitary Waves (ISWs) propagating between two large submarine canyons off the Western Iberian Peninsula (between May and October 2018), which are observed to intersect approximately along the mid-shelf and originate a naturally-occurring interaction hotspot between different ISW packets. ISW interactions are well documented in theory and in laboratorial and numerical studies, but their observations in the real ocean are limited to airborne observations over the Strait of Georgia. The frequent SAR imagery of interacting ISWs in this region provides additional case studies to the literature, and we investigate if an energy proxy taken from their sea surface signatures can be used as an indicator for high-energy interaction events (e.g. when comparing with a non-interacting background). In particular, a quasi-synergetic event captured both in SAR and in a moored thermistor chain reveals that the often used weakly nonlinear theory for small-amplitude waves may underestimate the amplitudes measured in the waves' interacting sections. ISWs provide the largest vertical displacements and velocities in the ocean. Understating how their vertical structure changes during wave-wave interactions may have important implications in the broader spectrum of ocean sciences, and SARs are shown in this study to be a first-approach tool to survey this frequent phenomenon in coastal regions. • SAR images document the internal solitary waves propagating between two canyons off the Iberian Peninsula. • The internal solitary waves intersect along the mid-shelf and originate a naturally-occurring interaction hotspot. • Weakly nonlinear theory for internal solitary waves may underestimate the amplitudes measured during interacting. • Understating wave-wave interactions may have important implications in the broader spectrum of ocean sciences. • SARs are shown in this study to be a first-approach tool to survey this frequent phenomenon in coastal regions. [ABSTRACT FROM AUTHOR]

Surface water waves is an important research topic in coastal and ocean engineering due to its influences on various human activities. In this study, our purpose is to gain a deeper insight on the effects of non-hydrostatic (NHS) pressure on surface wave motions and its role in numerical modeling, based upon the high-order NHS model and optional vertical accelerations. The relative contribution of non-hydrostatic effects (Pnhs/Phs) and its sensitivity on phase celerity and amplitude of dispersive waves are quantified. The vertical structure of Pnhs/Phs clearly indicates stronger NHS effects in deeper waters and its significance near the surface. The NHS effects mainly slow down wave celerity and maintain incident amplitude for linear dispersive waves. The NHS effects are also responsible for increased amplitude and phase speed under strong non-linearity. The inter-relation between (un)realistic physical responses and model errors is discussed. Further, four experimental conditions for waves with complicated interactions are examined. Overall, the NHS effects play a critical role in side-band generation of bi-chromatic waves, and increased celerity and amplitude during nonlinear shoaling, as well as velocity moderation under co-existence of depth-varying currents. Possibly owing to weaker wave–wave interactions, however, wave directionality does not strongly interfere with FNHS/QNHS (Fully/Quasi Non-HydroStatic) effects on a fast-modulated nonlinear evolution of spatial focusing or diffraction waves. [ABSTRACT FROM AUTHOR]