Articles | Volume 24, issue 4
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Brief communication: Multiscaled solitary waves
Oleg G. Derzho
Institute of Thermophysics, Russian Academy of Sciences, Novosibirsk, Russia
Related subject area
Subject: Nonlinear Waves, Pattern Formation, Turbulence | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphereParticle clustering and subclustering as a proxy for mixing in geophysical flowsExplosive instability due to flow over a rippled bottomInternal waves in marginally stable abyssal stratified flowsOn the phase dependence of the soliton collisions in the Dyachenko–Zakharov envelope equationLaboratory and numerical experiments on stem waves due to monochromatic waves along a vertical wallExceedance frequency of appearance of the extreme internal waves in the World OceanThe evolution of mode-2 internal solitary waves modulated by background shear currentsConnection between encounter volume and diffusivity in geophysical flowsMulti-scale phenomena of rotation-modified mode-2 internal wavesBrief communication: A nonlinear self-similar solution to barotropic flow over varying topographyOn the interaction of short linear internal waves with internal solitary wavesHead-on collision of internal waves with trapped coresAnalytic solutions for Long's equation and its generalizationKinematic parameters of internal waves of the second mode in the South China SeaBalanced source terms for wave generation within the Hasselmann equationModeling the dynamical sinking of biogenic particles in oceanic flowA simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortexOcean swell within the kinetic equation for water wavesLagrange form of the nonlinear Schrödinger equation for low-vorticity waves in deep waterTrajectory encounter volume as a diagnostic of mixing potential in fluid flowsSubharmonic resonant excitation of edge waves by breaking surface wavesStatistical analysis of Lagrangian transport of subtropical waters in the Japan Sea based on AVISO altimetry dataThe fully nonlinear stratified geostrophic adjustment problemVariational modelling of extreme waves through oblique interaction of solitary waves: application to Mach reflectionLaboratory experimental investigation of heat transport in fractured mediaParametric resonance in the dynamics of an elliptic vortex in a periodically strained environmentLocalized coherence of freak wavesIntermittent heat instabilities in an air plumeLimiting amplitudes of fully nonlinear interfacial tides and solitonsOcean–atmosphere–wave characterisation of a wind jet (Ebro shelf, NW Mediterranean Sea)Theoretical comparison of subgrid turbulence in atmospheric and oceanic quasi-geostrophic modelsDual-plane PIV investigation of acoustically excited jets in a swirl nozzleStudy of the overturning length scales at the Spanish planetary boundary layerComplex environmental β-plane turbulence: laboratory experiments with altimetric imaging velocimetrySteep unidirectional wave groups – fully nonlinear simulations vs. experimentsA dynamical systems approach to the surface search for debris associated with the disappearance of flight MH370Intermittent particle dynamics in marine coastal watersA method to calculate finite-time Lyapunov exponents for inertial particles in incompressible flowsDirect numerical simulation of intermittent turbulence under stably stratified conditionsThe evolution of mode-2 nonlinear internal waves over the northern Heng-Chun Ridge south of TaiwanDynamics of turbulence under the effect of stratification and internal wavesAn analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional currentTwo-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China SeaIncidence and reflection of internal waves and wave-induced currents at a jump in buoyancy frequencyTime-dependent Long's equationPropagation regimes of interfacial solitary waves in a three-layer fluidLarge eddy simulation of sediment transport over rippled bedsEffective coastal boundary conditions for tsunami wave run-up over sloping bathymetryOn quartet interactions in the California Current system
Rishiraj Chakraborty, Aaron Coutino, and Marek Stastna
Nonlin. Processes Geophys., 26, 307–324,Short summary
In this paper, we highlight a specific example of large-scale flows. We discuss a graph-theory-based Lagrangian technique for identifying regions of strong mixing (in the sense of diffusion) in the flow and compare it to previous Lagrangian approaches used in this context.
Anirban Guha and Raunak Raj
Nonlin. Processes Geophys., 26, 283–290,Short summary
Waves observed on the ocean surface often nonlinearly interact among themselves and undergo algebraic growth – a mechanism known as resonant triad interaction. Bragg resonance is a special resonant triad in which one of the constituent
wavesis the ocean's undulating bottom boundary. Here we show that, in the presence of an ocean current, two surface waves or a surface wave and an interfacial wave (wave existing at the ocean pycnocline) can undergo exponential growth.
Nikolay Makarenko, Janna Maltseva, Eugene Morozov, Roman Tarakanov, and Kseniya Ivanova
Nonlin. Processes Geophys., 25, 659–669,Short summary
The problem on internal waves in a weakly stratified two-layered fluid is studied semi-analytically. We discuss the 2.5-layer fluid flows with exponential stratification of both layers. The long-wave model describing travelling waves is constructed by means of a scaling procedure with a small Boussinesq parameter. It is demonstrated that solitary-wave regimes can be affected by the Kelvin–Helmholtz instability arising due to interfacial velocity shear in upstream flow.
Dmitry Kachulin and Andrey Gelash
Nonlin. Processes Geophys., 25, 553–563,Short summary
We consider the nonlinear model well known in geophysics for deep water surface gravity waves – the envelope version of the Dyachenko–Zakharov equation. This model predicts that waves can propagate as a stable localized groups – solitons. We study numerically in detail the soliton collisions and find fundamentally different effects when compared to the previously known results. We demonstrate the formation of extreme amplitude waves that may cause serious damage appearing in seas and oceans.
Sung Bum Yoon, Jong-In Lee, Young-Take Kim, and Choong Hun Shin
Nonlin. Processes Geophys., 25, 521–535,Short summary
Laboratory and numerical experiments are conducted to investigate stem waves due to incidence of monochromatic waves. For larger-amplitude waves with smaller angle of incidence, the measured data clearly show stem waves. The resonant interactions between the incident and reflected waves predicted for solitary waves are not observed for the periodic Stokes waves. The existence and the properties of stem waves found theoretically via simulations are favorably supported by the physical experiments.
Tatyana Talipova, Efim Pelinovsky, Oxana Kurkina, Ayrat Giniyatullin, and Andrey Kurkin
Nonlin. Processes Geophys., 25, 511–519,Short summary
Strong internal waves have a significant influence on underwater marine environment and off-shore engineering facilities. They induce noticeable currents and take part in the processes of mixing of water layers, suspension and transport of sediment particles, and formation of sea bottom relief. We consider probability of emergence of large-amplitude internal waves on the basis of instrumental measurements of internal wave fields in five different regions of the World Ocean.
Peiwen Zhang, Zhenhua Xu, Qun Li, Baoshu Yin, Yijun Hou, and Antony K. Liu
Nonlin. Processes Geophys., 25, 441–455,Short summary
We perform five sets of numerical experiments to examine the evolution processes of mode-2 internal solitary waves (ISWs) modulated by background shear currents. Three distinctly different shear-induced waves were identified as forward-propagating long waves, oscillating tails and amplitude-modulated wave packets. The background shear currents are found to play an important role for the
short-livednature and energy decay process of mode-2 ISWs observed previously by Shroyer et al. (2010).
Irina I. Rypina, Stefan G. Llewellyn Smith, and Larry J. Pratt
Nonlin. Processes Geophys., 25, 267–278,Short summary
Trajectory encounter volume – the volume of fluid that passes close to a reference fluid parcel over some time interval – has been recently introduced as a measure of mixing potential of a flow. We derived the analytical relationship between the encounter volume and diffusivity, which is the most commonly used characteristic of turbulent eddy diffusion. When applied to the altimetric velocities in the Gulf Stream region, the method illuminated transport properties of the Gulf Stream rings.
David Deepwell, Marek Stastna, and Aaron Coutino
Nonlin. Processes Geophys., 25, 217–231,Short summary
We have used numerical simulations to investigate the impact that rotation has on large waves existing internally in the ocean. In coastal regions these waves become trapped along the coast because of rotation. We have found that this trapping results in an adjustment of the form of the waves. The adjustment leads to heightened mixing along the coast, which has implications for nutrient and chemical distribution.
Ruy Ibanez, Joseph Kuehl, Kalyan Shrestha, and William Anderson
Nonlin. Processes Geophys., 25, 201–205,Short summary
We present a nonlinear analytic solution for barotropic flow relevant to the oceanographic slope region. A similarity approach is adopted and the solution takes the form of a Lambert W-function. A more general class of linear solutions is also discussed which take the form of error functions. The equations solved are similar to the heat equation and thus the results may be of interest beyond the geophysical community.
Chengzhu Xu and Marek Stastna
Nonlin. Processes Geophys., 25, 1–17,Short summary
This work contributes to the understanding of the interaction between internal waves of different length scales. A key finding is that, when the disparity in length scales between the participating waves is large, the interaction may lead to an almost complete destruction of the waves that have a relatively smaller length scale. This result suggests that the wavelengths of internal waves observed in the coastal oceans are likely to be deficient in short waves.
Vladimir Maderich, Kyung Tae Jung, Kateryna Terletska, and Kyeong Ok Kim
Nonlin. Processes Geophys., 24, 751–762,Short summary
When near-surface or near-bottom layers in the ocean are stratified, internal solitary waves (ISWs) of large amplitude can trap and transport fluid in their cores. The dynamics and energetics of a head-on collision of ISWs with trapped cores for a wide range of amplitudes and stratifications are studied numerically. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions. The interaction can trigger local wave instability of ISWs.
Nonlin. Processes Geophys., 24, 727–735,Short summary
Deriving a generalization of Long's equation to non-isothermal flow shows that Long's equation has (approximate) soliton-like solutions, provides a transformation that linearizes Long's equation (and analytic solutions), and provides analytic solutions for a base flow with shear.
Oxana Kurkina, Tatyana Talipova, Tarmo Soomere, Ayrat Giniyatullin, and Andrey Kurkin
Nonlin. Processes Geophys., 24, 645–660,Short summary
Large internal waves may be a great danger to offshore structures. The breaking of such waves may strongly modify the seabed. Their core properties depend on how temperature and salinity vary in the water column. These variations are represented by three vertical locations and four coefficients of the relevant equation. We established how these seven quantities vary in the South China Sea for waves of the second mode (which create compressions or expansions of the intermediate water layer).
Vladimir Zakharov, Donald Resio, and Andrei Pushkarev
Nonlin. Processes Geophys., 24, 581–597,Short summary
The Hasselmann equation (HE) is the basis of modern surface ocean wave prediction models. Currently, they operate in the
black box with the tuning knobsmodes, since there is no consensus on universal wind input and wave-breaking dissipation source terms, and require re-tuning for different boundary and external conditions. We offer a physically justified framework able to reproduce theoretical properties of the HE and experimental field data without re-tuning of the model.
Pedro Monroy, Emilio Hernández-García, Vincent Rossi, and Cristóbal López
Nonlin. Processes Geophys., 24, 293–305,Short summary
We study the problem of sinking particles in a realistic oceanic flow, with major energetic structures in the mesoscale, focussing on marine biogenic particles. By using a simplified equation of motion for small particles in a mesoscale velocity field, we estimate the influence of physical processes such as the Coriolis force and the particle's inertia, and we conclude that they represent negligible corrections to passive transport by the flow, with added vertical velocity due to gravity.
Víctor José García-Garrido, Jezabel Curbelo, Carlos Roberto Mechoso, Ana María Mancho, and Stephen Wiggins
Nonlin. Processes Geophys., 24, 265–278,Short summary
Our work shows that a simple kinematic model is able to retain the fundamental mechanisms responsible for complex fluid parcel evolution in the stratosphere. Our analysis justifies in a controlled manner the formation of filaments eroding the polar vortex and shows that the breaking and splitting of the polar vortex is explained by the sudden growth of a planetary wave and the decay of the axisymmetric flow.
Sergei I. Badulin and Vladimir E. Zakharov
Nonlin. Processes Geophys., 24, 237–253,Short summary
In our simulations of sea swell, we show that its evolution exhibits remarkable features of universality. At long stretches the swell ``forgets'' initial conditions and keeps its specific distribution of wave energy in scales and directions. Slow evolution of swell in time and space can be related to fundamental relationships of the so-called theory of weak turbulence that gives a solid basis for the swell prediction.
Anatoly Abrashkin and Efim Pelinovsky
Nonlin. Processes Geophys., 24, 255–264,Short summary
The nonlinear Schrödinger equation describing weakly rotational wave packets in a fluid in the Lagrangian coordinates is derived. Rogue effects are possible in low-vorticity waves, and the effect of vorticity is manifested in a shift of the wave number in the carrier wave. Special attention is paid to Gouyon and Gerstner waves. It is shown that this equation in the Eulerian variables can be obtained from the Lagrangian solution with an ordinary change in the horizontal coordinates.
Irina I. Rypina and Lawrence J. Pratt
Nonlin. Processes Geophys., 24, 189–202,Short summary
Fluid parcels exchange water properties when coming into contact with each other, leading to mixing. The trajectory encounter volume, defined here as the volume of fluid that passes close to a reference trajectory over a finite time interval, is introduced as a measure of the mixing potential of a flow. Regions with a low encounter volume (the cores of coherent eddies) have a low mixing potential. Regions with a large encounter volume (turbulent or chaotic regions) have a high mixing potential.
Nizar Abcha, Tonglei Zhang, Alexander Ezersky, Efim Pelinovsky, and Ira Didenkulova
Nonlin. Processes Geophys., 24, 157–165,Short summary
Parametric excitation of edge waves with a frequency 2 times less than the frequency of surface waves propagating perpendicular to the inclined bottom are investigated in laboratory experiments. The domain of instability on the plane of surface wave parameters (amplitude–frequency) is found. The subcritical instability is observed in the system of parametrically excited edge waves. It is shown that breaking of surface waves initiates turbulent effects and can suppress the parametric generation.
Sergey V. Prants, Maxim V. Budyansky, and Michael Yu. Uleysky
Nonlin. Processes Geophys., 24, 89–99,Short summary
Transport of subtropical waters in the Japan Sea is simulated based on altimeter data. Preferred transport pathways across the Subpolar Front are found. The cross-frontal transport is shown to be inhomogeneous with gates and barriers whose locations are determined by a local velocity field. The gates open due to suitable dispositions of mesoscale eddies facilitating propagation of subtropical waters to the north. There are forbidden zones where the northward transport has not been observed.
Aaron Coutino and Marek Stastna
Nonlin. Processes Geophys., 24, 61–75,Short summary
We have re-examined the classical geostrophic adjustment problem, where a disturbance of a density stratification is released from rest in a rotating frame of reference, from a numerical point of view. This has enabled us to consider the governing equations without approximations. We show that both the waves generated and the remaining state exhibit nonlinear effects. Due to advances in available computational power, we can now revisit classical problems and solve them completely.
Floriane Gidel, Onno Bokhove, and Anna Kalogirou
Nonlin. Processes Geophys., 24, 43–60,Short summary
Extreme water waves impacting ships and offshore structures can not only cause severe structural damage, but also threaten the safety of passengers and crew. Accordingly, the motivation for the present work is to better understand the dynamics of extreme waves in two cases: the case of "green water" and the case of "freak waves". Our methodology can simulate those two events in order to estimate the forces of such extreme waves and thus aid engineers in the design of safer maritime structures.
Claudia Cherubini, Nicola Pastore, Concetta I. Giasi, and Nicoletta Maria Allegretti
Nonlin. Processes Geophys., 24, 23–42,Short summary
Aquifers offer the possibility of exploiting geothermal energy. Especially in fractured aquifers, in order to increase the optimal efficiency of installations which use groundwater as a geothermal resource, flow and heat transport dynamics need to be well understood. This study is aimed at deepening the understanding of this topic through heat transport experiments in fractured networks and their interpretation.
Konstantin V. Koshel and Eugene A. Ryzhov
Nonlin. Processes Geophys., 24, 1–8,Short summary
The paper deals with the dynamics of an isolated vortex that evolves in a time-dependent strain environment. We establish parameters leading to parametric instability of stationary steady-state configuration using a combination of analytical and numerical techniques. Our findings may contribute to a deeper understanding of the coherent vortex dynamics in the ocean.
Arnida L. Latifah and E. van Groesen
Nonlin. Processes Geophys., 23, 341–359,Short summary
This paper showed the relevance of phase coherence by illustrations of signals with increasingly less restrictions on the phase function. Then the wavelet transform was used to determined the time–frequency spectrum of a time signal. We used the wavelet transform to identify critical group events of the influx signal and it is shown that the group event with the largest local energy signal is the most probable group to generate a freak wave. It gives a local mechanism of a freak wave appearance.
Jean-Louis Le Mouël, Vladimir G. Kossobokov, Frederic Perrier, and Pierre Morat
Nonlin. Processes Geophys., 23, 319–330,Short summary
Heating experiments carried out in a limestone quarry close to Paris have shown a classical shape of temperature distribution in steady-state plumes in averages over 24 h, along with rich dynamics of heat flow with intermittent trains of oscillations, spatially coherent, of large amplitudes and a ~ 400 s period, separated by relative quiescence whose duration can reach several hours. The observed behavior could be a universal feature of some turbulent plumes in real geophysical environments.
Borja Aguiar-González and Theo Gerkema
Nonlin. Processes Geophys., 23, 285–305,Short summary
We derive a new two-fluid layer model consisting of forced rotation-modified Boussinesq equations for studying the limiting amplitudes of tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial tides and solitons. Numerical solutions show that solitons attain in some cases a limiting table-shaped form, but may also be limited well below that state by saturation of the underlying quasi-linear internal tide under increasing barotropic forcing.
Manel Grifoll, Jorge Navarro, Elena Pallares, Laura Ràfols, Manuel Espino, and Ana Palomares
Nonlin. Processes Geophys., 23, 143–158,Short summary
In this contribution the wind jet dynamics in the northern margin of the Ebro River shelf (NW Mediterranean Sea) are investigated using coupled numerical models. The study area is characterized by persistent and energetic offshore winds during autumn and winter. However, the coupling effect in the wind resource assessment may be relevant due to the cubic relation between the wind intensity and power.
Vassili Kitsios, Jorgen S. Frederiksen, and Meelis J. Zidikheri
Nonlin. Processes Geophys., 23, 95–105,Short summary
To numerically simulate the atmosphere and ocean, the large eddies are resolved on a grid, and the effect the small unresolved eddies have on the large ones is modelled. Improper modelling leads to resolution-dependent results. We solve this long-standing problem by calculating the model coefficients from high-resolution simulations, and characterise the coefficients with a set of scaling laws. Low-resolution simulations adopting these laws reproduce the statistics of the high-resolution cases.
Gavita S. Regunath, William B. Zimmerman, and Julia M. Rees
Nonlin. Processes Geophys., 23, 83–89,Short summary
Helical structures are commonplace in geophysical flows, but their effect on turbulence is still enigmatic. A novel PIV laser technique has been used to analyze helical structures in a turbulent swirling jet where the underlying shear flow is subjected to external acoustic forcing. Although the acoustic excitation had an effect on the flow field, no evidence for the existence of large-scale helical structures with maximal helicity was found.
Pilar López and José L. Cano
Nonlin. Processes Geophys., 23, 75–82,Short summary
The focus of this paper is to improve our studies related to the novel use of the Thorpe method applied to atmospheric boundary layer (ABL) using new data from Spanish field experiments. We analyse the time behaviour of the maximum Thorpe displacement (dT)max and the Thorpe-scale LT during a day cycle. We also analyse the relation between (dT)max and LT. We deduce that they confirm a power law statistically significant, with differences between convective conditions and shear-driven conditions.
A. M. Matulka, Y. Zhang, and Y. D. Afanasyev
Nonlin. Processes Geophys., 23, 21–29,Short summary
In this paper, a turbulent ocean is modelled in the laboratory. The rotation of the Earth around its axis is represented by the rotation of a turntable. Similar to that in the Earth's ocean, the currents in the laboratory "ocean" are created by density effects when the water is heated or made salty. The laboratory currents are measured by a system which is not unlike the satellite altimetry system used by oceanographers to create "topographic" maps of the elevation of the water surface.
L. Shemer and B. K. Ee
Nonlin. Processes Geophys., 22, 737–747,
V. J. García-Garrido, A. M. Mancho, S. Wiggins, and C. Mendoza
Nonlin. Processes Geophys., 22, 701–712,Short summary
The disappearance of Malaysia Airlines flight MH370 on 8 March 2014 is one of the great mysteries of our time. The most relevant aspect is that not a piece of debris was found during the intensive surface search carried out for roughly 2 months following the crash. By combining different ocean data with dynamical systems tools, we propose a revised search strategy by showing why debris could not have been expected in some targeted search areas and determining regions where debris could be.
P. R. Renosh, F. G. Schmitt, and H. Loisel
Nonlin. Processes Geophys., 22, 633–643,Short summary
Intermittent dynamics of particle size distribution in coastal waters is studied. Particle sizes are separated into four size classes: silt, fine, coarse and macro particles. The time series of each size class is derived, and their multiscaling properties studied. Similar analysis has been done for suspended particulate matter and total volume concentration. All quantities display a nonlinear moment function and a negative Hurst scaling exponent.
D. Garaboa-Paz and V. Pérez-Muñuzuri
Nonlin. Processes Geophys., 22, 571–577,Short summary
The present study aims to improve the calculus of finite-time Lyapunov exponents (FTLEs) applied to describe the transport of inertial particles in a fluid flow. To this aim, the deformation tensor is modified to take into account that the stretching rate between particles separated by a certain distance is influenced by the initial velocity of the particles. Results are presented for two different flows and compared with the classical method by Shadden (2005).
P. He and S. Basu
Nonlin. Processes Geophys., 22, 447–471,Short summary
The present work, to the best of our knowledge, is the first DNS study reporting temporal (long-term) statistics of intermittent turbulence (a.k.a. bursting events) in stably stratified flows. The present paper not only accurately reproduces recently published key spatial statistics of intermittent turbulence but also reports some intriguing features, e.g., the coexistence of internal waves and intermittent turbulence.
S. R. Ramp, Y. J. Yang, D. B. Reeder, M. C. Buijsman, and F. L. Bahr
Nonlin. Processes Geophys., 22, 413–431,Short summary
Highly energetic mode-2 nonlinear internal waves were found to be generated at several sites near the northern Heng-Chun (western) Ridge south of Taiwan. The local environment however was highly dissipative, and the energy budget suggests that little wave energy escapes the ridge to contribute to the large transbasin waves that have been previously observed in other studies.
O. A. Druzhinin and L. A. Ostrovsky
Nonlin. Processes Geophys., 22, 337–348,Short summary
The objective of this paper is to study the dynamics of turbulence near a pycnocline, both in the free regime and under the action of an internal wave (IW) propagating along a pycnocline by direct numerical simulation (DNS). Turbulence is initially induced in a horizontal layer above the pycnocline. The DNS results show that turbulence kinetic energy (TKE) is significantly enhanced as compared to the TKE in the absence of IW, and most of the TKE is localized in the vicinity of the pycnocline.
I. V. Shugan, H. H. Hwung, and R. Y. Yang
Nonlin. Processes Geophys., 22, 313–324,Short summary
An analytical weakly nonlinear model of Benjamin–Feir instability of a Stokes wave on nonuniform unidirectional current is presented. In contrast to the models based on versions of the cubic Schrodinger equation the current variations could be strong, which allows us to examine the blockage of waves. Waves may overpass the blocking barrier produced by strong adverse current. We find reasonable correspondence between the results of model simulations and available experimental results.
K. G. Lamb and A. Warn-Varnas
Nonlin. Processes Geophys., 22, 289–312,Short summary
Two-dimensional numerical simulations of the shoaling of an internal solitary wave (ISW) in the South China Sea have been undertaken. Peak amplitudes are attained at depths of 250 and 600m. Horizontal resolutions of 50m are required to simulate the formation of a pedestal in shallow water behind the shoaling wave. At a depth of 200m, waves can exceed maximum ISW amplitudes by 50%. Sensitivity to the bathymetry and stratification and the effects of rotation are considered.
J. P. McHugh
Nonlin. Processes Geophys., 22, 259–274,
Nonlin. Processes Geophys., 22, 133–138,Short summary
Long's equation models the steady state of two-dimensional stratified flow over terrain. It has been used extensively to investigate the generation and properties of gravity waves and their impact on the structure constants of the atmosphere. In this paper we derive a time-dependent version of this equation which might be useful in the analysis of experimental data about gravity waves.
O. E. Kurkina, A. A. Kurkin, E. A. Rouvinskaya, and T. Soomere
Nonlin. Processes Geophys., 22, 117–132,Short summary
We have derived exact analytical expressions for the coefficients of evolution equations of long wave motion in the three-layer fluid with arbitrary parameters of the layers and established interrelations of these equations for different interfaces. To our understanding, the core advancement is the clarification and mapping of the regimes of soliton appearance and propagation in this environment that is much more realistic for the description of ocean internal waves.
J. C. Harris and S. T. Grilli
Nonlin. Processes Geophys., 21, 1169–1184,
W. Kristina, O. Bokhove, and E. van Groesen
Nonlin. Processes Geophys., 21, 987–1005,
L. M. Ivanov, C. A. Collins, and T. M. Margolina
Nonlin. Processes Geophys., 21, 887–900,
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It is analytically shown how competing nonlinearities yield multiscaled structures for internal solitary waves in stratified fluids. These solitary waves only exist for large amplitudes beyond the limit of applicability of the KdV/mKdV equations. Multiscaled waves without vortex cores are shown to be structurally unstable. It is anticipated that multiscaling phenomena will exist for solitary waves in various physical contexts.
It is analytically shown how competing nonlinearities yield multiscaled structures for internal...