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Zhan Wang - One of the best experts on this subject based on the ideXlab platform.
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dynamics of gravity capillary Solitary Waves in deep water
Journal of Fluid Mechanics, 2012Co-Authors: Zhan Wang, Paul A MilewskiAbstract:The dynamics of Solitary gravity–capillary water Waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify the full potential flow problem by using surface variables and taking a particular cubic truncation possessing a Hamiltonian with desirable properties. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of Solitary Waves for a two-dimensional fluid domain, and with higher-order truncations in three dimensions. Fully localized Solitary Waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized Solitary Waves are investigated via numerical time integration of the equations. There are many Solitary wave branches, indexed by their finite energy as their amplitude tends to zero. The dynamics of the Solitary Waves is complex, involving nonlinear focusing of wavepackets, quasi-elastic collisions, and the generation of propagating, spatially localized, time-periodic structures akin to breathers.
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dynamics of gravity capillary Solitary Waves in deep water
arXiv: Fluid Dynamics, 2012Co-Authors: Zhan Wang, Paul A MilewskiAbstract:The dynamics of Solitary gravity-capillary water Waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential flow problem by taking a cubic truncation of the scaled Dirichlet-to-Neumann operator for the normal velocity on the free surface. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of Solitary Waves for a two-dimensional fluid domain. Fully localised Solitary Waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized Solitary Waves are investigated via numerical time integration of the equations. The Solitary wave branches are indexed by their finite energy at small amplitude, and the dynamics of the Solitary Waves is complex involving nonlinear focussing of wave packets, quasi-elastic collisions, and the generation of propagating, spatially localised, time-periodic structures (breathers).
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hydroelastic Solitary Waves in deep water
Journal of Fluid Mechanics, 2011Co-Authors: Paul A Milewski, J M Vandenbroeck, Zhan WangAbstract:The problem of Waves propagating on the surface of a two-dimensional ideal fluid of infinite depth bounded above by an elastic sheet is studied with asymptotic and numerical methods. We use a nonlinear elastic model that has been used to describe the dynamics of ice sheets. Particular attention is paid to forced and unforced dynamics of Waves having near-minimum phase speed. For the unforced problem, we find that wavepacket Solitary Waves bifurcate from nonlinear periodic Waves of minimum speed. When the problem is forced by a moving load, we find that, for small-amplitude forcing, steady responses are possible at all subcritical speeds, but for larger loads there is a transcritical range of forcing speeds for which there are no steady solutions. In unsteady computations, we find that if the problem is forced at a speed in this range, very large unsteady responses are obtained, and that when the forcing is released, a Solitary wave is generated. These Solitary Waves appear stable, and can coexist within a sea of small-amplitude Waves.
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dynamics of steep two dimensional gravity capillary Solitary Waves
Journal of Fluid Mechanics, 2010Co-Authors: Paul A Milewski, J M Vandenbroeck, Zhan WangAbstract:In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary Solitary Waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type Solitary Waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation Solitary Waves, which were known to be linearly unstable, are shown to evolve into stable depression Solitary Waves, together with a radiated wave field. Depression Waves and certain large amplitude elevation Waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the Waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.
Paul A Milewski - One of the best experts on this subject based on the ideXlab platform.
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dynamics of gravity capillary Solitary Waves in deep water
Journal of Fluid Mechanics, 2012Co-Authors: Zhan Wang, Paul A MilewskiAbstract:The dynamics of Solitary gravity–capillary water Waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify the full potential flow problem by using surface variables and taking a particular cubic truncation possessing a Hamiltonian with desirable properties. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of Solitary Waves for a two-dimensional fluid domain, and with higher-order truncations in three dimensions. Fully localized Solitary Waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized Solitary Waves are investigated via numerical time integration of the equations. There are many Solitary wave branches, indexed by their finite energy as their amplitude tends to zero. The dynamics of the Solitary Waves is complex, involving nonlinear focusing of wavepackets, quasi-elastic collisions, and the generation of propagating, spatially localized, time-periodic structures akin to breathers.
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dynamics of gravity capillary Solitary Waves in deep water
arXiv: Fluid Dynamics, 2012Co-Authors: Zhan Wang, Paul A MilewskiAbstract:The dynamics of Solitary gravity-capillary water Waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential flow problem by taking a cubic truncation of the scaled Dirichlet-to-Neumann operator for the normal velocity on the free surface. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of Solitary Waves for a two-dimensional fluid domain. Fully localised Solitary Waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized Solitary Waves are investigated via numerical time integration of the equations. The Solitary wave branches are indexed by their finite energy at small amplitude, and the dynamics of the Solitary Waves is complex involving nonlinear focussing of wave packets, quasi-elastic collisions, and the generation of propagating, spatially localised, time-periodic structures (breathers).
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hydroelastic Solitary Waves in deep water
Journal of Fluid Mechanics, 2011Co-Authors: Paul A Milewski, J M Vandenbroeck, Zhan WangAbstract:The problem of Waves propagating on the surface of a two-dimensional ideal fluid of infinite depth bounded above by an elastic sheet is studied with asymptotic and numerical methods. We use a nonlinear elastic model that has been used to describe the dynamics of ice sheets. Particular attention is paid to forced and unforced dynamics of Waves having near-minimum phase speed. For the unforced problem, we find that wavepacket Solitary Waves bifurcate from nonlinear periodic Waves of minimum speed. When the problem is forced by a moving load, we find that, for small-amplitude forcing, steady responses are possible at all subcritical speeds, but for larger loads there is a transcritical range of forcing speeds for which there are no steady solutions. In unsteady computations, we find that if the problem is forced at a speed in this range, very large unsteady responses are obtained, and that when the forcing is released, a Solitary wave is generated. These Solitary Waves appear stable, and can coexist within a sea of small-amplitude Waves.
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dynamics of steep two dimensional gravity capillary Solitary Waves
Journal of Fluid Mechanics, 2010Co-Authors: Paul A Milewski, J M Vandenbroeck, Zhan WangAbstract:In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary Solitary Waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type Solitary Waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation Solitary Waves, which were known to be linearly unstable, are shown to evolve into stable depression Solitary Waves, together with a radiated wave field. Depression Waves and certain large amplitude elevation Waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the Waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.
T.r. Akylas - One of the best experts on this subject based on the ideXlab platform.
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Solitary Waves In Rotating Fluids
Solitary Waves in Fluids, 2007Co-Authors: T.r. AkylasAbstract:In this chapter, we discuss Solitary Waves when a swirl component is present in the background flow. Depending on the particular physical setting, rotation is responsible for inertial Solitary Waves but may significantly affect the propagation of gravity Solitary Waves as well. Here, two specific examples that illustrate this dual role of rotation are considered: (1) axisymmetric inertial Waves in a rotating homogeneous fluid in a rigid tube; (2) three-dimensional internal gravity Waves in a stratified fluid layer in a rotating channel. In (1), the propagation of weakly nonlinear long-wave disturbances is typical of a waveguide; each inertial wave mode is governed by a Korteweg–de Vries (KdV) equation to leading order, and Solitary Waves with sech2 profiles along the tube axis arise. In the special case of uniform rotation, it is also possible to construct finite-amplitude Solitary Waves analytically, and these solutions recently have been linked to the phenomenon of vortex breakdown. In (2), on the other hand, rotation primarily modifies the transverse structure of internal Solitary Waves propagating along the channel. When the rotation is relatively weak, in particular, so that the Rossby radius of deformation is comparable to the transverse wave scale, three-dimensional long-wave disturbances are governed by a rotation-modified Kadomtsev−Petviashvili (KP) equation. Consistent with laboratory observations, this equation predicts that an initially straight-crested KdV Solitary wave experiences radiation damping as it propagates along the channel, and its wave crest is curved backwards owing to the shedding of Poincare Waves behind.
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On asymmetric gravity–capillary Solitary Waves
Journal of Fluid Mechanics, 1997Co-Authors: Tian-shiang Yang, T.r. AkylasAbstract:Symme tric gravity–capillary Solitary Waves with decaying oscillatory tails are known to bifurcate from infinitesimal periodic Waves at the minimum value of the phase speed where the group velocity is equal to the phase speed. In the small-amplitude limit, these Solitary Waves may be interpreted as envelope solitons with stationary crests and are described by the nonlinear Schrodinger (NLS) equation to leading order. In line with this interpretation, it would appear that one may also co nstruct asymmetric Solitary Waves by shifting the carrier oscillations relative to the envelope of a symmetric Solitary wave. This possibility is examined here on the basis of the fifth-order Korteweg–de Vries (KdV) equation, a model for g ravity–capillary Waves on water of finite depth when the Bond number is close to 1/3. Using techniques of exponential asymptotics beyond all orders of the NLS theory, it is shown that asymmetric Solitary Waves of the form suggested by the NLS theory in fact are not possible. On the other hand, an infinity of symmetric and asymmetric Solitary-wave solution families comprising two or more NLS Solitary wavepackets bifurcate at finite values of the amplitude parameter. The asymptotic results are consistent with numerical solutions of the fifth-order KdV equation. Moreover, the asymptotic theory suggests that such multi-packet gravity–capillary Solitary Waves also exist in the full water-wave problem near the minimum of t he phase speed.
P K Shukla - One of the best experts on this subject based on the ideXlab platform.
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dust acoustic Solitary Waves in a quantum plasma
Physics of Plasmas, 2006Co-Authors: S Ali, P K ShuklaAbstract:By employing one-dimensional quantum hydrodynamic (QHD) model for a three species quantum plasma, nonlinear properties of dust acoustic Solitary Waves are studied. For this purpose a Korteweg-de Vries (KdV) equation is derived, incorporating quantum corrections. The quantum mechanical effects are also examined numerically both on the profiles of the amplitude and the width of dust acoustic Solitary Waves. It is found that the amplitude remains constant but the width shrinks for different values of a dimensionless electron quantum parameter He=(Zd0ℏ2ωpd2)∕memdCd4, where Zd0 is the dust charge state, ℏ is the Planck constant divided by 2π, ωpd is the dust plasma frequency, me (md) is the electron (dust) mass, and Cd is the dust acoustic speed.
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spherical and cylindrical dust acoustic Solitary Waves
Physics Letters A, 2001Co-Authors: A. A. Mamun, P K ShuklaAbstract:Abstract The nonlinear propagation of cylindrical and spherical dust acoustic (DA) Waves in an unmagnetized dusty plasma is considered. By employing the reductive perturbation technique, a modified Korteweg–de Vries (K–dV) equation is derived from the dust continuity and momentum equations, Poisson's equation as well as Boltzmann electrons and ions. Numerical solutions of the modified K–dV equation are obtained. It has been found that the propagation characteristics of the cylindrical and spherical DA Solitary Waves significantly differ from those of one-dimensional DA Solitary Waves.
Roger Grimshaw - One of the best experts on this subject based on the ideXlab platform.
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internal Solitary Waves propagation deformation and disintegration
Nonlinear Processes in Geophysics, 2010Co-Authors: Roger Grimshaw, Efim Pelinovsky, Tatiana Talipova, Oxana KurkinaAbstract:Abstract. In coastal seas and straits, the interaction of barotropic tidal currents with the continental shelf, seamounts or sills is often observed to generate large-amplitude, horizontally propagating internal Solitary Waves. Typically these Waves occur in regions of variable bottom topography, with the consequence that they are often modeled by nonlinear evolution equations of the Korteweg-de Vries type with variable coefficients. We shall review how these models are used to describe the propagation, deformation and disintegration of internal Solitary Waves as they propagate over the continental shelf and slope.
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Modelling Internal Solitary Waves in the Coastal Ocean
Surveys in Geophysics, 2007Co-Authors: Roger Grimshaw, Efim Pelinovsky, Tatiana TalipovaAbstract:In the coastal oceans, the interaction of currents (such as the barotropic tide) with topography can generate large-amplitude, horizontally propagating internal Solitary Waves. These Waves often occur in regions where the waveguide properties vary in the direction of propagation. We consider the modelling of these Waves by nonlinear evolution equations of the Korteweg–de Vries type with variable coefficients, and we describe how these models are used to describe the shoaling of internal Solitary Waves over the continental shelf and slope. The theories are compared with various numerical simulations.
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Damping of large-amplitude Solitary Waves
Wave Motion, 2003Co-Authors: Roger Grimshaw, Efim Pelinovsky, Tatiana TalipovaAbstract:Abstract We consider the damping of large-amplitude Solitary Waves in the framework of the extended Korteweg-de Vries equation (that is, the usual Korteweg-de Vries equation supplemented with a cubic nonlinear term) modified by the inclusion of a small damping term. The damping of a Solitary wave is studied for several different forms of friction, using both the analytical adiabatic asymptotic theory and numerical simulations. When the coefficient of the cubic nonlinear term has the opposite sign to the coefficient of the linear dispersive term, the extended Kortweg-de Vries equation can support large-amplitude “thick” Solitary Waves. Under the influence of friction, these “thick” Solitary Waves decay and may produce one or more secondary Solitary Waves in this process. On the other hand, when the coefficient of the cubic nonlinear term has the same sign as the coefficient of the linear dispersive term, but the opposite sign to the coefficient of the quadratic nonlinear term, the action of friction may cause a Solitary wave to decay into a wave packet.
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Atmospheric Internal Solitary Waves
Environmental Stratified Flows, 1Co-Authors: James W. Rottman, Roger GrimshawAbstract:The Solitary Waves that have been observed in the atmosphere fall broadly into two classes: those that propagate in a fairly shallow stratified layer near the ground and those that occupy the entire troposphere. We present a survey of the observations of both types of Solitary Waves. The generation mechanisms differ substantially for these two types of Solitary Waves. Those that propagate in a shallow stratified layer are generated by small scale or mesoscale phenomena such as thunderstorm outflows, sea breezes or katabatic winds. Those Solitary Waves that occupy the entire troposphere are generated by much larger scale phenomena, such as some kind of geostrophic adjustment process. We also review the previous attempts that have been made to compare these observations with weakly nonlinear Solitary wave theory. It appears that models with a deep passive upper layer are generally not applicable, while Korteweg-de Vries models, perhaps enhanced with higher-order nonlinearity, provide the best comparison; but it remains unclear what constitutes a suitable upper boundary condition.
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Internal Solitary Waves
Environmental Stratified Flows, 1Co-Authors: Roger GrimshawAbstract:The basic theory of internal Solitary Waves is developed, with the main emphasis on environmental situations, such as the many occurrences of such Waves in shallow coastal seas and in the atmospheric boundary layer. Commencing with the equations of motion for an inviscid, incompressible density-stratified fluid, we describe asymptotic reductions to model long-wave equations, such as the well-known Korteweg-de Vries equation. We then describe various Solitary wave solutions, and propose a variable-coefficient extended Korteweg-de Vries equations as an appropriate evolution equation to describe internal Solitary Waves in environmental situations, when the effects of a variable background and dissipation need to be taken into account.
