Effect of ion temperature on propagation of ion-acoustic solitary waves of small amplitudes in collisionless plasma

By using a perturbation technique, the Korteweg-de Vries equation is derived for a mixture of warm-ion fluid and hot, isothermal electrons. Stationary solutions are obtained for this equation and are compared with the corresponding solutions for a mixture consisting of cold-ion fluid and hot, isothermal electrons.

Effect of ionic temperature on propagation of ion-acoustic solitary waves in a collisionless plasma of warm-ion fluid and non-isothermal electrons

Using a perturbation technique, we derive Modified Korteweg—de Vries (MKdV) equations for a mixture of warm-ion fluid (γ i = 3) and hot and non-isothermal electrons (γ e> 1), (i) when deviations from isothermality are finite, and (ii) when deviations from isothermality are small. We obtain stationary solutions for these equations, and compare them with the corresponding solutions for a mixture of warm-ion fluid (γ i = 3) and hot, isothermal electrons (γ i = 1).

Some aspects of the solitary waves in a relativistic inhomogeneous plasma

In contrast to earlier observations on various solitary wave propagations, especially those bifurcated by the compressive and rarefactive solitary waves, the existence of spiky and explosive solitary waves is here believed to arise because of the presence of free and trapped electrons. So far, very few studies have been carried out to satisfactorily explain the presence of the solitary waves in space as observed by satellites. It is also attempted to highlight the probable impact on the various solitary wave propagations in a generalized multi-component, inhomogeneous plasma upon consideration of a relativistic treatment. It is expected that such a treatment will prove the existence of the solitary waves most expeditiously and exhibit the presence of chaos therein, thus giving a suitable explanation to the observations of various forms of spiky and explosive solitary waves in space-plasma. Copyright (C) 1996 Elsevier Science Ltd

Ion-Acoustic Solitary Waves in Multicomponent Plasmas with Negative Ions

By using the perturbation technique, a Kortewege-de-Vries (K-dV) equation for a multicomponent plasma with negative ions and isothermal electrons has been derived. We have discussed the stationary solutions of K-dV equation and it has shown that in the presece of multiple ions, the amplitude of solitons exhibits interesting behaviour, especiallY when the negative ions are present.

The effect of the surface tension on non-propagating solitary waves

In this paper, the effect of the surface tension is considered carefully in the study of non-propagating solitary waves. The parameter plane of the surface tension and the fluid depth is divided into three regions; in two of them a breather soliton can be produced. In literature the parameters of breather solitons are all in one of the parameter regions. The new region reported here has been confirmed by our experiments. In the third region, the theoretical solution is a kink soliton, but a kind of the non-propagating solitary wave similar to the breather soliton was found in our experiments besides the kink soliton.

The effect of variable currents on internal solitary waves

The effect of variable currents on internal solitary waves is described within the context of a variable coefficient Korteweg-de Vries (KdV) equation, and the approximate slowly varying, solitary-wave solution of this equation. The general theory which leads to the variable coefficient KdV equation is described; a derivation for the special case when the solitary wave and the current are aligned in the same direction is given in the Appendix. Using further simplifications and approximations, a number of analytical expressions are obtained for the variation in the solitary wave amplitude resulting from variable shear in the basic current or from when the basic current is a depth-independent flow which is a simple representation of a geostrophic current, tidal flow or inertial wave.

The interaction of two pairs of solitary waves in a two-fluid system

This paper deals with the interaction of solitary waves in a two-fluid system which consistsof two superimposed incompressible inviscid fluids with a free surface and a horizontal rigidbottom. Under the assumption of shallow water wave, we first derive the basic equationssuitable for the model considered, a generalized form of the Boussinesq equations, then usingthe PLK method and the reductive perturbation method, obtain the second-order approximatesolution for the head-on collision between two pairs of interface and surface solitary waves,and give their maximum amplitudes during the collision and the nonuniform phase shiftsafter the collision which lead to the distortion of the wave profiles.

Wave loading on floating platforms by internal solitary waves

Morison's equation is used for estimating internal solitary wave-induced forces exerted on SPAR and semi-submersible platforms. And the results we got have also been compared to ocean surface wave loading. It is shown that Morison's equation is an appropriate approach to estimate internal wave loading even for SPAR and semi-submersible platforms, and the internal solitary wave load on floating platforms is comparable to surface wave counterpart. Moreover, the effects of the layers with different thickness on internal solitary wave force are investigated.

Run-up of solitary waves on twin conical islands using a boussinesq model

This paper investigates the interaction of solitary waves (representative of tsunamis) with idealized flat-topped conical islands. The investigation is based on simulations produced by a numerical model that solves the two-dimensional Boussinesq-type equations of Madsen and Sørensen using a total variation diminishing Lax-Wendroff scheme. After verification against published laboratory data on solitary wave run-up at a single island, the numerical model is applied to study the maximum run-up at a pair of identical conical islands located at different spacings apart for various angles of wave attack. The predicted results indicate that the maximum run-up can be attenuated or enhanced according to the position of the second island because of wave refraction, diffraction, and reflection. It is also observed that the local wave height and hence run-up can be amplified at certain gap spacing between the islands, owing to the interference between the incident waves and the reflected waves between islands. © 2012 American Society of Mechanical Engineers.

Analysis of current induced by long internal solitary waves in stratified ocean

An approximate theoretical expression for the current induced by long internal solitary waves is presented when the ocean is continuously or two-layer stratified. Particular attention is paid to characterizing velocity fields in terms of magnitude, flow components, and their temporal evolution/spatial distribution. For the two-layer case, the effects of the upper/lower layer depths and the relative layer density difference upon the induced current are further studied. The results show that the horizontal components are basically uniform in each layer with a shear at the interface. In contrast, the vertical counterparts vary monotonically in the direction of the water depth in each layer while they change sign across the interface or when the wave peak passes through. In addition, though the vertical components are generally one order of magnitude smaller than the horizontal ones, they can never be neglected in predicting the heave response of floating platforms in gravitationally neutral balance. Comparisons are made between the partial theoretical results and the observational field data. Future research directions regarding the internal wave induced flow field are also indicated.

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19A degrees 35'N, 112A degrees E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

A study of internal solitary waves observed on the continental shelf in the northwestern South China Sea

Based on in-situ time series data from the acoustic Doppler current profiler (ADCP) and thermistor chain in Wenchang area, a sequence of internal solitary wave (ISW) packets was observed in September 2005, propagating northwest on the continental shelf of the northwestern South China Sea (SCS). Corresponding to different stratification of the water column and tidal condition, both elevation and depression ISWs were observed at the same mooring location with amplitude of 35 m and 25 m respectively in different days. Regular arrival of the remarkable ISW packets at approximately the diurnal tidal period and the dominance of diurnal internal waves in the study area, strongly suggest that the main energy source of the waves is the diurnal tide. Notice that the wave packets were all riding on the troughs and shoulders of the internal tides, they were probably generated locally from the shelf break by the evolution of the internal tides due to nonlinear and dispersive effects.

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.