Short Wave Packets Research Articles

High latitude gravity waves at the Venus cloud tops as observed by the Venus Monitoring Camera on board Venus Express

High resolution images of Venus Northern hemisphere obtained with the Venus Monitoring Camera (VMC/VEx) allow studying small-scale dynamical phenomena at the cloud tops (∼62–70km altitude) including features like wave trains. A systematic visual search of these waves was performed; more than 1500 orbits were analyzed and wave patterns were observed in more than 300 images. Four types of waves were identified in VMC images on the base of their morphology: long, medium, short and irregular type waves. With the aim to characterize the wave types and their possible excitation source, we retrieved wave properties such as location (latitude and longitude), local time, solar zenith angle, packet length and width, orientation, and wavelength of each wave. The long type waves appear as long and narrow straight features extending more than a few hundreds kilometers and with wavelengths between 7 and 17km. Medium type waves exhibit irregular wavefronts extending more than 100km and with wavelengths in the range 8–21km. Short wave packets have a width of several tens of kilometers and extend to few hundreds kilometers and are characterized by smaller wavelengths (3–16km). Irregular wave fields appear to be the result of wave interference. The waves are often identified in all VMC filters and are mostly found in the cold collar region at high latitudes (60–80°N) and are concentrated above Ishtar Terra, a continental size highland that includes the highest mountain belts of the planet. The high speed of the Venus Express spacecraft close to the pericentre does not allow to measure phase speed of waves due to the short temporal interval between image pairs. The lack of information on phase velocities does not allow us to establish with absolute confidence the nature of these waves. However, by comparing the morphology and properties of the wave features observed in VMC images to those seen by previous observations it is reasonable to assume that the waves studied here are gravity waves.

Energy fluctuations of high-frequency sound signals in a shallow water in the presence of nonlinear internal waves

The paper presents an analysis of energy fluctuations of high-frequency (2–4.5 kHz) sound signals propagating in a shallow water in the presence of nonlinear (soliton-like) internal waves (2006 Shallow Water experiment, US Atlantic shelf). Signals were received by three single hydrophones in different directions at distances of ∼4, ∼12, and ∼5 km from the source. The angle between the first two acoustic tracks was ∼15°. The third track was almost an extension of the first and was on the other side of the source. A relatively short (one to two solitons) nonlinear internal wave packet first moved approximately along the first two tracks and then along the third track. It is demonstrated that in the presence of solitons on the track in the frequency spectrum of energy fluctuations, there is an isolated frequency that depends, in particular, on the angle between the soliton front and the acoustic track. The experimental results agree well with the theory previously proposed by the authors, where the occurrence mechanism of fluctuations is explained using the ray approach.

A statistical analysis of low frequency geomagnetic field pulsations at two Antarctic geomagnetic observatories in the polar cap region

The aim of this study is to investigate the characteristics of low frequency (∼0.5–5mHz) geomagnetic field fluctuations as recorded at two Antarctic stations within the polar cap: the Italian observatory Mario Zucchelli Station (TNB) and the French–Italian observatory Dome C (DMC) in order to investigate the spatial extension and propagation characteristics of the phenomena observed at very high latitude. The stations have approximately the same geographic latitude, but a very different corrected geomagnetic latitude, being DMC close to the geomagnetic pole and TNB closer to the auroral oval.Our study focused on power spectra, coherence and phase difference between low frequency fluctuations analyzing the horizontal H component measured during the entire year 2006.The fluctuation power behavior during the day can be explained according to the positions of the stations with respect to the polar cap; indeed in the dayside sector it is higher in the cusp region, while in the nightside sector it is higher close to the geomagnetic pole. Furthermore the study of coherent fluctuations, focusing on their phase difference, indicated that the propagation direction within the cap is variable during the day: in the dayside and nightside regions it is from the auroral oval toward the geomagnetic pole, while in the magnetic local morning and afternoon sectors it is from the geomagnetic pole toward the dawn–dusk meridian. Finally the analysis of two individual pulsation events, consisting of short duration wave packets, is shown; it confirms the statistical considerations on the propagation direction and allows to estimate the wave number and apparent phase velocity, whose values are of the order of 3–4 and 30–15km/s, respectively.

High Frequency Wave Packet Concentrated near the moving Line on the Liquid Surface

Wave wall type solutions for waves on the surface of an ocean with slowly varying depth are constructed. It is a generalization of the solution of quasi-photon type. Wave wall is a packet of short waves concentrated near the moving line which forms the wave front. The approach is based on the representation of the solution in the form of asymptotic space-time rays (STR) series each term of which is a formal power series. The appropriate form of the ansatz is suggested. Chains of equations for coefficients of formal power series for phase and amplitude terms are derived. These equations are investigated and the solvability of the problem at each step is proved. As a result, asymptotic space-time series for the wave wall moving with group velocity on the surface of a heavy liquid is obtained.

Strong lensing, plane gravitational waves and transient flashes

Plane-symmetric gravitational waves are considered as gravitational lenses. Numbers of images, frequency shifts, mutual angles, and image distortion parameters are computed exactly in essentially all non-singular plane wave spacetimes. For a fixed observation event in a particular plane wave spacetime, the number of regular images is found to be the same for almost every pointlike source. This number can be any positive integer, including infinity. Wavepackets of finite width are discussed in detail as well as waves which maintain a constant amplitude for all time. Short wavepackets are found to generically produce up to two images of each source which appear (separately) only some time after the wave has passed. They are initially infinitely bright, infinitely blueshifted images of the infinitely distant past. Later, these images become dim and acquire a rapidly-increasing redshift. For sufficiently weak wavepackets, one such ‘flash’ almost always exists. The appearance of a second flash requires that the Ricci tensor inside the wave exceed a certain threshold. This might occur if a gravitational plane wave is sourced by, e.g., a sufficiently strong electromagnetic plane wave.

Statistics of quantum beats in the time dependence of the neutron scattering

The numerical calculations of the delay time distributions for the neutron scattering have been carried out. The scattering of the short wave packet of neutrons with the broad energy interval 500–800 keV by 58Ni nuclei has been studied. The decay curves and average times of the compound scattering were found as for the forward scattering as for the specific spin-parity states. The time oscillations of the decay curves were identified as quantum beats that were caused by the interference of the excited resonance set. The statistical analysis of the frequency spectra of the decay curves oscillations has been carried out. The behavior of the examined statistical observables turns out to be close to the Poisson law.

Multimodal structure of baroclinic tides in the South China Sea

Abstract. The modelling of baroclinic tides generated in the northern South China Sea is studied using a fully-nonlinear non-hydrostatic numerical model. The focus of the modelling efforts was on the vertical structure of internal waves in the vicinity of the Luzon Strait. The barotropic tidal flow interacting with a two-ridge bottom topography in the area of the Luzon Strait produces a complex baroclinic tidal signal. A multimodal baroclinic bore with counter-phase displacement of isopycnals generated over the ridges and propagating westward disintegrates into a series of large-amplitude solitary internal waves. The leading first-mode solitary wave of depression is followed by a second mode solitary wave coupled with a packet of short-scale internal waves riding it. Scrutiny of the characteristics of the both wave forms, i.e. the carrier second-mode solitary wave and the packet of short waves, revealed that the short-scale waves are basically concentrated in the upper 500 m layer and attenuate exponentially below it. The short waves exist only thanks to a specific structure of horizontal velocity produced by the second-mode solitary wave. Having equal phase speeds and propagating together for a long distance, this coupled system produces quite a remarkable signal at the free surface, which can be detected by means of remote sensing technique. It was found in a series of sensitivity experiments that the eastern ridge is responsible for the generation of progressive first-mode tidal waves disintegrated into packets of first-mode ISWs. The western ridge produces quite a strong higher-mode signal. The waves generated over the eastern and western ridges interfere in the near-field, and their nonlinear superposition enhances the multimodal signal in the whole domain.

Nonlinear effects for coda-type elastic waves in stressed granular media

Experimental results and their interpretations are presented on the nonlinear acoustic effects of multiple scattered elastic waves in unconsolidated granular media. Short wave packets with a central frequency higher than the so-called cutoff frequency of the medium are emitted at one side of the statically stressed slab of glass beads, and received at the other side after multiple-scattering and nonlinear elastic effects. Typical signals are strongly distorted compared to their initially radiated shape both due to nonlinearity and scattering. It is shown that acoustic waves with a deformation amplitude much lower than the mean static deformation of the contacts in the medium can modify the elastic properties of the medium. This addresses the problem of acoustic wave action on granular matter during and after acoustic excitation, which is necessary to understand in the nondestructive testing of the elastic properties of granular media by acoustic methods. Coda signal analysis is shown to be a powerful time-resolved tool in monitoring slight modifications in the elastic response of an unconsolidated granular structure.

Global Wellposedness in the Energy Space for the Maxwell-Schrödinger System

We prove that the Maxwell-Schrodinger system in \({\mathbb{R}^{3+1}}\) is globally well-posed in the energy space. The key element of the proof is to obtain a short time wave packet parametrix for the magnetic Schrodinger equation, which leads to linear, bilinear and trilinear estimates. These, in turn, are extended to larger time scales via a bootstrap argument.

Numerical simulations of boundary-layer bypass transition due to high-amplitude free-stream turbulence

Direct numerical simulations (DNS) of bypass transition due to high-amplitude free-stream turbulence (FST) are carried out for a flat-plate boundary layer. The computational domain begins upstream of the plate leading edge and extends into the fully turbulent region. Thus, there is noad hoctreatment to account for the initial ingestion of FST into the laminar boundary layer. We study the effects of both the FST length scale and the disturbance behaviour near the plate leading edge on the details of bypass transition farther downstream. In one set of simulations, the FST parameters are chosen to match the ERCOFTAC benchmark case T3B. The inferred FST integral length scaleL11is significantly larger (RL=UL11/ν = 6580) than that employed in previous simulations of bypass transition (RL≃ 1000). An additional set of simulations was performed atRL= 1081 to compare the transition behaviour in the T3B case with that of a smaller value of FST length scale. The FST length scale is found to have a profound impact on the mechanism of transition. While streamwise streaks (Klebanoff modes) are observed at both values of the FST length scale, they appear to have clear dynamical significance only at the smaller value ofRL, where transition is concomitant with streak breakdown. For the T3B case, turbulent spots form upstream of the region where streaks could be detected. Spot precursors are traced to quasi-periodic spanwise structures, first observed as short wavepackets in the wall-normal velocity component inside the boundary layer. These structures are reoriented to become horseshoe vortices, which break down into young turbulent spots. Two of the four spots examined for this case had a downstream-pointing shape, similar to those found in experimental studies of transitional boundary layers. Additionally, our simulations indicate the importance of leading-edge receptivity for the onset of transition. Specifically, higher fluctuations of the vertical velocity at the leading edge of the plate result in higher levels of streamwise Reynolds stress inside the developing boundary layer, facilitating breakdown to turbulence.

Tunable terahertz Bloch oscillations in chirped photonic crystals

We report simulations showing tunable terahertz oscillations of the electromagnetic field provided by the Bloch oscillations of a short photonic wave packet in a tilted band structure. The structure consists in a finite one-dimensional photonic crystal inhomogeneously chirped by a slowly-varying refractive index gradient. Tunability is obtained by relocating the Bloch oscillations center in regions characterized by different local band structure gradients. With reasonable refractive indexes, this mechanism may allow the generation of signals which cover a wide continuous part of the electromagnetic terahertz range, when used in combination of appropriate detection schemes.

Resonant quasiparticles in plasma turbulence.

A general view is proposed on wave propagation in fluids and plasmas where the resonant interaction of monochromatic waves with quasiparticles is considered. A kinetic equation for quasiparticles is used to describe the broadband turbulence interacting with monochromatic waves. Resonant interactions occur when the phase velocity of the long wavelength monochromatic wave is nearly equal to the group velocity of short wavelength wave packets, or quasiparticles, associated with the turbulent spectrum. It is shown that quasiparticle Landau damping can take place, as well as quasiparticle beam instabilities, thus establishing a direct link between short and large wavelength perturbations of the medium. This link is distinct from the usual picture of direct and inverse energy cascades, and it can be used as a different paradigm for the fluid and plasma turbulence theories.

A wavelet analysis of quasi-periodic variability across a solar coronal hole region

High time resolution ( ≈ 13 s cadence) Solar and Heliospheric Observatory (SOHO) Coronal Diagnostic Spectrometer (CDS) Grazing Incidence Spectrometer (GIS) time series data is analysed for evidence of quasi-periodic variability in the solar corona. The observations are obtained from a GIS study of a coronal hole boundary region taken in October 1997. A wavelet analysis is applied to EUV emission lines covering a temperature range of $\log T_{\rm e}=$ 5.3–6.1 K. Wavelet analysis allows the frequency and temporal information of any periods present within the data to be analysed. Statistically significant periods are found within the range 100–900 s and 1500 s. Observations of short wavepackets with periods of the order 50–100 s with durations of 2–5 cycles are reported. Observations of a decay in the driving period over time are also described.

Nonlinear modulation of multidimensional lattice waves.

The equations governing weakly nonlinear modulations of N-dimensional lattices are considered using a quasidiscrete multiple-scale approach. It is found that the evolution of a short wave packet for a lattice system with cubic and quartic interatomic potentials is governed by the generalized Davey-Stewartson (GDS) equations, which include mean motion induced by the oscillatory wave packet through cubic interatomic interaction. The GDS equations derived here are more general than those known in the theory of water waves because of the anisotropy inherent in lattices. The generalized Kadomtsev-Petviashvili equations describing the evolution of long-wavelength acoustic modes in two- and three-dimensional lattices are also presented. Then the modulational instability of an N-dimensional Stokes lattice wave is discussed based on the N-dimensional GDS equations obtained. Finally, the one- and two-soliton solutions of two-dimensional GDS equations are provided by means of Hirota's bilinear transformation method.

Tunneling of the Closed Friedmann Universe with Generation of Scalar Waves

The evolution of the closed Friedmann Universe with a packet of short scalar waves is considered with the help of the Wheeler--DeWitt equation. The packet ensures conservation of homogeneity and isotropy of the metric on average. It is shown that during tunneling the amplitudes of short waves of a scalar field can increase catastrophically promptly if their influence to the metric do not take into account. This effect is similar to the Rubakov-effect of catastrophic particle creation calculated already in 1984. In our approach to the problem it is possible to consider self-consistent dynamics of the expansion of the Universe and amplification of short waves. It results in a decrease of the barrier and interruption of amplification of waves, and we get an exit of the wave function from the quantum to the classically available region.

Short intense wave packets in smoothly inhomogeneous media

The propagation of short (of the order of a few wavelengths) intense wave packets in smoothly inhomogeneous media with an arbitrary profile of the potential is considered within the framework of the third-order nonlinear Schrödinger equation with inhomogeneous potential. An equation for trajectories of the center of mass of a packet is studied under the Hirota conditions. Parabolic and periodic profiles of inhomogeneity are considered in detail.

Interaction between a stokes wave packet and a solitary wave

This paper is a theoretical and experimental study of the propagation of a short gravity wave packet (modulated Stokes wave) over a solitary wave. The theoretical approach used here relies on a nonlinear WKB-type perturbation method. This method yields a theory of gravity waves that can describe both short and long waves simultaneously. We obtain explicit analytical solutions describing the interaction between the soliton and the short wave packet: phase shifts, variations of wavelengths and of frequencies (Doppler effects). In the experimental part of this work the phase shift experienced by the Stokes wave is measured. The theoretical conclusions are confirmed.

On phase kinks, negative frequencies, and other third-order peculiarities of modulated surface waves

Numerous laboratory and field experiments on nonlinear surface wave trains propagating in deep water (Lake & Yuen 1978; Ramamonjiarisoa & Mollo-Christensen 1979; Mollo-Christensen & Ramamonjiarisoa 1982; Melville 1983) have showed a specific wave modulation that so far has not been explained by nonlinear theories. Typical effects were the so-called wave phase reversals, negative frequencies, and crest pairing, experimentally observed in some portions of the modulated wave train. In the present paper, in order to explain these modulation manifestations, the equations for wavenumber, frequency, and velocity potential amplitude are derived consistently in the third-order approximation related to the wave steepness. The resulting model generalizes, for instance, the well-known nonlinear Schrödinger equation theory, to which it transforms at certain values of the governing parameters.The stationary solutions to the derived set of equations are found in quadrature and then analysed. Within well-defined ranges of the model parameters, these solutions explicitly manifest the above-mentioned wave modulation effects. In particular, they show the wave phase kinks to arise on areas of relatively small free-surface displacement in complete accordance with the experiments.The model with deeply modulated wavenumber and frequency permits one also to analyse the appropriately short surface wavepackets and modulation periods. In this case, a variety of new interesting wave solutions arises revealing complicated alteration of smooth and rough portions of the free surface. Of special importance are solitary waves, naturally generalizing envelope solitons of the nonlinear Schrödinger equation, but having a varying frequency (as a principle of the proposed theory) and a non-zero wave ‘pedestal’ at infinity. These new types of modulated surface waves should be also observable in laboratory tanks and under field conditions, because the relevant free parameters of theory are not extreme.

Waves described by higher approximations of the nonlinear schrödinger equation

We analyze nonlinear waves within the framework of the basic equation of the third approximation of the theory of dispersion of nonlinear waves. This equation, which includes terms of nonlinear and linear dispersion of the third order, adquately describes short wave packets with a width of up to several wavelengths.

Pulsed beam pre- and post-processing for localized inverse scattering

Well-collimated short pulse wave packets, also termed pulsed beams (PB), provide new options for local forward and inverse probing of targets or of a propagation environment. The spatial-temporal resolution achieved under the PB excitation conditions furnishes an unambiguous measure of where the ‘‘physical’’ signal resides, in contrast to frequency-domain procedures that must rely on more intricate phase discrimination. In this paper, PB forward and inverse modeling is applied to scattering by three-dimensional weak (Born-type) inhomogeneities with finite support in an otherwise homogeneous background fluid. By performing space–time and wave number–frequency analysis and synthesis in a phase space setting, conventional slant-stack tomography is pushed to its ultimate localization by PB pre- and post-processing. The implications of this scenario with respect to resolution and related issues are discussed. It is shown that this strategy reduces the inversion of the illuminated space-time scattering cell to a pseudo-one-dimensional problem determined by the orientation of the incident and scattered beam axes. Illustrative examples are included.