Divergent Waves Research Articles

Differences between More Divergent and More Rotational Types of Convectively Coupled Equatorial Waves. Part I: Space–Time Spectral Analyses

Abstract Precipitation-related differences in different types of convectively coupled equatorial waves are examined here and in a companion paper. Here the authors show spectra and cross-spectra among tropical-belt time sections of satellite-derived surface rain, infrared brightness temperature Tb, precipitable water (PW), and Japan Meteorological Agency reanalysis of divergence and PW. Cross-spectra between rain and divergence at 1000- and 200-hPa levels show significant coherence peaks oriented along the dispersion curves of Kelvin, n = 1 equatorial Rossby (ERn1), mixed Rossby–gravity (MRG), n = 0 eastward inertial gravity (EIGn0), and n = 1 and n = 2 westward inertial gravity (WIG) waves, as well as the spectral signatures of the Madden–Julian oscillation (MJO) and tropical depression (TD)-type disturbances. Middle-troposphere divergence (indicative of stratiform rain and half-depth convection involvement in the coupling) is coherent with rain for the higher-frequency and more divergent wave types (Kelvin, EIGn0, WIG) but shows little coherence with rain for more rotational disturbance types (ERn1, MRG, TD). These two broad families also exhibit different rain–PW phase lags, a result supportive of the notion that stratiform rain (which occurs in dry conditions after peak PW and rain) is more involved in the more divergent wave types.

Cellular structure of divergent cylindrical detonation waves

Cellular structure of divergent cylindrical detonation waves

Partially coherent nano-focused x-ray radiation characterized by Talbot interferometry

We have studied the spatial coherence properties of a nano-focused x-ray beam by grating (Talbot) interferometry in projection geometry. The beam is focused by a fixed curvature mirror system optimized for high flux density under conditions of partial coherence. The spatial coherence of the divergent exit wave emitted from the mirror focus is measured by Talbot interferometry The results are compared to numerical calculations of coherence propagation. In view of imaging applications, the magnified in-line image of a test pattern formed under conditions of partial coherence is analyzed quantitatively. Finally, additional coherence filtering by use of x-ray waveguides is demonstrated. By insertion of x-ray waveguides, the beam diameter can be reduced from typical values of 200 nm to values below 15 nm. In proportion to the reduction in the focal spot size, the numerical aperture (NA) of the projection imaging system is increased, as well as the coherence length, as quantified by grating interferometry.

Initiation of detonation in explosives on an U-70 proton accelerator

Detonation initiation in a composite explosive based on HMX and TATB loaded by a divergent shock wave was studied on a U-70 proton accelerator using proton radiography. Density distributions behind the initiating shock front at various times were obtained. Detonation failure due to collision of shock and detonation waves was studied for a plastic-bonded TATB sample using radiography. Characteristic features of the explosive transformation under shock-wave loading were determined from the images obtained.

Kelvin Ship Wake in the Wind Waves Field and on the Finite Sea Depth

ABSTRACTA kinematics model of the ship wake in the presence of surface waves, generated by wind is presented. It was found that the stationary wave structure behind the ship covered a wedge region with the 16.9° half an angle at the top of the wake and only divergent waves are present in a ship wake for co propagating wind waves. Wind waves field directed at some nonzero angle to the ship motion can cause essential asymmetry of the wake and compressing of its windward half. The extension of Whitham-Lighthill kinematics theory of ship wake for the intermediate sea depth is also presented. The ship wake structure essentially depends from the Froude (Fr) number based on the value of the sea depth and ship velocity. For Froude number less than unit both longitudinal and cross waves are presented in the wake region and Kelvin wake angle increased with Fr. For Fr > 1 wake angle decreased with Froude number and finally only divergent waves are presented in the very narrow ship wake.

Time-domain simulation of spherical electromagnetic waves

Spherical electromagnetic waves excited by external surface electric currents in a homogeneous isotropic space are considered. It is shown that, in contrast to the harmonic excitation, in the case when the electromagnetic field is excited by external-current pulses, there is always an isolated convergent spherical wave in a bounded space-time region. The possibility of the existence of an isolated convergent spherical wave in a bounded spatial region at all instants is investigated for the cases of harmonic and pulse electromagnetic field excitations. It is proved that such a wave can exist when the divergent spherical wave arriving from the origin is compensated with the use of additional external currents. The excitation of isolated convergent spherical waves is illustrated by examples.

Atomic ionization by intense laser pulses of short duration: Photoelectron energy and angular distributions

We introduce an adequate integral representation of the wave function in the asymptotic region, valid for the stage postinteraction between a one-electron atom and a laser pulse of short duration, as a superposition of divergent radial spherical waves. Starting with this representation, we derive analytic expressions for the energy and angular distributions of the photoelectrons and we show their connection with expressions used before in the literature. Using our results, we propose a method to extract the photoelectron distributions from the time dependence of the wave function at large distances. Numerical results illustrating the method are presented for the photoionization of hydrogenlike atoms from the ground state and several excited states by extreme ultraviolet pulses with a central wavelength of $13.3$ nm and several intensities around the value ${I}_{0}\ensuremath{\approx}3.51\ifmmode\times\else\texttimes\fi{}{10}^{16} {\mathrm{W}/\mathrm{cm}}^{2}$.

Generation of Three-Dimensional Fully Nonlinear Water Waves by a Submerged Moving Object

This paper describes a numerical investigation on the generation of three-dimensional (3D) fully nonlinear water waves by a submerged object moving at speeds varied from subcritical to supercritical conditions in an unbounded fluid domain. Considering a semispheroid as the moving object, simulations of the time evolutions of 3D free-surface elevation and flow field are performed. The present 3D model results are found to agree reasonably well with other published vertical two-dimensional (2D) and quasi-3D numerical solutions using Boussinesq-type models. Different from the 2D cases with near critical moving speeds, the 3D long-term wave pattern suggests that in addition to the circularly expanded upstream advancing solitonlike waves, a sequence of divergent and transverse waves are also developed behind the moving object. The velocity distributions and associated fluid-particle trajectories at the free-surface and middle layers are presented to show the 3D feature of the motion. The results under various vertical positions (referred as gap) of a moving object are also compared. It is found the gap has shown a substantial influence on the generated waves, especially in the wake region, when an object moves at a near critical or subcritical speed. However, the results under the case with a high supercritical moving speed indicate the gap has a negligible effect on the generated upstream and downstream waves.

Soft X-ray holographic microscopy of chromosomes with high aspect ratio pinholes

We used digital in-line soft X-ray holography (DIXH) in the Gabor geometry to image human chromosomes. The divergent wave front was generated by diffraction of synchrotron radiation from a high aspect ratio pinhole. As under our experimental conditions the achievable resolution depends on the pinhole radius, high aspect ratio holes with diameters in the 100 nm range were prepared by focused ion beam (FIB) milling. The central maximum of the obtained Airy pattern was used to image chromosomes prepared from metaphase HeLa cells at experimental resolutions of 370 ± 40 nm with soft X-rays at 260 eV photon energy provided by the BESSY II synchrotron radiation facility.

Normalization of optical Weber waves and Weber-Gauss beams

The normalization of energy divergent Weber waves and finite energy Weber-Gauss beams is reported. The well-known Bessel and Mathieu waves are used to derive the integral relations between circular, elliptic, and parabolic waves and to present the Bessel and Mathieu wave decomposition of the Weber waves. The efficiency to approximate a Weber-Gauss beam as a finite superposition of Bessel-Gauss beams is also given.

Transformation of optical-vortex beams by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by the “fork” holograms from incident circular Laguerre–Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most cases its structure is formed under the influence of the divergent spherical wave originating from the discontinuity caused by the hologram’s groove bifurcation. Presence of this wave is manifested by the ripple structure in the near-field beam pattern and by the power-law amplitude decay at the beam periphery. Conditions when the divergent wave is not excited are discussed. The diffracted beam carries a screw wavefront dislocation (optical vortex) whose order equals to algebraic sum of the incident beam azimuthal index and the topological charge of the singularity imparted by the hologram. The input beam singularity can be healed when the above sum is zero. In such cases the diffracted beam can provide better energy concentration in the central intensity peak than the Gaussian beam whose initial distribution coincides with the Gaussian envelope of the incident beam. Applications are possible for generation of optical-vortex beams with prescribed properties and for analyzing the optical-vortex beams in problems of information processing.

An experimental investigation of divergent bow waves simulated by a two-dimensional plus temporal wave maker technique – ERRATUM

In the published article Shakeri et al. (2009) the title should read as above (i.e. ‘wave maker technique’, not ‘wave marker technique’ as in the published article).

The mechanism of the increase in penetration depth upon impact of a group of low-deformable spherical particles

Divergent compression and rarefaction waves propagating in a target upon impact of a group low-deformable particles were numerically investigated to reveal the physical mechanisms of the increase in penetration depth. An original approach was used where a depression (crater) in a target simulated the result of impact of a previous particle. Repeated reflection of rarefaction waves from the depression wall, their arrival at the impact axis, and subsequent propagation deep in the target has been revealed. It has been supposed that these repeated rarefaction waves produces stage-by-stage local damage to the target material ahead of the particle followed by the formation of a cylindrical crack, and this eventually provides the increase in penetration depth observed in experiment.

An experimental investigation of divergent bow waves simulated by a two-dimensional plus temporal wave marker technique

Divergent ship bow waves were simulated experimentally with a two-dimensional wavemaker that employs a flexible wave board. The wavemaker was programmed so that the wave board created a time sequence of shapes that simulated the line of intersection between one side of the hull of a slender ship model moving at constant speed and an imaginary vertical plane oriented normal to the ship model track. The time history of the water surface shape was measured with a cinematic laser-induced fluorescence technique for eight Froude numbers (FD = U/, where U is the forward speed of the equivalent three-dimensional ship model, g the acceleration of gravity and D the ship model draft). The waves produced ranged from small-amplitude non-breaking waves at the lowest Froude numbers to plunging breakers at the highest Froude numbers. These waves are strongly forced and at the higher Froude numbers begin breaking before leaving the wave board. The time histories of various geometric characteristics of the water surface shape including the hull contact line, the wave crest, the plunging jet and the splash zone, which is here defined as both the turbulent zone on the front face of the wave in the spilling breakers and the turbulent zone generated ahead of the jet impact point in the plunging breakers, were measured. The phase speed of the primary wave generated during each run ranged from 2.56Uwl (where Uwl is the maximum speed of the wave board at the undisturbed water level in the tank) at the lowest Froude number to about 1.7Uwl at the three highest Froude numbers. The maximum heights of the primary wave, the contact point on the wavemaker and the splash zone increased in a nearly linear fashion with increasing FD. In the cases with plunging jets, the jet tip trajectory was parabolic with a vertical acceleration ranging from 0.6g at FD = 1.467 to 0.8g at FD = 1.817 (the highest Froude number).

Synthesis of quasioptical waveguide mode converters on the basis of the Fox–Li method

We consider a generalization of the Fox-Li method to the problems of analysis and synthesis of weakly irregular quasioptical waveguides. It is shown that the field representation in the form of integral expansions in terms of convergent and divergent cylindrical waves makes it possible to efficiently solve such problems with allowance for the effects of nonparaxiality of wave beams and the vector character of electromagnetic fields. An example of synthesizing a converter of the output radiation of a gyroklystron with an operating frequency of 30 GHz at the TE 5,3 mode to the Gaussian wave beam is considered.

X-ray Holographic Microscopy using Total-Reflection Mirror Interferometer

An optical system for X-ray holographic microscopy has been developed using a Fresnel zone plate objective lens and a wavefront-dividing interferometer with total-reflection mirror optics. A plane mirror is placed behind the back focal plane of the objective lens, and half of a divergent wave from the focal point is deflected by the total-reflection mirror and overlapped onto the magnified image of the object. This interferometer is an analogue of a Lloyd's mirror interferometer, which is well known in visible light optics. By using fully coherent illumination to the objective lens, holographic microscopy was successfully performed. A quantitative phase image was obtained by the fringe scan method using a rotating phase shifter. The spatial resolution of the phase image is approximately 200 nm, and the phase sensitivity is estimated to be better than λ/60 at an X-ray wavelength of 1.0 Å.

Quantum tunneling and the resonant states

Using model systems we construct exact solutions of the Schr\"odinger equation for the tunneling effect in terms of the so-called resonant states. Two models of atomic ionization by an electrostatic field $E$ are studied in detail with a special emphasis on strong fields where the decay exponents become proportional to ${E}^{2∕3}$. The tunneling process, initiated by the field, is presented by an infinite sum of exponentially decaying terms without a usual slow decaying component at longer times. The sum of this series in some cases, including our models, lead to a nonexponential decay. The normalization techniques of the spatially divergent resonant wave functions via regularization of divergent integrals are considered. In particular, we apply an approximate semiclassical cutoff procedure which allows us to place the resonant states on a similar footing as the usual bound states and even use the standard normalization of the probability density. An application of such approach can illuminate and simplify calculation schemes for the study not only of ionization in electrostatic fields but also the multiphoton ionization by low frequency laser beams.

Eastward propagating MJO during boreal summer and Indian monsoon droughts

Improved understanding of underlying mecha- nism responsible for Indian summer monsoon (ISM) droughts is important due to their profound socio-economic impact over the region. While some droughts are associated with 'external forcing' such as the El-Nino and Southern Oscillation (ENSO), many ISM droughts are not related to any known 'external forcing'. Here, we unravel a funda- mental dynamic process responsible for droughts arising not only from external forcing but also those associated with internal dynamics. We show that most ISM droughts are associated with at least one very long break (VLB; breaks with duration of more than 10 days) and that the processes responsible for VLBs may also be the mecha- nism responsible for ISM droughts. Our analysis also reveals that all extended monsoon breaks (whether co-occurred with El-Nino or not) are associated with an eastward propagating Madden-Julian Oscillation (MJO) in the equatorial Indian Ocean and western Pacific extending to the dateline and westward propagating Rossby waves between 10� and 25� N. The divergent Rossby wave asso- ciated with the dry phase of equatorial convection propagates westward towards Indian land, couple with the northward propagating dry phase and leads to the suste- nance of breaks. Thus, the propensity of eastward propagating MJO during boreal summer is largely the cause of monsoon droughts. While short breaks are not accompanied by westerly wind events (WWE) over equa- torial western Pacific favorable for initiating air-sea interaction, all VLBs are accompanied by sustained WWE. The WWEs associated with all VLB during 1975-2005 initiate air-sea interaction on intraseasonal time scale, extend the warm pool eastward allowing the convectively coupled MJO to propagate further eastward and thereby sustaining the divergent circulation over India and the monsoon break. The ocean-atmosphere coupling on interannual time scale (such as El-Nino) can also produce VLB, but not necessary.

Laser mirrors in which the phase of the reflected wave front is variable over the surface of the optical element

This paper discusses the formation of the wave front of a reflected wave as a function of the character of the thickness distribution of the layers included in laser mirrors. It is shown that, if the thickness of the layers decreases from the center to the edge, a divergent or convergent wave is formed whose radius of curvature is determined by the number, refractive indices, and thicknesses of the layers, as well as by the thickness distribution of the dielectric layer(s) over the surface of the optical element and the number of gradient layers that form the reflecting coating.

Nonlinear spherically divergent shock waves propagating in a relaxing medium

The propagation of nonlinear spherically diverging N-waves in atmosphere was studied experimentally and theoretically. The relative effects of nonlinear, dissipation, and relaxation phenomena on the N-wave duration and amplitude were investigated based on the numerical solutions of the modified Burgers equation. It is shown that, under the experimental conditions, the duration of a pulse increases mainly due to nonlinear propagation, whereas the amplitude depends on the combined effects of nonlinearity, dissipation, and relaxation. The frequency response of the measuring system is obtained. The calibration of the amplitude and duration of the experimental waveforms is performed based on the nonlinear lengthening of the propagating pulse. The results of numerical modeling show good agreement with experimental data.