Divergent Waves Research Articles

Pressure Threshold for Shock Wave Induced Renal Hemorrhage

Studies were performed with an interest in determining a pressure threshold for extracorporeal shock wave induced renal damage. Histological evidence of intraparenchymal hemorrhage was used as an indicator of tissue trauma. Depilated C3H mice were anesthetized and placed on a special frame to enhance visualization and treatment of the kidneys in situ. A Wolf electrohydraulic generator and 9 French probe designed for endoscopic use were utilized to expose the kidneys to 10 double spherically divergent shock waves. Measurements of the shock waves revealed two positive pressure peaks of similar magnitude for each spark discharge. The kidneys were exposed to different peak pressures by choice of distance from the spark source and were removed immediately after treatment for histologic processing. A dose response was noted with severe corticomedullary damage apparent following 15 to 20 MPa shocks. Hemorrhage was more apparent in the medulla where evidence of damage could be seen following pressures as low as three to five MPa. When a latex membrane was interposed to prevent possible collapse of the initial bubble from the spark source against the skin surface, histological evaluation revealed substantial reduction of severe tissue damage associated with the highest pressures tested, 20 MPa. However, the threshold level for evidence of hemorrhage remained about three to five MPa. Hydrophonic measurements indicated that the membrane allowed transmission of the acoustic shock waves and suggested that collapse of the bubble generated by electrohydraulic probes may have local effects due to a cavitation-like mechanism.

航走波中における小型船の動揺と横転に関する水槽実験

A ship-generated waves, i.e., ship-waves, may very possibly be caused the capsizing or beamends to a small boat with poor stability. In this paper authors deal with some problems on the strong rolling of a boat in ship-waves from a viewpoint of manoeuvring. Main experimental results from model tests and actual ship tests are as follows, (1) The effect of ship-waves on the strong rolling of a boat is more of the divergent wave than the transevere wave, and the clear relations are observed between the magnitude of these wave height and the speed, boat-clearance, block coefficient of a sailing vessel. (2) The strongest rolling of a boat in the ship-waves causes in case that a boat is set on the direction line of cross angles 30°〜45° to the sailing line of a vessel. This result agrees approximately with the result of actual ship test. (3) When the head of a small ship with very lower freeboard and poor stability is set on the direction line of cross angles 60°〜90° to the sailing line of a vessel, the small ship get into quite frequently the beam-ends.

Three-dimensional wave patterns generated by moving disturbances at transcritical speeds

Disturbances in the form of pressure fields, source distributions and time-dependent bottom topographies are discussed and found to produce similar wave patterns. Results obtained for wide channels are discussed in the light of the features of soliton reflection at a wall. Comparison with experiments shows excellent agreement. The introduction of radiation conditions enables long-time simulation of the development of wave patterns in infinite and semi-infinite fluids. A stationary wave pattern is also found to emerge for slightly supercritical Froude numbers, but contrary to linear results the leading divergent waves may originate ahead of the disturbance. This behaviour is due to nonlinear interactions similar to those governing collisions between solitons. This study on wave generation by a moving disturbance is based on numerical solutions of Boussinesq-type equations. The equations in their most general form are integrated by an implicit difference method. Strongly supercritical cases are described by a simplified set of equations which is solved by a semi-implicit difference scheme.

30-50日周期波動の経年変動

In this observational study the 30-50 day motion fields, at 850mb and 200mb, for 1980 to 1984 are analysed using the synoptic approach. The present analysis examines their interannual variability.A similar analysis of the 30-50 day motion fields during the FGGE (1979) year showed, a) eastward propagating planetary scale divergent waves around the globe throughout the FGGE year at 200mb and b) a family of northward propagating trough and ridge lines over the MONEX region (30E-150E, 30S-40N) during the summer of 1979 at 850mb.We have performed a careful analysis of the sensitivity of the calculations of low frequency waves to the width of the time filter. Our results show that the phenomenon is quite robust and is not very sensitive to the width of the filters.The 850mb streamline-isotach analysis of the 30-50 day time scale waves over the MONEX region for the years 1980 to 1984 shows the northward propagating trough and ridge systems during May, June and July of 1982 and during May, June and July of 1983. The speed of northward propagation is approximately 0.7 degree latitude/day during the summers of 1979, 1982 and 1983. During the summer seasons of 1980, 1981 and 1984 the trough and ridge lines do not exhibit a steady northward propagation. The direction and the speed of propagation are found to be variable from month to month during these years. The trough and ridge systems during 1980 and 1981 are either stationary or show some northward propagation. During the summer of 1984 the propagation of the trough and ridge system is northward in May and June and southward in July and August.Interannually the onset and break periods of the Indian summer monsoon exhibit a close relationship to the passage of the 30-50 day trough and ridge systems over India.A global analysis of velocity potential at 200mb shows eastward propagating waves during 1979 and between October 1982 to October 1983. During the remaining period the direction of propagation is less well defined. The amplitude of the divergent wave is found to be variable from one year to the next. The 30-50 day wave motions exhibit a similar behaviour during 1979, 1982 and 1983, both at the 200 and the 850mb levels. 1982-83 was an El Nino year and 1979 was characterized by weak warm sea surface temperature anomalies of the order of 1°C over the eastern equatorial Pacific Ocean. Both of these years were characterized by deficient rainfall over India, with somewhat above normal rainfall over the region south of India.

The Bakerian Lecture, 1986 Ships from space

Narrow V-shaped wakes extending some 20 km behind surface ships were first found on Synthetic Aperture Radar(sar) images from SEASAT in 1978. The V-wake geometry differed strikingly from the traditional Kelvin wake geometry consisting of divergent and transverse wave components generated by a travelling pressure point. The sar images can be accounted for in terms of Bragg scatter from relatively short waves generated by the surface vessel. An essential ingredient of this hypothesis is that the wave generation is by an intermittent rather than a steady point source. Optical images from a hand-held camera on a 1985 space shuttle mission revealed many V-like wakes behind surface ships. There is no Bragg scattering from the ocean surface at optical wavelengths, so an alternative hypothesis is called for. We can interpret the observed features in terms of sun glitter from the tilted facets of a Kelvin wake. An essential ingredient is the generation by complex sources rather than by a single point source. We regard the present study as a step towards the interpretation of many unexplained naturally occurring features at the edge of the Sun glitter.

Holographic zone plates for f · θ and collimating lenses

A holographic zone plate generated by subtracting the spherical wave phase is proposed, that is, a hologram generated by using two divergent or convergent spherical waves. This holographic zone plate can correct the increase in focal power in a radial direction in contrast with the interferometric zone plate. Use of this holographic zone plate for f x O and collimating lenses is analyzed. For an f x O lens, it is shown that an optimum combination of recording spherical waves exists that satisfies both scan linearity and image field flatness. For a collimating lens for a laser diode, it is shown that aberration can be corrected for different playback wavelengths from that used during recording.

Wave drag of a membrane

The hydromechanical efficiency of swimming styles is of major interest in the theory of submarine animal locomotion. For larger species, a complication arises when the forward motion occurs near the surface where gravity waves are generated. Near-surface activities of aquatic and other animals, including man, can be difficult to model successfully; for example, an anguilliform motion with an associated divergent wave system appears computationally unpromising. However, for many seagoing creatures the forward thrust is derived from dorsiventral undulations of the caudal region, as in the Cetacea, and these movements are simulated by the motions of a shallowly submerged horizontal membrane. Based upon a two-dimensional linearized inviscid theory, an expression is found for the drag for a general flexing of the membrane with a given frequency. Some numerical results are presented graphically for threshing flexures with exaggerated tail movements intended to partly imitate carangiform or ostraciiform propulsion. The excitation of transverse waves might be expected to impede the forward propulsion, suggesting that maximum efficiency would occur when wave making is least. It is shown that this is not necessarily true because the longer waves supply a forward thrust. For a given maximum amplitude of flexure this is often a weaker force, but in terms of hydrodynamic efficiency it can rival the thrust from the wake at higher frequencies. A corresponding formula for the power is also derived; in particular this shows that energy may be extracted from a mainstream flow with a free surface by oscillations of a hydrofoil that generates shorter waves.

Encoding apparatus having an acoustic member with mirror-image tabs

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Influence of hydroacoustic perturbations of the active medium upon the divergence of liquid-laser radiation

uced) divergence could not be reached. The optical inhomogeneity of the dye solution or inhomogeneity of its excitation are the possible reasons. Hydroacoustic perturbations of the active medium of the dye laser, which are caused by inhomogeneity of the pumping over the cuvette cross section [4, 5], are one of the inevitable reasons for optical inhomogeneity of the solution. We consider in the present work the influence of hydroacoustic perturbations of the active medium upon the divergence of the radiation of a pulsed dye laser with an unstable confocal reasonator (see Fig. i). In general, the emission pattern of a laser with annular outputting in single-mode operation is determined by the diffraction of a divergent wave (or a plane wave when confocal conditions exist) at the edges of the aperture and by additional phase runs kA which change during the generation pulse and are caused by nonstationary inhomogeneities of the medium. Since the perturbations to be expected in the density of the medium are small, the well-known "aberration" approximation [6, 7] can be used to calculate the influence of the perturbations upon the divergence. When the problem is assumed tohave axial symmetry and when the amplitude factor in the diffracted wave is disregarded as less important than the phase factor, the total emission pattern l(e) during a generation pulse is given by the formula

Generation and propagation of the coherently scattered boundary wave over a ridge

Recent theoretical studies by I. Tolstoy and experiments by H. Medwin and co‐workers have shown that a low‐frequency sound at near grazing incidence to a surface of rigid hemispherical bosses generates a coherently scattered boundary wave which can be much larger than the spherically divergent direct radiation wave. In the present experiment the axial grazing diffraction of the boundary wave over a slightly rough wedge is measured. Two components of the boundary wave are identified in the shadow region of the wedge: one (RS) develops along the rough upslope then diffracts over the crest in the same manner as the volume wave; the ratio of this boundary wave amplitude to the volume wave amplitude (BWA/VWA) grows as range r01/2 upslope and is constant with increasing range r beyond the crest. The other component (SR) is generated by the diffracted volume wave along the rough downslope and BWA/VWA grows initially as range r0.6 from the crest. For both components the amplitude ratio has a frequency dependence ∫2. Low wave‐number grazing propagation over a rough wedge thereby produces a boundary wave in the shadow region whose amplitude can be several times greater than that of a diffracted volume wave over a smooth wedge. [Work supported by Office of Naval Research.]

Divergent Barotropic Instability of the Tropical Asymmetric Easterly Jet

The divergent barotropic instability of a zonally averaged, observed, tropical, upper tropospheric, monsoon easterly jet is investigated by numerical integration of a linear spectral model. The Rossby radius of deformation for the upper troposphere is computed from a three-layer model of the atmosphere. It is shown that the antisymmetric zonal flow components in the jet contribute in stabilizing the short waves and destabilizing the long waves. Furthermore, the maximum amplitude of the asymmetric preferred wave is shifted southward (to 6°N) to a region where a largest positive maximum of −ūvv is located for the asymmetric profile. A large decrease in the meridional scale of the wave and a threefold increase in the ratio of the computed maximum southward-to-northward easterly momentum transports is also found for the asymmetric jet compared to the symmetric jet. The divergence is found to increase the growth rates of all the waves and, also to increase the preferred wavelength. The most unstable divergent asymmetric wave is shown to have a wavelength of 6500 km, an e-folding time of 6.5 days and a westward phase speed of 23.5 m s−1. The zonal scale of the preferred wave is nearly equal to the Rossby radius of deformation.

Dark waves in liquid homogeneous explosives with unstable detonation front

An explanation is given of the detailed mechanism of the divergent and convergent dark waves that originate at the charge boundary in detonating liquid homogeneous explosives with unstable detonation front. The mechanism involves the propagating failure wave that transmits the breakdown of the chemical reaction, and two different propagation modes for spreading the reinitiated detonation into the charge. Experiments with artificially induced divergent dark waves show that there are three different induction times for the reinitiating adiabatic thermal explosion. The size of a boundary irregularity in relation to the pertinent induction time is shown to be the controlling parameter that decides what kind of dark wave will result. The conditions for transition from convergent to divergent dark wave are given with reference to experiments that demonstrate the transition. The boundary-induced dark waves traverse the charge and become part of the general pattern of transverse reaction breakdown and reinitiating triple waves that are inherent in the normal process of propagation of a detonation with unstable front.

Punctual Padé approximants as a regularization procedure for divergent and oscillatory partial wave expansions of the scattering amplitude

Previous theorems on the convergence of the [n,n+m] punctual Padé approximants to the scattering amplitude are extended. The new proofs include the cases of nonforward and backward scattering corresponding to potentials having 1/r and 1/r2 long-range behaviors, for which the partial wave expansions are divergent and oscillatory, respectively. In this way, the ability of the approximation scheme as a summation method is established for all of the long-range potentials of interest in potential scattering.

Wavefront conversion by volume holograms between cylindrical and plane waves

The efficiency of lossless volume holograms in converting plane and cylindrical waves into each other is analysed and the results are plotted as a function of the normalised thickness of the hologram. A coupler consisting of two separate holograms, and capable of converting a divergent cylindrical wave into a convergent cylindrical wave, is also investigated, and it is shown that under favourable conditions an overall efficiency of 98.3% may be obtained.

Electromagnetic contributions to the nucleon-nucleon interaction

The helicity amplitudes of the nucleon-nucleon one-photon exchange interaction are calculated. The anomalous magnetic moments of the proton and neutron are included in the calculations. The formalism is especially suitable for the small angle proton-proton interaction at intermediate energies. The electromagnetic phase shifts in the Born approximation are defined and calculated. The three cases of the proton-proton, the neutron-proton and the neutron-neutron interactions are dealt with separately. Analytic expressions are given for sums defined by divergent partial waves. We indicate the pecularities of the neutron-proton interaction: the singlet-triplet transitions and the t −1 singularity in the differential cross section. These peculiarities require an improved treatment of the neutron-proton interaction. A modified formalism is suggested.

Resolving power of a parametric image converter in the case of a nonmonochromatic signal and a divergent pump wave

Numerical methods are used to find the form of the scatter function and the resolving power of a parametric image (frequency) converter in the case of a nonmonochromatic signal and of a divergent and nonmonochromatic pump wave.

Long period divergent planetary waves

Abstract A simple first order perturbation procedure is used to obtain an equation for divergent planetary waves when the period is much greater than the pendulum day. For unbounded regions the equation is the s2me as one derived by Longuet-Higgins (1965), but in bounded basins it is different. As an example, the eigen frequencies of a rectangular basin are calculated for a number of values of the parameters. The energy density of planetary waves is also considered with results which correct those of Buchwald (1972) in the case of bounded basins.

Scalar Rayleigh–Sommerfeld and Kirchhoff diffraction integrals: A comparison of exact evaluations for axial points*

The second Rayleigh–Sommerfeld (RS) diffraction integral, wherein the normal derivative is specified, is evaluated in simple closed form for all axial points when a divergent or convergent spherical wave is incident upon a circular aperture or disk. These evaluations (solutions) are compared with known corresponding solutions of the first RS diffraction integral. These sets of solutions are intercompared with their mean value, i.e., the derived solutions of the Kirchhoff diffraction integral. The three diffraction formulations are shown to be in agreement for incident divergent spherical waves when the source and observation points are equally distant from the aperture or disk. Conversely, for convergent spherical waves, the three formulations are never in exact agreement for focal and observation points located at finite distances from the aperture, though at optical frequencies the relative error at the geometric focal point is vanishingly small. The second RS formulation predicts, in the limit of plane waves incident on a disk, that the axial irradiance is everywhere equal to the incident irradiance, whereas the first RS formulation predicts that the irradiance goes to zero at the back of the disk.

Experimental analysis of spherical wave propagation

Analyses coupling in-material stress and particle velocity gage measurements with the equations of hydrodynamic flow are presently used for determining stress-volume paths during transient one-dimensional plane wave propagation in solids. In this work a method is described that allows analysis of attenuating experimental wave profiles of arbitrary shape in spherically symmetric flow. The method is applied to radial stress and particle velocity data for spherically divergent wave propagation in Westerly granite. The resulting relations among pressure, volume, and deviatoric stress are compared and are found to be consistent with other available data on Westerly granite. It is concluded that the analysis promises to be a useful tool for relating observed wave structure to physical processes occurring in the material and for developing better constitutive relations to predict the transient dynamic behavior of material.

Energy and energy flux in planetary waves

The propagation of planetary waves on a sphere and on a β plane has been extensively studied by Longuet-Higgins (1964 a , 1965), in connexion with problems concerning the long period oscillations of the atmosphere and oceans. However, the concepts of energy and its propagation in planetary waves is not well understood, and in this paper we make a thorough study of the energy of these waves in the β plane approximation with constant depth. In the case of non-divergent waves on a β plane, two energy conservation equations are derived, both of which are consistent with energy flux in the direction of the group velocity c g . The total energy density E of a plane wave is shown to be the sum of the kinetic energy density T and a ‘ Rossby energy ’ density V , where V = - 1/2 ρβψn ψ is the stream function, and rj the northward particle displacement. The principle of virtual work is used to derive a similar result for a basin enclosed by rigid walls. The flux of E is given by Ec g , and the equipartition principle T = V = 1/2 E is observed. The results are extended to the case of divergent planetary waves, the total energy density being E = T + U + V , where U = ( f 2 / gh )ψ 2 and T + U = V = 1/2 E A special case of reflexion of a plane wave at a straight wall is discussed at the end of the paper. It is shown that ψ* = a exp (iω t ) is a non-trivial solution of the non-divergent planetary wave equation. In certain cases, ψ* is needed to represent waves which are incident to or reflected from the wall.