Showing papers on "Phase velocity published in 1975"

Polarization changes of geomagnetic Pi 2 pulsations associated with the plasmapause

Abstract: The polarization characteristics of substorm-associated Pi 2 pulsations are studied in detail on statistical and nonstatistical bases by using magnetic data from a network of stations (L = 3.2–4.4) along a geomagnetic meridian and a conjugate station (L ∼ 4) in the southern hemisphere. The predominant periods in the Pi 2 wave trains are usually constant at all latitudes, whereas the polarization characteristics of the predominant oscillations change drastically among the stations. That is, reversals of the sense of polarization between two stations were often observed. Such polarization reversals result from the latitude dependence of the wave phase: the D (azimuthal) pulsation components oscillate in phase at all stations, whereas the oscillations in the H (north-south) components have large phase shifts among the stations. The H component phase shift is often 180° between Durham (L = 3.2) and Lac Rebours (L = 4.0). A satellite measurement of the plasmapause location during one Pi 2 event showed that the large H component phase shift occurred near the plasmapause. Therefore the Pi 2 oscillations, which are originally excited at high latitudes in the magnetosphere, apparently couple to the shear Alfven waves of the resonant local field lines at the plasmapause because of the sharp decrease in the wave phase velocity just inside the plasmapause. This result suggests the possibility of determining the location of the night side plasmapause by monitoring the polarization changes of Pi 2 pulsations along a geomagnetic meridian. The Pi 2 data from the conjugate pair stations showed that the H components oscillate in phase, whereas the D components oscillate out of phase. Therefore it is concluded that the Pi 2 waves observed near L = 4 can be characterized as odd mode standing Alfven waves.

Variation of the Kuroshio south of Japan

Abstract: The variations of the velocity and path of the Kuroshio are investigated by using the data obtained after the World War II. The time scales of these variations are classified into three categories,i.e. long-, medium- and short-terms. Period of the long-term variations seems to be about 7 to 9 years. Large meanders of the Kuroshio off Enshu-nada in 1953–1955 and 1959–1962 are accompanied with the low mean velocity of the Kuroshio. These large meanders are explained as a stationary Rossby wave by applying the equation for the phase velocity of the barotropic Rossby wave with the disturbance of finite width. To obtain the above conclusion, it is assumed that the Kuroshio extends down to the depth of 2,300 db and that the east component of the over-all mean velocity of the meandering Kuroshio should be substituted for the velocity of the eastward basic current in the above equation. As for the medium-term variation of the Kuroshio, there seems to exist variations in the velocity with the periods of 4, 6, 8 and 12 months and those in the position of the Kuroshio axis with the periods of 8 and 12 months. These meanders of the Kuroshio progress towards east with the mean phase velocity of about 5 miles a day, which is nearly the same as the calculated mean phase velocity of a progressive Rossby wave.

Higher Rayleigh modes in western Europe

Abstract: An array of standard long period stations is applied to measure phase velocities of seismic surface waves by way of frequency-wavenumber analysis. The number of interfering modes is reduced by windowing the signal for successive group velocity intervals. The method is powerful, even with relatively small arrays: up to 6 higher Rayleigh modes at periods between 20 and 100 sec. have been resolved.

The effect of the gradient drift term on type 1 electrojet irregularities

Abstract: We hypothesize that type 1 VHF radar echoes can only be observed when the electrojet plasma is linearly unstable at half the radar wavelength and that further, for reasons not yet understood, the phase velocity of the unstable waves always corresponds to the threshold conditions for instability, even when the destabilizing forces (electron drift and plasma density gradient) exceed the threshold. This phase velocity, which produces the Doppler shift of the radar echoes, is usually close to the ion acoustic velocity of the medium but can differ from it to some extent because of the effect of the density gradient. This difference can be positive or negative, is proportional to λ², and can be substantial at night, when the vertical density gradients in the equatorial E region are large and variable. Nighttime equatorial radar observations do seem to indicate considerable variability in the type 1 velocity. These effects may also be important in explaining auroral radar observations.

A theory of auroral hiss and implications on the origin of auroral electrons

Abstract: A theory for auroral hiss is developed based on the existence of a beam of energetic particles that is also believed responsible for the visual aurora. A dispersion relation for electromagnetic waves in a plasma consisting of an electron beam and a background plasma is derived. The Hermitian part of the dispersion relation is assumed to be governed by the denser cold background plasma, whereas the anti-Hermitian part is governed by the electron beam. It is shown that the electron beam can excite an electron whistler mode instability near the resonance cone by the Landau interaction because near the resonance cone the phase velocity of the wave can be made arbitrarily small. The instability can be excited at all frequencies between the lower hybrid resonance and the electron plasma frequencies. The wave normal angles along the resonance curve vary between 0° and 90° with respect to the magnetic field. Waves whose wave normal angles are small have the largest growth rates and are most likely to grow to observable amplitudes. Only waves generated within a few degrees of the vertical can reach the ground. The results of the calculations are applied to auroral hiss observations. From the fact that auroral hiss is observed on the ground at frequencies less than 10 kHz it is concluded that at least some of the auroral hiss is generated at altitudes where the ambient electron density is of the order of 1 cm−3. This suggests that auroral electrons are energized in regions where the ambient density is of the order of 1 cm−3 or less.

Parallel propagation effects on the type 1 electrojet instability

Abstract: The Farley-Buneman instability has been extended to consider higher-frequency shorter-wavelength modes (thus including finite Debye length effects), and these modes are allowed to propagate with a com- ponent parallel to the magnetic field (k  0). When the current is driven sufficiently hard (drift speeds in the range 2-3 times the ion thermal velocity o), the growth rates of these modes maximize slightly away from the perpendicular to the magnetic field, and thus the importance of k  0 is shown. Although the wavelengths of these maximum growing modes are in the regime of tens of centimeters, the phase velocities are closer to the ion thermal ¾elocity than those modes propagating at 90 o (k = 0). Maximum growth rates of off-angle p{opagation for different densities and collision frequencies are sh6wn. Also, growth rates o'f unstable waves in the radar regime (1-10 m) are shown for drift velocities 1.5v, and 3v. These also maximize with k  0 and have phase velocities closer tothan they have for purely perpen- dicular propagation. In all cases considered the phase velocity of the waves is a rapidly decreasing func- tion of angle as one moves away from pure perpendicular propagation. Observations of backscattered radar signals from the equatorial electrojet have provided the impetus for substantial theoretical research on the source of the density fluctuations that can provide the observed enhancements in the received signals. There is general agreement that the source of the den- sity fluctuations is an electron current across the magnetic field produced by E x B type particle drifts due to the disparity in the electron-neutral and ion-neutral collision frequencies (Farley, 1963a, b). Since the relative drifts produced are of the order of the ion sound speed vand since the electron and ion temperatures Te, are equal, the system would have been linearly stable to ion sound on collisionless time scales. However, for collisional time scales the system becomes un- stable to low-frequency long-wavelength modes (Bunernan, 1963). The nature of this instability is purely resistive. That is, the resistive medium extracts energy from the ion drift and transfers it to the negative energy wave (slow wave) associated with the drifting ions. This instability has been examined first by Farley (1963a, b) for a kinetic plasma and subsequently by Bunernan (1963) in the fluid approximation. In Farley's kinetic description, which neglected finite Debye length effects (kXo - 0), it was shown that the important modes were perpendicular,to the magnetic field. Lee et al. (1971) have extended Farley's results by in- cluding Debye length effects and found higher-frequency shorter-wavelength instabilities. Their calculation was restricted to modes propagating exactly perpendicular to the magnetic field (k = 0). Very recently, Lee and Kennel (1973) have considered a simple parallel propagation effect analysis on type 1 instabilities in the fluid limit, and they note that these modes may be more unstable than those that propagate across the magnetic field. Recent theoretical results (Krall and Liewer, 1971; McBride et al., 1972) have shown that even for a collisionless plasma with TeT, a current perpendicular to the magnetic field produces an instability with small but finite k (k/k  (rne/m)/'). This instability, usually called the modified two- stream instability, is a strong reactive type instability, and non- linear considerations show that one has to go to the strong- turbulence regime for saturation. We therefore feel that an examination of whether and when such modes (k,  0) be- come unstable in the electrojet is necessary before going to the

A new method of measuring propagation coefficients and characteristic impedance in blood vessels.

Abstract: True propagation coefficients of pulse wave harmonics in an artery can be determined in vivo by measuring pulsatile blood pressure and flow at each of two points along the length of the vessel. These coefficients, which are complex numbers that describe the attenuation and the phase shift imposed on a traveling wave, are independent of the reflected waves in the circulation and thus provide information about the viscoelastic state and other properties of an artery. The equations involved are implicit in standard transmission-line theory, but they have not previously been applied in this particular way to blood vessels. The femoral artery, exposed in situ, was studied in 11 anesthetized dogs. At 1.5 Hz, true attenuation constants averaged 0.0151 nepers/cm, and true phase constants averaged 0.0155 radians/cm. As frequency increased, the apparent phase velocity of flow, in contrast, was relatively low at the first harmonic and rose as frequency increased. True phase velocities lay between the apparent pressure and flow values. Characteristic impedance at 1.5 Hz had an average modulus of 1.76 times 10-4 dyne sec/cm5 and a phase of minus 0.31 radians. The modulus diminished as frequency increased, and the phase became less negative. These results show that true phase constants and characteristic impedances determined by this method are consistent with data reported by others and provide information not previously available about flow wave propagation.

Tidal effects in the E region from incoherent scatter radar observations

Abstract: Measurements of the neutral temperature in the altitude region 100 to 130 km during the past several years at Millstone Hill (42$sup 0$N) and St. Santin (45$sup 0$N) have revealed that, on the average, there exist strong semidiurnal tidal effects which can be identified with the (2,4) tidal mode propagating from the stratomesosphere. The average amplitude of the temperature oscillation reaches a maximum of about 35 K at 116 km with maxima at 0630 and 1830 hr LT. At each station, large variability is found in amplitude and phase from one observing period to another, particularly during winter. The average temperature behavior implies a semidiurnal zonal wind oscillation with an amplitude of about 45 m sec$sup -1$ at 110 km having eastward maxima at about 0500 and 1700 hr LT, and a meridional component with similar amplitude having southward maxima at 0800 and 2000 hr LT. The downward phase velocity is about 4 km hr$sup -1$. These results are in good agreement with direct wind measurements at St. Santin, and with some recently reported characteristics of the height variations of sporadic-E at midlatitudes. At Arecibo (18$sup 0$N), semidiurnal oscillations have also been found to dominate the E-region temperature and windmore » structure with similar amplitude and phase velocities as above; however, the observed phase behavior is more variable than at midlatitudes and the average results do not allow reliable mode identification. Some results of recent simultaneous observations at low and midlatitudes are presented which imply that during any particular observing period, the E-region structure must be controlled by local effects. (auth)« less

Onset, growth, and saturation of the current‐driven ion cyclotron instability

Abstract: The temporal evolution of the current‐driven electrostatic ion cyclotron instability was investigated experimentally. The critical destabilizing electron drift velocity for different values of mode phase velocity was measured. The phase velocity was changed by varying the effective plasma column length and hence the parallel wavelength. Ion cyclotron damping was observed to dominate over electron Landau damping at low phase velocities. The temporal growth rate was experimentally determined for several values of electron drift and found to agree very well with linear theory. The observed saturated mode amplitudes compare favorably with the saturation levels predicted by a theory of nonlinear stabilization due to wave induced collisions.

Phase and amplitude relationships of wave structure observed in the lower thermosphere

Abstract: Data from the Atmosphere Explorer-C satellite clearly exhibit wavelike variations in neutral composition, ion density, and electron temperature, which appear to be a general feature of the atmosphere. The neutral constituents do not exhibit uniform wave characteristics since the density variations of argon are approximately twice those of molecular nitrogen and helium structure has about one-half the amplitude of the N2 variation. The waves evident in the ion density are nearly in phase with the heavy neutrals, while the electron-temperature variations are predominantly out of phase with those in the ion density. A simple model is suggested to explain the neutral composition results, wherein the enhancements in the major gas densities are in phase with the vertical component of the perturbation velocity of the gas. The vertical velocity modifies the composition by transporting parcels of air to higher or lower regions where the composition is different. The phase relationship between density and velocity implies phase velocities (assuming that these are gravitational waves) of the order of 500 meters per sec.

A new method for the analysis of multi-mode surface-wave dispersion: Application to Love-wave propagation in the east Pacific

Abstract: A new technique is presented for simultaneously measuring the average, regional phase velocity of two or more surface-wave modes, even if they travel with the same group velocity. Many observations are required over paths of varying length with earthquake sources of known focal mechanism. The phase of the signal observed at each station can be predicted if the initial phase of the source and the phase velocity and relative amplitude of each mode is known. The square of the difference between the observed phase and the predicted phase is summed over all paths for a set of trial phase velocities. The trial velocities which give the minimum sum correspond to the average phase velocity of each mode. By applying this technique to Love-wave data from the east Pacific, the dispersion of the first higher Love mode was measured for the first time in an oceanic area. The phase velocity of the fundamental mode was found to increase with increasing age of the sea floor, probably as a result of the cooling of the oceanic lithosphere. The region was found to be anisotropic for Love-wave propagation, with the fastest velocities roughly perpendicular to the ridge. The degree of anisotropy appears to increase with increasing period.

Experimental evidence on the mechanism for the instability of flow in collapsible vessels.

Abstract: Results are presented showing that the instability of flow observed in collapsible vessels can be associated with the fluid velocity approaching the phase velocity in a narrowed segment of the vessel. Phase velocity is measured using capacitance displacement transducers, and is found to vary with frequency and with the state of collapse, reaching a minimum just prior to when opposite sides of the vessel come into contact. The mean fluid velocity is calculated from the measured area-pressure relationship for several values of flow in the range associated with instability. It is found that the mean fluid velocity and phase velocity curves intersect at the flow corresponding to instability, provided that transmural pressure is less than zero. A simple formulation is proposed to predict the critical flow at which this instability can develop.

Boundary effects on M=0,±1 Alfvén waves in a cylindrical, collisionless plasma

Abstract: The dispersion relations for Alfven waves with exp(jmϑ) azimuthal dependency are calculated for a cylindrical, cold, collisionless plasma. If the electron inertia term is included in the dielectric tensor, then, in a bounded plasma, there are two transverse wavenumbers for each axial wavenumber. The phase velocities for m=0, ±1 fast and slow waves are calculated for different vacuum thicknesses between the uniform plasma and the metal walls. It is found that m=0 and −1 fast waves each experience a cutoff below a given frequency, but the m=+1 fast wave can propagate even at very low frequencies provided the vacuum layer is of sufficient thickness. The calculations are shown to agree with previously reported experimental results.

Heated electron distributions from resonant absorption

Abstract: A simplified model of resonant absorption of obliquely incident laser light has been developed. Using a 1.5 dimensional electrostatic simulation computer code, it is shown that the inclusion of ion motion is critically important in determining the heated electron distributions from resonant absorption. The electromagnetic wave drives up an electron plasma wave. For long density scale lengths (L≃103λDe), the phase velocity of this wave is very large (ω/k≳10Vth) so that if heating does occur, a suprathermal tail of very energetic electrons is produced. However, the pressure due to this wave steepens the density profile until the density gradient scale length near the critical density (where the local plasma frequency equals the laser frequency) is of order 20λDe. The electrostatic wave is thus forced to have a much lower phase velocity (ω/k≃2.5Vth). In this case, more electrons are heated to much lower velocities. The heated electron distributions are exponential in velocity space. Using a simple theory it ...

Critical-level behaviour and wave amplification of a gravity wave incident upon a shear layer

Abstract: The properties of reflexion, refraction and absorption of a gravity wave incident upon a shear layer are investigated. It is shown that one must expect these properties to be very different depending upon the parameters (such as the Richardson number Ri, the wavelength normalized by the length scale of the shear and the ratio of the flow speed to the phase speed of the wave) characterizing the interaction of a gravity wave with a shear layer. In particular, it is shown that for all Richardson numbers there is a discontinuity in the net wave-action flux across the critical level, i.e. at a height where the flow speed matches the horizontal phase speed of the wave. When Ri > ¼, this is accompanied by absorption of part of the energy of the incident wave into the mean flow. In addition it is shown that the phenomenon of wave amplification (over-reflexion) can arise provided that the ultimate shear flow speed exceeds the horizontal phase speed of the wave and Ri is less than a certain critical value Ric ≃ 0·1129, in which case the reflected wave extracts energy from the streaming motion. It is also pointed out that wave amplification can lead to instability if the boundary conditions are altered in such a way that the system can behave like an ‘amplifier’.

Several effects of baroclinic currents on the three‐dimensional propagation of inertial‐internal waves†

Abstract: A ray theory is applied to the problem of three‐dimensional propagation of inertial‐internal waves in the presence of a mean baroclinic current which does not vary in the downstream coordinate. As time increases, the Doppler‐shifted wave frequency, or intrinsic frequency, tends to a limiting value determined by the horizontal and vertical variations of the mean current and density fields. The limiting value of the intrinsic frequency determines critical surfaces where energy is transferred to the mean motion. Also, the group velocity tends to the mean current velocity, and the phase velocity tends to be oriented towards or away from the core of the mean current, depending upon whether the wave is either initially propagating with a wave number component antiparallel or parallel to the mean current.

Momentum modulation of a free electron beam with a laser

Abstract: A Nd : YAG laser has been used to modulate the energy of a free electron beam. With a single pass of the 2−MW laser light through the 100−MeV electrons we have measured a 37−keV increase in the width of the energy spectrum for the particles. The interaction occurred in helium at standard temperature and pressure over a distance corresponding to 105 optical wavelengths, and a phase synchronism condition was maintained by means of the inverse Cerenkov effect. That is, along the direction of motion of the electrons the phase velocity of the electromagnetic wave equaled the electron velocity. Therefore, the electrons remained in an electric field of constant phase, resulting in significant energy exchange.

The correction of great circular surface wave phase velocity measurements for the rotation and ellipticity of the Earth

Abstract: Normal mode perturbation theory is combined with a geometrical optics approximation in order to establish a procedure for correcting great circular Love and Rayleigh surface wave phase velocity measurements for the effects of the rotation and the hydrostatic ellipsoidal shape of the earth. The necessary correction can be made by utilizing in the measurement process an apparent path length Lapp(T, Θ) for great circular propagation of surface waves of period T around any path with a positive pole inclined at an angle Θ to the rotation axis of the earth. The apparent great circular path length Lapp(T, Θ) is given by Lapp(T, Θ) = 2πa[1 - χ1(T) cos Θ - χ2(T)(1 - 3 cos2 Θ)], where a is the mean radius of the earth and χ1(T) and χ2(T) can be expressed, respectively, in terms of the normal mode multiplet rotational and elliptical splitting parameters of the earth. For some models of the earth, especially those having sharp discontinuities or steep gradients in radial structure in the upper mantle, the apparent path length Lapp(T, Θ) appropriate to fundamental long-period Love and, especially, Rayleigh waves can differ from the actual path length by several tenths of a percent, in which case the need for correction becomes real.

Acoustic oscillator fluid velocity measuring device

Abstract: A fluid velocity measuring device for the accurate fast measurement of the velocity of a fluid whether liquid or gas using the time of passage of acoustic energy through the fluid as the frequency determining element in a continuous wave oscillator. The frequencies or periods of oscillations of two anti-parallel acoustic paths are used to compute fluid velocity between the electro-acoustic transducers at the ends of the acoustic paths. The device in accordance with this invention may utilize a single reversing acoustic path or two anti-parallel acoustic paths. The velocity resolution can be selected by the operator in accordance with a stated uncertainty principle limiting the ratio of frequency response to velocity resolution. Mode ambiguities due to fluid phase velocity variations are avoided by varying the path lengths. The frequency range of the oscillator is limited by a phase locked loop.

The long-period internal waves in Lake Biwa

Abstract: The long-period internal wave in a two-layered model of Lake Biwa is treated numerically by the USC of linear hydrodynamic difference equations for the equivalent volume transport rate and elevation. Fourier analysis for the calculated time series of the interface at 29 sampling points in the model lake shows that the wave of the fundamental mode has a period of 66.1 h, about tbc same as the period of longitudinal internal seiches without the effect of the earth’s rotation, and that the wave progresses along the shore in a countcrclockwisc direction with an apparent phase velocity of about 1.5 km h-l. Such rotatory behavior of the internal wave is consistent with the results of spectral analysis of the temperature records and with the result of an approximate analytical solution of the two-layered-rotating rectangular lake. Lake Biwa, the largest lake in Japan, has an area of 674 km2, a length of about 60 km, and a maximum depth of 110 m (Fig. 1). IIeating of the surface layer by solar radiation makes remarkable growth of the thermocline in this lake during early summer to late autumn and the density of the water becomes less in the upper layer than in the deeper layer. The density distribution in the lake during the season of thermal stratification can be considered to approximate a two-layer structure. Kanari ( 1970) considered the internal seiches in Lake Biwa to be a simple longitudinal standing oscillation because the observed period seemed to agree well with the predicted one through the equation

Baroclinic instability of stratified shear flows in the ocean and atmosphere

Abstract: As an extension of Eady's model, two new baroclinic models are studied in this paper: Model 1 consists of a layer with constant shear surmounting a quiescent layer, and model 2 consists of a more statically stable uniform layer of constant zonal flow surmounting a layer with constant shear. In model 1 two special cases are considered, one in which the upper shear layer is more stably stratified than the lower quiescent layer (1a) and another in which the upper layer is less stably stratified than the lower layer (1b). The stability properties of model 16 and model 2 turn out to be very similar, since for the same shear, depth ratio, and static stability ratio the growth rates are the same and the wave structure of model 1b is the symmetric image of that of model 2. The wavelengths of the stability cutoff wave and the most unstable wave and the growth rate of the most unstable wave are considerably influenced by the presence of a quiescent layer in model 1a but are only moderately influenced by this quiescent layer in model 1b or by the uniform layer in model 2. The unstable wave moves eastward with a velocity slower than that of the vertically averaged mean current in the shear layer in model 1 but faster than the mean current in the shear layer in model 2. The deviation of the phase velocity from this mean current becomes larger the longer the wave. Typical parameters for an oceanic current system, such as the Gulf Stream, are applied to model 1a, and typical parameters for an atmospheric mid-latitude zonal flow are applied to model 2. The implications regarding long waves are that just as the long atmospheric waves penetrate the tropopause into the stratosphere, so the long oceanic waves penetrate the base of the thermocline to great depths, although the horizontal scales for the two systems are considerably different.

Measurements of ion wave turbulence by microwave scattering

Abstract: Ion wave turbulence spontaneously excited in a current‐carrying plasma is investigated by the microwave scattering method. The dispersion relation, the wavenumber spectra, and the angular spectra of the ion wave turbulence are determined from the angular distribution of the scattered wave. The wavenumber spectrum has a peak around k ≃ νin/ vp, and decreases as k−4.8±0.5 with increasing k, where νin is the ion‐neutral collision frequency and vp is the phase velocity of the ion wave. The angular spectrum of the wave energy is found to broaden as the total wave energy, W, increases along the electron drift. The effective collision frequency, νf, for electrons is also measured by the rf probe method as well as the dc method. An anomalous increase in νf is observed with the increase in W along the electron drift. The present experimental results are consistent with the theory of perturbed ion orbits.

on a crossed field two-stream plasma instability in the auroral plasma

Abstract: This paper presents a detailed analysis of the Buneman-Farley two-stream plasma instability. We use a fluid plasma model appropriate for the E region ionosphere, including the effects of the geomagnetic field and electron and ion temperatures and their collisions with neutrals. We derive a linearized dispersion equation for the coupled electron thermal wave and ion thermal wave. The results are compared with those derived from a kinetic theory. It is shown that in the long-wavelength limit the agreement between the above described fluid theory and kinetic theory is exact. The physical arguments for the agreement are clearly stated. From the dispersion equation we obtain closed form expressions for the phase velocities, frequencies, and growth rates describing the threshold condition and the unstable region. With these closed form results we are able to determine the physical behavior of the instability under a variety of ionospheric conditions. The closed form results show that unstable plasma waves having the maximum growth rate propagate at finite off-perpendicular angles with respect to the geomagnetic field. This property, together with the fact that the two-stream instability is a convective instability, is used to infer that radar auroral echoes scattered from these waves should occur at finite off-perpendicular angles. Spatial maps of radar auroral echoes obtained with a 1210-MHz backscatter radar at Homer, Alaska, are presented as supporting evidence. By taking data during different magnetic conditions, we were able to exclude magnetic field line distortion as a possible contributing factor.

The theoretical time-dependent behavior of a Münch pressure-flow system: the effect of sinusoidal time variation in sucrose loading and water potential

Abstract: Using the iterative model for the Munch pressure-flow mechanism derived by Christy and Ferrier (1973), the theoretical time-dependent behavior of the Munch pressure-flow system in a 15-m tree is computed in response to sinusoidal time variation in sucrose loading and water potential. Our calculations predict a "concentration wave" moving down the transport path of the type reported by Huber et al. (1937) in Quercus borealis L. The "waves" move with a phase velocity (= 3.5 cm min−1) greatly in excess of the velocity of the sieve-tube solution (= 0.4 cm min−1). It seems very likely that Huber et al. (1937) measured a phase velocity and erroneously interpreted it as the true solution velocity.

Gaussian‐Laguerre/Hermite formulation for the nearfield of an ultrasonic transducer

Abstract: The orthonormal sets of functions known as Gaussian‐Laguerre and Gaussian‐Hermite functions (G‐L/H) have previously been used in quantum mechanisms, electromagnetic waves, and laser optics. These functions satisfy a modified Helmholtz equation which amounts to a Fresnel approximation. Experimental mappings of sound fields using liquid crystals suggest that the problem of the nearfield of an ultrasonic transducer can be rendered in terms of these functions. This field can be expressed as a linear combination of modes, each described by a (G‐L/H) function. Each mode has a slightly different phase velocity in the nearfield but has the same spreading nature and phase velocity in the farfield. By using this formulation, the transition from nearfield to farfield is readily explained.

Current status of the electrodynamics of moving media (infinite media)

Abstract: Recently there has been an increase of interest in the electrodynamics of moving media. This is primarily due to the emergence of new experimental possibilities. High-current accelerators give dense beams of relativistic electrons or of plasma cluster. In addition, moderating structures exist in which the velocity of propagation of electromagnetic waves is much less than the velocity of light in a vacuum, and this facilitates observation of relativistic effects. These successes have rendered realistic the consideration of a whole number of applications. These include the amplification of electromagnetic waves and the augmentation of frequency by reflection from interfaces with moving media, and also the diagnostics of material flows. Various astrophysical and ionosphere applications are of interest. In this review, the fundamental equations of the electrodynamics of moving media are presented. The treatment is carried out by the Mandel'shtam- Tamm method, which permits introduction of potentials and of the Hertz tensor for the description of the electromagnetic field in a moving medium. The laws of propagation of free electromagnetic waves are considered. A derivation is given of Green's function in the electrodynamics of moving media. This makes possible a unified determination of the fields in the presence of sources. Consideration is given to peculiar effects that occur at faster-than-light velocity of motion of the medium (when the velocity of motion of the medium exceeds the phase velocity of light in the rest system of the medium). In the appendix, expressions are found for the fields of a stationary point charge and magnetic dipole, and the Lienard?Wiechert potentials in a moving medium are also obtained.

Further Study of the Atmospheric Gravity Waves over the Eastern Seaboard on 18 March 1969

Abstract: Washington, D.C., microbarograph records for Mar. 18, 1969 reveal gravity-wave-associated pressure oscillations which appear to be directly related to upper tropospheric wave structure observed at the same time with a Wallops Island 10-cm wavelength radar. The consistency between the two sets of data provides observational support for the hypothesis that shear instability in the upper tropospheric flow is the mechanism responsible for the generation of such waves. The comparison presented suggests that microbarograph arrays might be useful adjuncts to future radar studies of upper tropospheric wave dynamics, supplying such wave parameters as phase velocity and wavelength in favorable cases. The radar data pertinent to this event show an apparent vertical wave phase variation, permitting a very approximate and somewhat uncertain estimate of the wave-associated vertical flux of horizontal momentum, which is found to be about 4 dyn per sq cm. Wave generation by shear instability in the upper tropospheric air flow and the resulting vertical momentum transport may be an important element of the global atmospheric momentum budget.