Some aspects of the interpretation of spectra in meteorology

The meaningfulness of spectral presentations, and of spectral peaks in particular, is considered by the use of simple examples. First, we derive analytically the spectra of sinusoidal finite-length waves and subject the spectra to several area-conserving transformations. The peak of the logarithmic spectrum (power density per unit natural logarithm of frequency) is shown to be the most appropriate for defining the scales (or frequencies) of the waves. The advantage of the logarithmic spectrum becomes even more apparent when a wave consisting of the positive part of a sine wave is considered. In that case, the conventional frequency presentation is misleading because in addition to the erroneous location of the spectral peak, an increase of power density towards low frequencies occurs, giving the spectra the appearance of red noise. For the same wave, it is shown that the logarithmic spectrum has a single peak at the position corresponding with the actual wave frequency.     

Apatite nodules as an indicator of depositional environment and ore genesis for the Mesoproterozoic Broken Hill-type Gamsberg Zn–Pb deposit,Namaqua Province,South Africa

Nodules consisting of fluorapatite are concentrated as a discrete band in the polymetallic sulfide ore of the Gamsberg deposit in central Bushmanland, South Africa. Their shape, zonal features, and geochemistry, in particular rare earth element (REE) abundances, are similar to authigenic francolite concretions that precipitate during diagenesis in organic-rich muds. As a result, the apatite nodules are regarded as primary. The nodules have a strong lithostratigraphic control, occurring at the transition of siliciclastic-hosted pyrite–sphalerite–graphite mineralization to calc-silicate-hosted pyrrhotite–sphalerite mineralization. Mineralogical and chemical evidence indicates that this transition also corresponds to a paleo-redox boundary that separates sediments deposited under oxygen-deficient conditions from those that developed in a more oxygenated environment. The apatite nodules can morphologically and chemically clearly be distinguished from coarse apatite grains that occur in oxide-facies iron formations stratigraphically above the ore horizon. However, similar REE profiles and in particular positive Eu anomalies in both types of apatite are indicative of a close genetic relationship between the two units and favor a common hydrothermal origin of the P. The contrasting morphologies and chemical signatures of the two occurrences can rather be attributed to differences in behavior of the phosphates during precipitation within the contrasting host sediments (chemical versus fine-grained clastic). Taking modern phosphorites as an analogue, these results are used to postulate a genetic model for the deposition of the sulfide ore and associated iron formations. The model envisages differentiation of the depositional basin into oxygen-deficient basin facies hosting the sulfide ore and oxygenated shelf facies, which are composed of manganiferous iron formations. The intimate association of sedimentary apatite with base metal sulfides indicates that basin conditions were conducive to the precipitation of both phases. This relationship might act as a potential exploration guide in similar basins elsewhere.Editorial handling: E. Frimmel     

Particle acceleration by ultrarelativistic shocks: theory and simulations

We consider the acceleration of charged particles near ultrarelativistic shocks, with Lorentz factor     . We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultrarelativistic shocks is a power law,     , with a nearly universal value     for the slope of this power law.
We confirm that the ultrarelativistic equivalent of the Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurrence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle     around the shock normal.
We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount:     . This limits the energy change per shock crossing cycle to     , except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor     for those particles that are scattered back across the shock into the upstream region.     

The Effect of Multipath on the Envelope Statistics of Bottom Clutter

Active sonar systems operating in shallow-water environments are often faced with high numbers of false alarms, generically referred to as clutter, arising from among other sources bottom scattering that results in heavy tails in the matched filter envelope probability density function compared with the Rayleigh distribution. In this paper, the effect of multipath propagation on the envelope statistics (i.e., the disparity from the Rayleigh distribution) is modeled through the use of the -distribution where the shape and scale parameters are formed from the autocorrelation function of the transmit waveform, the multipath structure, and the strength and spatial density of the bottom scatterers. Use of the -distribution is justified by showing that it is the limiting distribution of the sum of independent but not identically distributed -distributed random variables, which is representative of multipath when the bottom produces -distributed backscatter. The shape parameter, which drives the clutter statistics, is seen to be inversely proportional to bandwidth at bandwidths low enough that the multipath is not resolved and again at bandwidths high enough that all of the paths are resolved. As has been previously reported by LePage [IEEE J. Ocean. Eng., vol. 29, no. 2, pp. 330-346, 2004], multipath is shown to make clutter statistics more Rayleigh-like, which in this analysis equates to an increase in the -distribution shape parameter. The model is used to evaluate the effect on clutter statistics of varying environmental characterizations and system configurations where it is seen that, for a constant sound-speed profile, increasing the vertical aperture of the sonar, the center frequency, or surface roughness can lead to less multipath and, therefore, a reduction in the -distribution shape parameter and an increase in the probability of false alarm.     

COHERENT GENERATION OF NARROW-BAND CIRCULARLY POLARIZED RADIO BURSTS FROM THE SUN AND FLARE STARS

It is shown that narrow-band radio bursts of right- and left-hand circular polarizations from the Sun and flare stars can be produced via nonlinear conversion of Langmuir waves into high-frequency electromagnetic electron cyclotron waves near the plasma frequency by coupling to low-frequency electromagnetic cyclotron waves such as Alfvén-ion cyclotron or magnetosonic-whistler waves.     

Near-infrared imaging of the host galaxies of BL Lacertae objects

Near-infrared images have been obtained of nine BL Lacertae objects in order to investigate their host galaxy properties. From numerical modelling of the data we find that five of the nine BL Lacs have contributions from extended galaxy emission in their profiles. Tentative morphologies were derived for two of the BL Lacs, namely B2 0752+258, for which a disc morphology is slightly preferred, and S4 0954+65, for which an elliptical morphology is preferred. From our modelling we derive host galaxy absolute magnitudes of M_H =−25.6±0.5 for B2 0752+258, and M_H =−26.3±0.8 for S4 0954+65. We also find an average K -band absolute K -corrected host galaxy magnitude, for the BL Lacs, of 〈 M_K 〉=−26.3±0.6 asssuming an elliptical galaxy model, and 〈 M_K 〉=−26.1±0.9 assuming a disc galaxy model. The derived absolute magnitudes are similar to those found for the putative parent population of FRI radio galaxies, predicted by unified schemes. For those BL Lacs in which host galaxies have been previously detected at optical wavelengths we derive rest frame colours which are generally consistent with those of 'normal' galaxies. However, for TEX 0836+182 we find a rather blue colour which, together with the elongated morphology, may be indicative of interaction or spiral structure. Our results suggest that the host galaxies of BL Lacs are indeed similar to those of FRI radio galaxies, adding further weight to the unification scenario. In our present infrared frames of relatively modest resolution, we do not find that infrared observations are any more or less effective than optical observations at revealing the underlying host galaxy.     

The climatology of the lower stratosphere during the IGY and its implications for the regime of circulation

Summary Three-monthly mean statistics, show that throughout the year in the layer between about 200 and 30 mb large-scale eddies transport both heat and momentum against the north-south gradient of, respectively, the temperature and the angular rotation. Furthermore, it is found that in this layer, warm air masses tend to sink and cold air masses tend to rise, thereby converting kinetic into potential energy. The eddy circulations have, therefore, no source of energyin situ and must be forced by the circulation systems in the adjacent layers, probably in the troposphere. A comparison is drawn between the transport of angular momentum and heat by transient eddies in the lower troposphere, the upper troposphere and the lower stratosphere. Finally, the necessary sloping of the trajectories of the forced air parcels is discussed.

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Zusammenfassung Dreimonatige Durchschnitts-Statistiken zeigen, daß während des Jahres großräumige Wirbel in den Schichten zwischen ungefähr 200 und 30 mb Wärme und Bewegungsgröße gegen den Gradienten der Temperatur beziehungsweise der Winkelrotation transportieren. Ferner, wurde festgestellt, daß in diesen Schichten warme Luftmassen die Neigung haben abzusinken und kalte Luftmassen aufzusteigen und daß auf diese Art kinetische Energie in potentielle Energie umgewandelt wird. Die Wirbel-Zirkulation hat daher in sich keine Energiequelle und muß durch die Zirkulationssysteme in den anliegenden Schichten, vermutlich in der Troposphäre, angetrieben werden. Es wird ein Vergleich zwischen dem Transport von Drehimpuls und Wärme von wandernden Wirbeln in der unteren Troposphäre, der oberen Troposphäre und der unteren Stratosphäre angestellt. Schließlich wird die für das Zustandekommen der erzwungenen Bewegungen erforderliche Neigung der Trajektorien diskutiert.

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Résumé En se basant sur des statistiques tri-mensuelles on montre que tout au long de l'année, dans la couche entre 200 et 30 mb environ, les perturbations à grande échelle transportent à la fois chaleur et quantité de mouvement contre le gradient de la température et de la rotation angulaire. En outre, on a trouvé que dans cette couche les masses d'air chaud ont la tendance à descendre et les masses d'air froid ont la tendance à monter, en transformant de cette manière l'énergie cinétique en énergie potentielle. Par conséquent, les circulations perturbées n'ont pas disponible de source d'énergie et doivent être, forcées par des systèmes de circulation dans des couches adjacentes, probablement dans la troposphère. On compare le transport du moment cinétique et de la chaleur par des perturbations transitoires dans la basse troposphère, la haute troposphère et la basse stratosphère. Einfin on discute la pente des trajectoires des parcelles d'air forcées.

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With 8 Figures

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The research reported in this paper was sponsored principally by the Atomic Energy Commission under Contract No. AT(30-1)2241; before March 1962, the research was supported jointly by the Atomic Energy Commission and the U.S. Air Force under Contracts No. AT(30-1)2241 and AF 19(604)-5223.     

Indirect evidence for sediment transport on the continental shelf off Israel

The geographical distribution of coal particles that fell during nine years to the sea bottom from the open sea coal terminal off Hadera, Israel, shows a consistent northerly transport path, and it is inconceivable that the sand at that location would move in an opposite direction. Semicircular, current-scoured moats associated with small mounds found at the edge of the continental shelf off Ashdod and Haifa, Israel, also suggest a general northward-directed sediment transport. The northward sediment flow on the Israeli continental shelf inferred from this evidence therefore supports the model of Emery and Neev about general sand transport patterns along the Israeli coastline and continental shelf.