Planetons: An example of large amplitude solitary waves

Abstract

The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation).

The FSGE is shown to reduce to the KdV equation at small amplitudes. Classical sech² solitons thus represent a limiting class of solutions to the FSGE. The primary new effect on planetons at finite amplitudes is nonlinear dispersion. It is argued that due to this effect the propagation rates of finite amplitude planetons differ significantly from the ‘‘weak planeton'', or KdV, dispersion relation. Planeton structure is found to be simple and reminiscent of KdV solitons. Numerical evidence is presented which suggests that collisions between finite amplitude solitary waves are weakly inelastic, indicating the loss of true soliton behavior of the FSGE at moderate amplitudes. Lastly, the sensitivity of solitary waves to the existence of a nontrivial far field is demonstrated and the role of this analysis in the interpretation of lab experiments and the evolution of the thermocline is discussed.     

Structural controls of lode-gold mineralization by mafic dykes in late-Paleozoic granitoids of the Kochkar district, southern Urals, Russia

The Kochkar gold district in the East Uralian Zone of the southern Urals is located in late-Paleozoic granite gneisses of the Plast massif. Gold mineralization is associated with tabular quartz lodes that are preferentially developed along the margins of easterly trending mafic dykes. Fabric development indicates that dykes had a profound influence on the development of shear zones in granitoids. ENE- and SE-trending dykes have been reactivated as dextral and sinistral oblique strike-slip shear zones, respectively, forming a set of approximately conjugate shear zones related to the Permian, regional-scale E-W directed shortening. Dyke-shear zone relationships in the Plast massif are the result of strain refraction due to the presence of biotite-rich, incompetent dykes in more competent granite-gneisses. Deformation and the formation of associated gold-quartz lodes occurred close to peak-metamorphic, upper-greenschist to lower-amphibolite facies conditions. Strain refraction has resulted in partitioning of the bulk strain into a component of non-coaxial mainly ductile shear in mafic dykes, and a component of layer-normal pure shear in surrounding granitoids where deformation was brittle-ductile. Brittle fracturing in granitoids has resulted in the formation of fracture permeabilities adjacent to sheared dykes, that together with the layer-normal dilational component, promoted the access of mineralizing fluids. Both ore-controlling dykes and gold-quartz lodes were subsequently overprinted by lower greenschist-facies, mainly brittle fault zones and associated hydrothermal alteration that post-date gold mineralization. Received: 15 October 1998 / Accepted: 18 August 1999     

Green's function of one group transport equation for a finite slab of passive and multiplying media by Wiener-Hopf technique

We have applied the method of Wiener-Hopf technique to obtain the Green's functions of one-group transport equations (with anisotropic unit plane source and with isotroic unit plane source) for a finite slab of passive and multiplying media.     

Composition of the core,I. Solubility of oxygen in molten iron at high temperatures

Experiments on the solubility of FeO in molten iron have been carried out at temperatures between 2100 and 2550°C. The results show that liquid FeO is extensively soluble in molten iron at 2500°C and indicate that they probably become completely miscible above 2800°C. Liquid iron in equilibrium with crystalline magnesiowüstite (Mg_0.8Fe_0.2)O which is believed to be an important mineral in the lower mantle, would dissolve about 14 mol.% of FeO at 2500°C and 40 mol.% of FeO at 2800°C. The geochemical implications of these results are discussed. It is concluded that the outer core probably contains a large amount of dissolved FeO and that oxygen is probably the principal light element in the outer core.     

Studies of the ionospheric <Emphasis Type="Italic">D</Emphasis> region using partial reflections and radiowave scattering by artificial periodical irregularities

Results of the studies of the ionospheric D region during spring periods of 2004 and 2005 using partial reflections and radiowave scattering by artificial periodical irregularities are presented. It has been found that the vertical profile of the electron density during this period has a local minimum at a height of ～75 km, which is absent in summer. The causes of the minimum appearance are discussed.     

Uniform half-plane elastodynamic problems by an approximate boundary element method

In this paper the applicability of an approximate Boundary Element Method to uniform half-plane elastodynamic problems is investigated. This method employs the concept of images to construct approximate fundamental solutions for the half-plane and does not require any half-plane surface discretization. The method is formulated in the frequency domain for the case of harmonic disturbances or the Laplace transform domain for the case of transient disturbances. In the latter case a numerical inversion of the transformed solution is necessary to obtain the time domain response. The proposed method can be used as an alternative to boundary element methods that either utilize the infinite plane fundamental solution and thus require a half-plane surface discretization, or employ the exact half-plane fundamental solution, which even though leads to no surface discretization, is of a very lengthy and complicated form. Two characteristics numerical examples are used to illustrate the proposed method and study its advantages and disadvantages.     

Combined method for detecting hidden anomalies in galactic cosmic ray variations

A method has been proposed for detecting hidden periodicities in nonstationary finite time series with strong noise. The successive application of the spectral singular expansion and wavelet transform makes it possible to calculate the energy of short signals with an arbitrary form against a suppressing noise back-ground, the amplitude of which is several times as large as that of a useful signal. This method has been used to identify variations in the galactic cosmic ray (GCR) flux related to IMF disturbances due to the earthward propagation of solar magnetic clouds in the heliosphere.     

The response of ionospheric convection in the polar cap to substorm activity

We report multi-instrument observations during an isolated substorm on 17 October 1989. The EISCAT radar operated in the SP-UK-POLI mode measuring ionospheric convection at latitudes 71°-78°. SAMNET and the EISCAT Magnetometer Cross provide information on the timing of substorm expansion phase onset and subsequent intensifications, as well as the location of the field aligned and ionospheric currents associated with the substorm current wedge. IMP-8 magnetic field data are also included. Evidence of a substorm growth phase is provided by the equatorward motion of a flow reversal boundary across the EISCAT radar field of view at 2130 MLT, following a southward turning of the interplanetary magnetic field (IMF). We infer that the polar cap expanded as a result of the addition of open magnetic flux to the tail lobes during this interval. The flow reversal boundary, which is a lower limit to the polar cap boundary, reached an invariant latitude equatorward of 71° by the time of the expansion phase onset. A westward electrojet, centred at 65.4°, occurred at the onset of the expansion phase. This electrojet subsequently moved poleward to a maximum of 68.1° at 2000 UT and also widened. During the expansion phase, there is evidence of bursts of plasma flow which are spatially localised at longitudes within the substorm current wedge and which occurred well poleward of the westward electrojet. We conclude that the substorm onset region in the ionosphere, defined by the westward electrojet, mapped to a part of the tail radially earthward of the boundary between open and closed magnetic flux, the “distant” neutral line. Thus the substorm was not initiated at the distant neutral line, although there is evidence that it remained active during the expansion phase. It is not obvious whether the electrojet mapped to a near-Earth neutral line, but at its most poleward, the expanded electrojet does not reach the estimated latitude of the polar cap boundary.     

Solar Spectral Irradiance Variability in November/December 2012: Comparison of Observations by Instruments on the International Space Station and Models

Onboard the International Space Station (ISS), two instruments are observing the solar spectral irradiance (SSI) at wavelengths from 16 to 2900 nm. Although the ISS platform orientation generally precludes pointing at the Sun more than 10?–?14 days per month, in November/December 2012 a continuous period of measurements was obtained by implementing an ISS ‘bridging’ maneuver. This enabled observations to be made of the solar spectral irradiance (SSI) during a complete solar rotation. We present these measurements, which quantify the impact of active regions on SSI, and compare them with data simultaneously gathered from other platforms, and with models of spectral irradiance variability. Our analysis demonstrates that the instruments onboard the ISS have the capability to measure SSI variations consistent with other instruments in space. A comparison among all available SSI measurements during November–December 2012 in absolute units with reconstructions using solar proxies and observed solar activity features is presented and discussed in terms of accuracy.