The weak friction approximation and tidal evolution in close binary systems     

M. E. Alexander 《Astrophysics and Space Science》1973,23(2):459-510

The aim of this paper is to study the dynamical problem of tidal friction in a binary system consisting of deformable components, with the restriction that the angle of lag or advance of the tidal distortion with respect to the direction of the disturbing companion is small. The fractional distortion of the bodies due to rotation and tidal interaction is also treated as a first-order small quantity, and terms up to the fourth harmonic in the tidal potential are retained. In this linear approximation, the time-dependent tidal potential can be Fourier decomposed into a spectrum of simple harmonic terms, each of which is responsible for raising a partial wave in the body; each such partial wave can then be treated independently of the others. This is the method first employed by Darwin.In Section 2, it is assumed that the phase lag in the response of the body (due to dissipation of kinetic energy of deformation) is proportional to the forcing frequency, which is justified for small amplitude oscillations of a viscous fluid or visco-elastic body. A simple expression is then obtained for the potential function for the distortion in terms of the disturbing potential and the structure of the body.In Section 3, the distortion potential function is employed in deriving the componentsR, S andW of the disturbing force which are then substituted in the Gaussian form of the equations for variation of the elements. In Section 4, the Eulerian equations for motion of deformable bodies are derived, using the so-called mean axes of the body as the rotating axes of reference. In Section 5, it is shown that the dynamical effects of rotational distortion occur on a much shorter time scale than those arising from tidal friction, which allows one to consider the two phenomena as acting independently of one another. The collected set of Gaussian (orbital) and Eulerian (body) equations is re-written in terms of dimensionless variables for the tidal friction case, and the stability of the system is examined on the basis of these equations.In Section 6, the tidal friction equations are integrated numerically for the close binary system AG Persei and for the Earth-Moon system. In the former, the integrations were started from a highly elliptical orbit and the system was found to relax into a circular orbit, with synchronous rotation perpendicular to the orbit. In the latter, the integrations were performed backwards in time from the present day, and it was found that the lunar orbit rapidly becomes highly elliptical at the time of closest approach, thus indicating a probable capture of the Moon by the Earth. This result is in agreement with that obtained by other investigators; however, it is shown that the detailed behaviour of the system at the time of capture, in particular the inclination of the lunar orbit to the ecliptic, depends critically on the chosen rate of dissipation in the Moon's interior. A simple argument is presented which allows an estimation for the mean viscosity of a fluid body from the known age of the system: for the components of AG per, the result is 2×10¹¹ g cm^–1 s^–1, indicating that the stars must have possessed turbulent convective outer regions during some part of their tidal evolution, while for the Earth, the result, is 1.4×10¹² g cm^–1 s^–1. It is shown that the angle of tidal lag in nonsynchronous close binary systems in general is expected to be extremely small, and not observationally detectable.  相似文献   

Jovian sodium cloud geometry     

Alexander I. Ershkovich  Yuri B. Mekler 《Astrophysics and Space Science》1975,38(1):L1-L2

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Precession and nutation in close binary ststems     

M. E. Alexander 《Astrophysics and Space Science》1976,45(1):105-117

The precession of the orbital plane in a close binary system can provide an important observational tool for investigating dynamical properties of the components. Tidal evolution will always tend to align the rotation axes perpendicular to the orbital plane, thereby eliminating precession. It is pointed out, however, that if observations indicate the existence of a circular orbit and synchronous rotation of the components-which is the outcome of tidal evolution-then precession may still be present, provided the interior of one of the components is, or recently has been, radiative, and is not strongly coupled to the surface layers (where tidal dissipation is greatest). The equations governing precession and nutation are derived in a concise form, and applied to the numerical study of two binary systems. The observational effects are also discussed. Finally, it is pointed out that precession may be present in a subclass of the X-ray binary systems, and its observational significance is briefly discussed.  相似文献   

Fluorite Deposits at Voznesenka in the Khanka Massif, Russia: Geology and Age of Mineralization   总被引：1，自引：0，他引：1  

Kohei Sato  Kazuhiro Suzuki  Munetomo Nedachi    Shigeru Terashima    Margarita D. Ryazantseva    Anatoly A. Vrublevsky  + Alexander I. Khanchuk  ++ 《Resource Geology》2003,53(3):193-211

Abstract. A huge fluorite deposit at Voznesenka in the Khanka massif, Far East Russia is concluded to have formed at ca. 450 Ma in Late Ordovician time based on the K‐Ar ages for Li‐micas in the fluorite ore and greisenized leucogranite within the deposit. This conclusion is inconsistent with the current view of Devonian mineralization that stemmed from widely scattered whole‐rock Rb‐Sr isotope data for the heterogeneous leucogranite stocks influenced by strong alteration. The Voznesenka and neighboring fluorite deposits may have formed in Cambrian limestone in relation to the intrusion of the Li‐F‐rich felsic magma which has a similar chemistry to representative Li‐F‐rich felsic rocks including topaz granite and ongonite or topaz rhyolite; these rocks may be classified as a specific group of highly fractionated felsic magmas. Biotite granite plutons exposed in the Voznesenka district are divided in age into two groups based on the CHIME age data for zircon, monazite and xenotime: Ordovician and Permian. The Ordovician plutons seem to be coeval to the fluorite deposits and are characterized by F‐rich chemistry, reduced nature and association of tin mineralization with the deposition of fluorite and tourmaline. The biotite granite magmas of initially enhanced F contents could have been highly fractionated to form Li‐F‐rich leucogranite cupolas that provided fluorite deposits within the host limestone. Future prospecting for similar fluorite deposits is to be focused on areas of intersection between Ordovician Li‐F‐rich granite and Cambrian carbonate sequences. The Permian granite of southeastern margin of the Grodekovo batholith is characterized by lesser F content, oxidized nature and the lack of tin and fluorite mineralization in contrast to the Ordovician granite. The result of Permian age does not support the current view of Silurian age for the batholith and requires overall chronological reinvestigation in connection with the tectonic history of the Khanka massif because the Grodekovo is a representative of Paleozoic batholiths in Primorie.  相似文献   

Lotic communities of two small temporary karstic stream systems (East Westphalia, Germany) along a longitudinal gradient of hydrological intermittency   总被引：1，自引：0，他引：1  

Alexander Meyer  Elisabeth I. Meyer  Christina Meyer 《Limnologica》2003,33(4):271-279

The spatial and temporal discharge regime and its effects on benthic communities were studied in two small temporary karstic stream systems of the Paderborner Hochfläche (East Westphalia, Germany). Both streams are characterized by very small perennial springbrook sections. Benthic invertebrates were sampled three times at 12 sites and discharge was measured monthly from March to September 2000. The spatial extension of streamflow was observed regularly to evaluate the duration of drought. Both streams showed a longitudinal gradient of hydrological intermittency from very small perennial reaches with low intermittency to an extremely harsh hydrological situation. The benthic communities displayed a decreasing species richness at increasing intermittency. The different hydrological stream sections were colonized by different lotic communities, characterized by typical species of temporary streams and by several typical species of springs. Particularly the perennial springs and springbrooks are very important for the species richness in these karstic stream systems.  相似文献   

Decoupled elastic prestack depth migration   总被引：1，自引：0，他引：1  

Alexander Druzhinin   《Journal of Applied Geophysics》2003,54(3-4):369

This paper presents a new decoupled form of the formula for common-shot or common-receiver amplitude-preserving elastic prestack depth migration (PreSDM), which can be used for estimating angle-dependent elastic reflection coefficients in laterally inhomogeneous anisotropic media. The multi-shot or multi-receiver extension of this formula is suitable for automated prestack amplitude-versus-angle (AVA) elastic inversion of ocean-bottom cable (OBC), walkaway VSP (WVSP) or standard towed-cable data at any subsurface location. The essence of the theory is a systematic application of the stationary-phase principle and high-frequency approximations to the basic elastic Green's theorem. This leads to nonheuristic explicit wave mode decoupling and scalarization of vector PreSDM. Used in combination, ray-trace and finite-difference (FD) eikonal solvers create a useful tool to calculate accurate Green's function travel time and amplitude maps. Examples of synthetic OBC data and applications to field WVSP data show that the new imaging technique can produce a clear multi-mode elastic image.  相似文献   

Momentum Transfer By A Mountain Meadow Canopy: A Simulation Analysis Based On Massman's (1997) Model     

Georg Wohlfahrt  Alexander Cernusca 《Boundary-Layer Meteorology》2002,103(3):391-407

Using a mountain meadow as a case study it is the objective of the present paper todevelop a simple parameterisation for the within-canopy variation of the phytoelementdrag (C_d) and sheltering (P_m) coefficients required for Massman's model of momentum transfer by vegetation. A constant ratio between C_d and P_m is found to overestimate wind speed in the upper canopy and underestimate it in the lower canopy.Two simple parameterisations of C_d/P_m as a function of the plant area density and the cumulative plant area index are developed, using values optimised by least-squares regression between measured and predicted within-canopy wind speeds. A validation with independently measured data indicates that both parameterisations work reliably for simulating wind speed in the investigated meadow. Model predictions of the normalised zero-plane displacement height and the momentum roughness length fall only partly within the range of values given in literature, which may be explained by the accumulation of plantmatter close to the soil surface specific for the investigated canopies. The seasonal course of the normalised zero-plane displacement height and the momentum roughness length are discussed in terms of the seasonal variation of the amount and density of plant matter.  相似文献   

Remobilization of authigenic uranium in marine sediments by bioturbation   总被引：1，自引：0，他引：1  

Yan Zheng  Robert F. Anderson  Alexander van GeenMartin Q. Fleisher 《Geochimica et cosmochimica acta》2002,66(10):1759-1772

Uranium behaves as a nearly conservative element in oxygenated seawater, but it is precipitated under chemically reducing conditions that occur in sediments underlying low-oxygen bottom water or in sediments receiving high fluxes of particulate organic carbon. Sites characterized by a range of bottom-water oxygen (BWO) and organic carbon flux (OCF) were studied to better understand the conditions that determine formation and preservation of authigenic U in marine sediments. Our study areas are located in the mid latitudes of the northeast Pacific and the northwest Atlantic Oceans, and all sites receive moderate (0.5 g/cm² kyr) to high (2.8 g/cm² kyr) OCF to the sediments. BWO concentrations vary substantially among the sites, ranging from <3 to ∼270 μM. A mass balance approach was used to evaluate authigenic U remobilization at each site. Within each region studied, the supply of particulate nonlithogenic U associated with sinking particles was evaluated by means of sediment traps. The diffusive flux of U into sediments was calculated from pore-water U concentration profiles. These combined sources were compared with the burial rate of authigenic U to assess the efficiency of its preservation. A large fraction (one-third to two-thirds) of the authigenic U precipitated in these sediments via diffusion supply is later regenerated, even under very low BWO concentrations (∼15 μM). Bioturbating organisms periodically mix authigenic U-containing sediment upward toward the sediment-water interface, where more oxidizing conditions lead to the remobilization of authigenic U and its loss to bottom waters.  相似文献   

The preservation of high-pressure rocks during exhumation: metagranites and metapelites     

Alexander Proyer 《Lithos》2003,70(3-4):183-194

Metagranites in the NKFMASH system require external hydration during prograde high-pressure metamorphism in order to equilibrate to ambient HP conditions by producing more siliceous muscovite. Any lack of external fluid or the disappearance of biotite stops re-equilibration and thus prevents recording of high-pressure conditions. The same hydration reactions cause dehydration during exhumation. Orthogneiss from shear zones or adjacent to metapelites and metabasites will take up external fluid during subduction and record the highest P–T conditions, but will also be the first to dehydrate upon exhumation, now hydrating other lithologies and probably refuelling shearzones.

The (de)hydration behavior of Ca-bearing metagranitoids is similar to that in the Ca-free system. However, the anorthite component of plagioclase decomposes with increasing pressure to form either (clino)zoisite or a grossular-rich garnet. Both reactions are fluid-consuming. If H₂O is supplied from an external source, the garnet-bearing assemblage can record P–T conditions up to very high pressures, but dehydrates again during heating and/or decompression to form a more Fe-rich garnet and Al-rich mica(s). The garnet compositions observed in natural HP-metagranites are mostly too Fe-rich to be formed in the presence of an H₂O-rich fluid.

N(C)KFMASH metapelites generally have a more complex mineralogy and succession of mineral assemblages along a P–T path. The H₂O contained in hydrous silicates like chlorite and chloritoid is only partly released, but partly transferred to other minerals like paragonite, glaucophane or phengite during subduction and further dehydration during exhumation is common. The mineral assemblage preserved by the rock may then record P–T conditions way below those of the actual pressure and temperature peak of the path. Contouring of the P–T pseudosection of a specific metapelite composition with mode isopleths for H₂O shows which P–T conditions along a given path are the ones most likely recorded by the rock.  相似文献   

Architecture and mineral deposit settings of the Altaid orogenic collage: a revised model   总被引：19，自引：0，他引：19  

Alexander Yakubchuk 《Journal of Asian Earth Sciences》2004,23(5):761

The Altaids are an orogenic collage of Neoproterozoic–Paleozoic rocks located in the center of Eurasia. This collage consists of only three oroclinally bent Neoproterozoic–Early Paleozoic magmatic arcs (Kipchak, Tuva–Mongol, and Mugodzhar–Rudny Altai), separated by sutures of their former backarc basins, which were stitched by new generations of overlapping magmatic arcs. In addition, the Altaids host accreted fragments of the Neoproterozoic to Early Paleozoic oceanic island chains and Neoproterozoic to Cenozoic plume-related magmatic rocks superimposed on the accreted fragments. All these assemblages host important, many world-class, Late Proterozoic to Early Mesozoic gold, copper–molybdenum, lead–zinc, nickel and other deposits of various types.In the Late Proterozoic, during breakup of the supercontinent Rodinia, the Kipchak and Tuva–Mongol magmatic arcs were rifted off Eastern Europe–Siberia and Laurentia to produce oceanic backarc basins. In the Late Ordovician, the Siberian craton began its clockwise rotation with respect to Eastern Europe and this coincides with the beginning of formation of the Mugodzhar–Rudny Altai arc behind the Kipchak arc. These earlier arcs produced mostly Cu–Pb–Zn VMS deposits, although some important intrusion-related orogenic Au deposits formed during arc–arc collision events in the Middle Cambrian and Late Ordovician.The clockwise rotation of Siberia continued through the Paleozoic until the Early Permian producing several episodes of oroclinal bending, strike–slip duplication and reorganization of the magmatic arcs to produce the overlapping Kazakh–Mongol and Zharma-Saur–Valerianov–Beltau-Kurama arcs that welded the extinct Kipchak and Tuva–Mongol arcs. This resulted in amalgamation of the western portion of the Altaid orogenic collage in the Late Paleozoic. Its eastern portion amalgamated only in the early Mesozoic and was overlapped by the Transbaikal magmatic arc, which developed in response to subduction of the oceanic crust of the Paleo-Pacific Ocean. Several world-class Cu–(Mo)-porphyry, Cu–Pb–Zn VMS and intrusion-related Au mineral camps, which formed in the Altaids at this stage, coincided with the episodes of plate reorganization and oroclinal bending of magmatic arcs. Major Pb–Zn and Cu sedimentary rock-hosted deposits of Kazakhstan and Central Asia formed in backarc rifts, which developed on the earlier amalgamated fragments. Major orogenic gold deposits are intrusion-related deposits, often occurring within black shale-bearing sutured backarc basins with oceanic crust.After amalgamation of the western Altaids, this part of the collage and adjacent cratons were affected by the Siberian superplume, which ascended at the Permian–Triassic transition. This plume-related magmatism produced various deposits, such as famous Ni–Cu–PGE deposits of Norilsk in the northwest of the Siberian craton.In the early Mesozoic, the eastern Altaids were oroclinally bent together with the overlapping Transbaikal magmatic arc in response to the northward migration and anti-clockwise rotation of the North China craton. The following collision of the eastern portion of the Altaid collage with the Siberian craton formed the Mongol–Okhotsk suture zone, which still links the accretionary wedges of central Mongolia and Circum-Pacific belts. In the late Mesozoic, a system of continent-scale conjugate northwest-trending and northeast-trending strike–slip faults developed in response to the southward propagation of the Siberian craton with subsequent post-mineral offset of some metallogenic belts for as much as 70–400 km, possibly in response to spreading in the Canadian basin. India–Asia collision rejuvenated some of these faults and generated a system of impact rifts.  相似文献