Effective stability around the Cassini state in the spin-orbit problem

We investigate the long-time stability in the neighborhood of the Cassini state in the conservative spin-orbit problem. Starting with an expansion of the Hamiltonian in the canonical Andoyer-Delaunay variables, we construct a high-order Birkhoff normal form and give an estimate of the effective stability time in the Nekhoroshev sense. By extensively using algebraic manipulations on a computer, we explicitly apply our method to the rotation of Titan. We obtain physical bounds of Titan’s latitudinal and longitudinal librations, finding a stability time greatly exceeding the estimated age of the Universe. In addition, we study the dependence of the effective stability time on three relevant physical parameters: the orbital inclination, $i$ , the mean precession of the ascending node of Titan orbit, $\dot{\varOmega }$ , and the polar moment of inertia, $C$ .     

Risk occurrences of damaging frosts during the growing season of vegetables in the Elbe River lowland,the Czech Republic

This study has, for the first time, analysed in detail the risk occurrences of the last spring frost, first fall frost and the length of the frost-free period during the growing season of vegetable crops at a high horizontal resolution of 10 km in the Elbe River lowland in the Czech Republic. The daily minimum air temperature from 116 grid points throughout the studied area for the period 1961–2011 was used. The daily values of minimum air temperature ranges of 0 to ?1.1 °C, ?1.2 to ?2.2 °C and below ?2.2 °C were considered to constitute mild, moderate and severe frost intensities, respectively. Firstly, the spatiotemporal variability of the date of the last spring frost, the date of the first fall frost and the length of the frost-free period in the Elbe River lowland is provided. Secondly, the estimation of the probability of a later date in the spring and an earlier date in the fall for various severe frost events and the length of the frost-free period is determined. Third, the changes in the timing of the last and first frosts of the three severities, as well as the length of the frost-free period, are evaluated. From 1961 to 2011, the Elbe River lowland has experienced a decrease in the number of frost days, while the length of the frost-free period between the last spring frost and the first fall frost has increased. The temporal evolution of the frost-free period anomalies displays two distinct periods: a shortening of the frost-free period in the 1960s and an intensified lengthening of the frost-free period since the 1980s. Whereas the latest spring frost has ended on an earlier date across the Elbe River lowland, the first frost date in the fall has generally been delayed to a later date. The dates of the last spring frost have advanced by ?0.21 days per year on average. The fall dates are delayed up to 0.18 days per year, whereas the frost-free period is lengthening by up to 0.39 days per year on average. However, regional frost series suggests that the frost-free period exhibits a large amount of inter-annual variability. In terms of the growth of field vegetables, a late spring frost remains a risk factor, but the degree of risk has decreased. There is a 25 % chance of the occurrence of dangerous spring frosts during the planting of field vegetables after 3rd May, but after 15th May, the risk is only 10 %.     

Review of solutions for 3D hydrodynamic modeling applied to aquaculture in South Pacific atoll lagoons

A workshop organized in French Polynesia in November 2004 allowed reviewing the current methods to model the three-dimensional hydrodynamic circulation in semi-enclosed atoll lagoons for aquaculture applications. Mollusk (e.g. pearl oyster, clam) aquaculture is a major source of income for South Pacific countries such as French Polynesia or Cook Islands. This aquaculture now requires a better understanding of circulation patterns to improve the spatial use of the lagoons, especially to define the best area to set larvae collectors. The pelagic larval duration of the relevant species (<20 days) and the size of the semi-closed lagoons (few hundreds of km2) drive the specifications of the model in terms of the spatial and temporal scale. It is considered that, in contrast with fish, mollusk larvae movements are limited and that their cycle occurs completely in the lagoon, without an oceanic stage. Atolls where aquaculture is productive are generally well-bounded, or semi-closed, without significant large and deep openings to the ocean. Nevertheless part of the lagoon circulation is driven by oceanic water inputs through the rim, ocean swells, tides and winds. Therefore, boundary conditions of the lagoon system are defined by the spatial structure of a very shallow rim (exposition and number of hoas), the deep ocean swell climate, tides and wind regimes. To obtain a realistic 3D numerical model of lagoon circulation with adequate forcing, it is thus necessary to connect in an interdisciplinary way a variety of methods (models, remote sensing and in situ data collection) to accurately represent the different components of the lagoon system and its specific boundary conditions. We review here the current methods and tools used to address these different components for a hypothetical atoll of the Tuamotu Archipelago (French Polynesia), representative of the semi-closed lagoons of the South Pacific Ocean. We hope this paper will serve as a guide for similar studies elsewhere and we provide guidelines in terms of costs for all the different stages involved.     

Eclipsing Binaries with Possible Light-Time Effect

The period changes of six eclipsing binaries have been studied with focus on the light-time effect. With the least squares method we also calculated parameters of such an effect and properties of the unresolved body in these systems. With these results we discussed the probability of presence of such bodies in the systems with respect to possible confirmation by another method. In two systems we also suggested the hypothesis of fourth body or magnetic activity for explanation of the "second-order variability" after subtraction of the light-time effect of the third body.     

Assessment of Fish Assemblages Before Dredging of the Shipping Channel Near the Mouth of the Savannah River in Coastal Georgia

Evaluating the effects of anthropogenic activities is dependent upon data collection prior to impact, though funds are rarely allocated to conduct an assessment before a critical need arises. The Savannah Harbor Expansion Project is one such activity that includes dredging of the Savannah River. It may potentially change physical conditions of the estuary thereby altering fish assemblages. The purpose of the present study was to characterize pre-impact fish assemblages along a salinity gradient near the mouth of the river and determine which abiotic factors most influence them. One site within the mouth of the Savannah River and two sites immediately outside the river mouth were sampled monthly for 2 years using both a beam trawl and seine net. Salinity, temperature, dissolved oxygen, and sediment grain size were assessed. All four factors had a significant effect on fish assemblages. A total of 3943 fishes representing ≥55 species formed three statistically distinct fish assemblages and at least three seasonal assemblages. Only 24 species (43.6 %) were collected by both gear types indicating the importance of using multiple gear types to assess fish assemblages. We conclude that the fish assemblages near the mouth of the Savannah River may be altered or may shift given the predicted increase in salinity and/or the possible changes in sediment composition from channel dredging. Understanding the abiotic factors that most influence spatial and seasonal fish distributions prior to dredging will be invaluable in predicting how organisms will be impacted by similar public projects elsewhere.     

On the vertical velocity component in the mesoscale Lofoten vortex of the Norwegian Sea

For the first time, the concepts of the theory of helical vortices have been applied to the Lofoten vortex of the Norwegian Sea. The estimates for azimuthal and vertical velocities have been obtained from the Massachusetts Institute of Technology general circulation model (MITgcm) for 1992–2012. The columnar vortex model with helical vorticity lines and distributions has been adapted to Scully and Rayleigh vortices. It has been shown that the vortex parameters can be determined simply from mass balance equations. The parameters of the helical vortex simulating the structure of the Lofoten vortex have been found and the radial distributions of azimuthal and vertical velocity components have been constructed. The resulting data can be interesting for an analysis of the three-dimensional structure of mesoscale vortices in the ocean.     

Palaeomagnetic evidence for the Gondwanian origin of the Taurides and rotation of the Isparta Angle,southern Turkey

The Taurides, the southernmost of the three major tectonic domains that constitute present‐day Turkey, were emplaced following consumption of the Tethyan Ocean in Late Mesozoic to mid‐Tertiary times. They are generally assigned an origin at the northern perimeter of Gondwana. To refine palaeogeographic control we have investigated the palaeomagnetism of a range of Jurassic rocks. Forty‐nine samples of Upper Jurassic limestones preserve a dual polarity remanence (D/I=303/−9°, α₉₅=6°) interpreted as a primary magnetization acquired close to the equator and rotated during emplacement of the Taurides. Result from mid‐Jurassic dolerites confirm a low palaeolatitude for the Tauride Platform during Jurassic times at the Afro–Arabian sector of Gondwana. Approximately 4000 km of Tethyan closure subsequently occurred between Late Jurassic and Eocene times. Although related Upper Jurassic limestones and Liassic redbeds preserve a sporadic record of similar remanence, the dominant signature in these latter rocks is an overprint of probable mid‐Miocene age, probably acquired during a single polarity chron and imparted by migration of a fluid front during nappe loading. This is now rotated consistently anticlockwise by c. 30° and conforms to results of previous studies recording bulk Neogene rotation of the Isparta region following Lycian nappe emplacement. The regional distribution of this overprint implies that the Isparta Angle (IA) has been subject to only small additional closure (<10°) since Late Miocene time. A smaller amount (c. 6°) of clockwise rotation within the IA since Early Pliocene times is associated with an ongoing extensional regime and reflects an expanding curvature of the Tauride arc produced by southwestward extrusion of the Anatolian collage as a result of continuing northward motion of Afro–Arabia. Copyright © 2002 John Wiley & Sons, Ltd.     

P–T–t–D records of Early Palaeozoic Andean-type shortening of a hot active margin: The Dunhuang block in NW China

High-pressure (HP) granulites form either in the domain of the subducted plate during continental collision or in supra-subduction systems where the thermally softened upper plate is shortened and thickened. Such a discrepancy in tectonic setting can be evaluated by metamorphic pressure–temperature–time-deformation (P–T–t–D) paths. In the current study, P–T–t–D paths of Early Palaeozoic HP granulite facies rocks, in the form of metabasic lenses enclosed in migmatitic metapelite, from the Dunhuang block, NW China, are investigated in order to constrain the nature of the HP rocks and shed light on the geodynamic evolution of a modern hot orogenic system in an active margin setting. The rocks show a polyphase evolution characterized by (1) relics of horizontal or gently dipping fabric (S1) preserved in cores of granulite lenses and in garnet porphyroblasts, (2) a N-S trending sub-vertical fabric (S2) preserved in low-strain domains and (3) upright folds (F3) associated with a ubiquitous steep E-W striking axial planar foliation (S3). Garnet in the granulites preserves relics of a prograde mineral assemblage M1a equilibrated at ~11.5 kbar and ~770–780°C, whereas the matrix granulite assemblage (M1b) from the S1 fabric attained peak pressure at ~13.5 kbar and ~850°C. The granulites were overprinted at ~8–11 kbar and ~850–900°C during crustal melting (M2) followed by partial re-equilibration (M3) at ~8 kbar and ~625°C. A garnet Lu–Hf age of 421.6 ± 1.2 Ma dates metamorphism M1, while a garnet Sm–Nd age of 385.3 ± 4.0 Ma reflects M3 cooling of the granulites. The mineral assemblage, M1, of the host migmatitic metapelite formed at ~9–12.5 kbar and ~760–810°C, partial melting and migmatization (M2) occurred at ~7 kbar and ~760°C and re-equilibration (M3) at ~5–6 kbar and ~675°C. A garnet Lu–Hf age of 409.7 ± 2.3 Ma dates thermal climax (M2) and a garnet Sm–Nd age of 356 ± 11 Ma constrains M3 for the migmatitic metapelites. The timing of this late phase is also bracketed by an emplacement age of syntectonic granite dated at c. 360 Ma. Decoupling of M1 and M2 P–T evolutions between the mafic granulites and migmatitic metapelites indicates their different positions in the crustal column, while the shared pressure–temperature (P–T) evolution M3 suggests formation of a mélange-like association during the late stages of orogeny. The high-pressure event D1-M1 is interpreted as a result of Late Silurian–Early Devonian moderate crustal thickening of a thermally softened and thinned pre-orogenic crust. The high-temperature (HT) re-equilibration D2-M2 is interpreted as a result of Mid-Devonian shortening of the previously thickened crust, possibly due to ‘Andean-type’ underthrusting. The D3-M3 event reflects Late Devonian supra-subduction shortening and continuous erosion of the sub-crustal lithosphere. This tectono-metamorphic sequence of events is explained by polyphased Andean-type deformation of a ‘Cascadia-type’ active margin, which corresponds to a supra-subduction tectonic switching paradigm.