Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions

The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.     

Cretaceous Environments of Afghanistan:A Synthesis Based on Selected Sections

1IntroductionThe Late Mesozoic sequences of Afghanistan are important in understanding the geodynamic evolu-tion of the northwestern part of South Asia, in par-ticular the transgressive and regressive history of the northwestern part of the Tethys connecting Iran to the west and the northern Indian Subcontinent to the east. Jurassic to Upper Cretaceous sedimentary seque-nces were initially studied by Griesbach (1885 ~1887) and Hayden (1880~1901) through several traverses in northern an…     

Late Hercynian–Mesozoic thinning in the Alboran domain: metamorphic data from the northern Rif, Morocco

In the Alboran domain, two crustal-thickening late-orogenic extension cycles are superposed. The importance of the late Alpine thinning of the Alpujarride-Sebtide crustal section on top of the Beni Bousera peridotites is discussed here in metamorphic petrological terms. The Alpine metamorphism operated first under a HP–LT gradient, and reached the eclogite facies in the Permian–Triassic phyllites, before retrogression under a high geothermal gradient. A contrasting, higher temperature metamorphism characterizes the pre-Permian section, reaching the HP-granulite facies at the bottom of the crustal section. By reference to the western European setting, the granulites relate to the Hercynian orogeny, as supported by the isotopic ages of the enclosed, armoured monazite crystals. Thus, thinning of an overthickened crust might have occurred there during the late Hercynian extension and Tethyan opening, before being reactivated during the late Oligocene.     

Comparison of arsenic concentrations in simultaneously-collected groundwater and aquifer particles from Bangladesh,India, Vietnam,and Nepal

One of the reasons the processes resulting in As release to groundwater in southern Asia remain poorly understood is the high degree of spatial variability of physical and chemical properties in shallow aquifers. In an attempt to overcome this difficulty, a simple device that collects groundwater and sediment as a slurry from precisely the same interval was developed in Bangladesh. Recently published results from Bangladesh and India relying on the needle-sampler are augmented here with new data from 37 intervals of grey aquifer material of likely Holocene age in Vietnam and Nepal. A total of 145 samples of filtered groundwater ranging in depth from 3 to 36 m that were analyzed for As (1–1000 μg/L), Fe (0.01–40 mg/L), Mn (0.2–4 mg/L) and S (0.04–14 mg/L) are compared. The P-extractable (0.01–36 mg/kg) and HCl-extractable As (0.04–36 mg/kg) content of the particulate phase was determined in the same suite of samples, in addition to Fe(II)/Fe ratios (0.2–1.0) in the acid-leachable fraction of the particulate phase. Needle-sampler data from Bangladesh indicated a relationship between dissolved As in groundwater and P-extractable As in the particulate phase that was interpreted as an indication of adsorptive equilibrium, under sufficiently reducing conditions, across 3 orders of magnitude in concentrations according to a distribution coefficient of 4 mL/g. The more recent observations from India, Vietnam and Nepal show groundwater As concentrations that are often an order of magnitude lower at a given level of P-extractable As compared to Bangladesh, even if only the subset of particularly reducing intervals characterized by leachable Fe(II)/Fe >0.5 and dissolved Fe >0.2 mg/L are considered. Without attempting to explain why As appears to be particularly mobile in reducing aquifers of Bangladesh compared to the other regions, the consequences of increasing the distribution coefficient for As between the particulate and dissolved phase to 40 mL/g for the flushing of shallow aquifers of their initial As content are explored.     

Nonlinear effects of the distribution of amplitudes of sea waves

The effect of nonlinearities, such as wave-breaking and vertical asymmetry associated with sea waves, on the distribution of wave amplitudes is explored. Semiclosed theoretical expressions are derived to describe the distributions of breaking-limited crest and trough amplitudes for Stokes-type nonlinear sea waves. These are compared with the conventional Rayleigh distribution appropriate to linear wave amplitudes. The construction of nonlinear wave envelopes with the fast Fourier transform technique is described. The technique can be utilized to enlarge the data base in empirical analyses of field records which typically contain limited information on amplitude characteristics. The theoretical distributions and the proposed data enlargement technique are demonstrated with the analysis of a nonlinear wave record.     

Effects of spectrum band width on the distribution of wave heights and periods

The statistical distribution of the crest-to-trough heights of narrowband nonlinear sea waves is derived in a semi-closed form. A quantitative comparison of the resulting density and exceedance probability distributions with those of the linear theory is given. It is shown that the nonlinearity of waves, even with steepnesses typical of extreme sea states, has an insignificant influence on the distribution of crest-to-trough heights.     

Atmospheric forcing of the eastern tropical Pacific: A review

The increase in marine, land surface, atmospheric and satellite data during recent decades has led to an improved understanding of the air–sea interaction processes in the eastern tropical Pacific. This is also thanks to extensive diagnoses from conceptual and coupled ocean–atmosphere numerical models. In this paper, mean fields of atmospheric variables, such as incoming solar radiation, sea level pressure, winds, wind stress curl, precipitation, evaporation, and surface energy fluxes, are derived from global atmospheric data sets in order to examine the dominant features of the low level atmospheric circulations of the region. The seasonal march of the atmospheric circulations is presented to depict the role of radiative forcing on atmospheric perturbations, especially those dominating the atmosphere at low levels.In the tropics, the trade winds constitute an important north–south energy and moisture exchange mechanism (as part of the low level branch of the Hadley circulation), that determines to a large extent the precipitation distribution in the region, i.e., that associated with the Inter-Tropical Convergence Zone (ITCZ). Monsoonal circulations also play an important role in determining the warm season precipitation distribution over the eastern tropical Pacific through a large variety of air–sea–land interaction mechanisms. Westward traveling waves, tropical cyclones, low latitude cold air intrusions, and other synoptic and mesoscale perturbations associated with the ITCZ are also important elements that modulate the annual rainfall cycle. The low-level jets of the Gulf of California, the Intra-Americas Sea (Gulf of Mexico and Caribbean Sea) and Chocó, Colombia are prominent features of the eastern tropical Pacific low-level circulations related to sub-regional and regional scale precipitation patterns. Observations show that the Intra-Americas Low-Level Jet intensity varies with El Niño/Southern Oscillation (ENSO) phases, however its origin and role in the westward propagation and development of disturbances that may hit the eastern tropical Pacific, such as easterly waves and tropical cyclones, are still unclear. Changes in the intensity of the trade winds in the Caribbean Sea and the Gulf of Mexico (associated with eastern tropical Pacific wind jets) exert an important control on precipitation by means of wind–topography interactions. Gaps in the mountains of southern Mexico and Central America allow strong wind jets to pass over the continent imprinting a unique signal in sea surface temperatures and ocean dynamics of the eastern tropical Pacific.The warm pools of the Americas constitute an important source of moisture for the North American Monsoon System. The northeastern tropical Pacific is a region of intense cyclogenetic activity, just west of the coast of Mesoamerica. Over the oceanic regions, large-scale properties of key variables such as precipitation, moisture, surface energy fluxes and wind stress curl are still uncertain, which inhibits a more comprehensive view of the region and stresses the importance of regional field experiments. Progress has been substantial in the understanding of the ocean and atmospheric dynamics of the eastern tropical Pacific, however, recent observational evidence such as that of a shallow meridional circulation cell in that region, in contrast to the classic concept of the Hadley-type deep meridional circulation, suggests that more in situ observations to validate theories are still necessary.This paper is part of a comprehensive review of the oceanography of the eastern tropical Pacific Ocean.     

National ocean policy—new opportunities for Malaysian ocean development

Being a littoral state, Malaysian maritime sectors provide the basis for the growth and development of marine-related activities. As the country enters the new millennium along with the ‘2020 Vision’ which serves as the basic template against which the economic performance of these sectors should be judged, it poses a new challenge for Malaysia in developing these sectors. This paper attempts to address three basic issues: Firstly, is there any national ocean policy in place? Secondly, are the maritime sectors adequately organized to play an important role in achieving the objectives? Thirdly, what are the opportunities available in developing the ocean?It can be seen that existing policies to develop comprehensive ocean governance have not received the full attention they deserve. Organizational structures governing the ocean for implementing national policies are well in place but in a fragmented and uncoordinated fashion. As a result, sectoral and intersectoral management problems were created such as multiple-use conflicts, overlapping of jurisdiction and duplication of efforts. Environmental problems have also not been properly addressed. A few sectors have been identified as offering opportunities to further develop the Malaysian maritime areas. Among these are marine education and human resources development, marine tourism and the seafood industry.     

Statistics of nonlinear wave crests and groups

Groups of large nonlinear waves with sharper higher crests can pose hazards to ships, induce harbor resonance and cause wave-overtopping of fixed and floating structures. Past interest in wave groups has mostly been focused on the statistics and modeling of linear wave groups. Studies on nonlinear wave groups are surprisingly few, and address deep water waves only. Here, statistics of nonlinear wave crests and wave-crest groups in deep and transitional water depths are considered, using an appropriate second-order representation for crest heights and the continuous wave-envelope approach. In particular, theoretical expressions describing the statistics of nonlinear wave crests and their groups are posed in the form of a simple second-order transformation of well-known results on linear waves. Predictions from the transformation so posed compare well with nonlinear wave data gathered in the North Sea, and demonstrate that nonlinearities do affect the statistics of large wave crests and their groups significantly.