Continuation of normal doubly symmetric orbits in conservative reversible systems

In this paper we introduce the concept of a quasi-submersive mapping between two finite-dimensional spaces, we obtain the main properties of such mappings, and we introduce “normality conditions” under which a particular class of so-called “constrained mappings” are quasi-submersive at their zeros. Our main application is concerned with the continuation properties of normal doubly symmetric orbits in time-reversible systems with one or more first integrals. As examples we study the continuation of the figure-eight and the supereight choreographies in the N-body problem.     

Stable isotope tracers as diagnostic tools in upscaling flow path understanding and residence time estimates in a mountainous mesoscale catchment

δ¹⁸O measurements of precipitation and stream waters were used as a natural tracer to investigate hydrological pathways and residence times in the River Feshie, a complex mesoscale (231 km²) catchment in the Cairngorm Mountains of Scotland. Precipitation δ¹⁸O exhibited strong seasonal variation over the 2001–02 hydrological year, ranging from −6·9‰ in the summer, to −12·0‰ during winter snowfalls (mean δ¹⁸O −9·59‰). Although damped, this seasonality was reflected in stream water outputs at seven sampling sites in the catchment, allowing δ¹⁸O variations to be used to infer hydrological source areas. Thus, stream water δ¹⁸O was generally controlled by a seasonally variable storm flow end member, mixing with groundwater of more constant isotopic composition. Periodic regression analysis allowed the differences in this mixing process between monitoring subcatchments to be assessed more quantitatively to provide a preliminary estimate of mean stream water residence time. This demonstrated the importance of responsive hydrological pathways associated with peat and shallow alpine soils in the headwater subcatchments in producing seasonally variable runoff with short mean residence times (33–113 days). In contrast, other tributaries with more freely draining soils and larger groundwater storage in shallow aquifers provided more effective mixing of variable precipitation inputs, resulting in longer residence time estimates (178–445 days). The mean residence time of runoff leaving the Feshie catchment reflected an integration of these contrasting influences (110–200 days). These insights from δ¹⁸O measurements extend the hydrological understanding of the Feshie catchment gained from other hydrochemical tracers, and demonstrate the utility of isotope tracers in investigating hydrological processes at the mesoscale. Copyright © 2005 John Wiley & Sons, Ltd.     

Groundwater–surface water interactions in a large semi‐arid floodplain: implications for salinity management

Flow regulation and water diversion for irrigation have considerably impacted the exchange of surface water between the Murray River and its floodplains. However, the way in which river regulation has impacted groundwater–surface water interactions is not completely understood, especially in regards to the salinization and accompanying vegetation dieback currently occurring in many of the floodplains. Groundwater–surface water interactions were studied over a 2 year period in the riparian area of a large floodplain (Hattah–Kulkyne, Victoria) using a combination of piezometric surface monitoring and environmental tracers (Cl⁻, δ²H, and δ¹⁸O). Despite being located in a local and regional groundwater discharge zone, the Murray River is a losing stream under low flow conditions at Hattah–Kulkyne. The discharge zone for local groundwater, regional groundwater and bank recharge is in the floodplain within ∼1 km of the river and is probably driven by high rates of transpiration by the riparian Eucalyptus camaldulensis woodland. Environmental tracers data suggest that the origin of groundwater is principally bank recharge in the riparian zone and a combination of diffuse rainfall recharge and localized floodwater recharge elsewhere in the floodplain. Although the Murray River was losing under low flows, bank discharge occurred during some flood recession periods. The way in which the water table responded to changes in river level was a function of the type of stream bank present, with point bars providing a better connection to the alluvial aquifer than the more common clay‐lined banks. Understanding the spatial variability in the hydraulic connection with the river channel and in vertical recharge following inundations will be critical to design effective salinity remediation strategies for large semi‐arid floodplains. Copyright © 2005 John Wiley & Sons, Ltd.     

Use and application of CFC-11,CFC-12,CFC-113 and SF_6 as environmental tracers of groundwater residence time:A review

Groundwater residence time is a fundamental property of groundwater to understand important hydrogeological issues,such as deriving sustainable abstraction volumes,or,the evolution of groundwater quality.The anthropogenic trace gases chlorofluorocarbons(CFC-11,CFC-12 and CFC-113)and sulphur hexafluoride(SF_6)are ideal in this regard because they have been released globally at known rates and become dissolved in groundwater following Henry's Law,integrating over large spatial(global)and temporal(decades)scales.The CFCs and SF_6 are able to date groundwater up to～100 years old with the caveat of certain simplifying assumptions.However,the inversion of environmental tracer concentrations(CFCs and SF_6)to derive groundwater age rests on the accurate determination of groundwater recharge parameters,namely temperature,elevation,salinity and excess air,in addition to resolving the potential for contamination,degradation and unsaturated zone effects.This review explores the fundamentals of CFC-11,CFC-12,CFC-113 and SF_6 as environmental tracers of groundwater age and recommends complementary techniques throughout.Once this relatively simple and inexpensive technique has been used to determine initial concentrations at the recharge zone,setting the groundwater dating'clock' to zero,this review then explores the meaning of groundwater'age' in relation to measured environmental tracer concentrations.It is shown that the CFCs and SF_6 may be applied to a wide-range of hydrogeological problems and suggests that environmental tracers are particularly powerful tools when integrated with numerical flow and transport models.     

岩溶山区不同利用方式下土地蓄水能力研究——以重庆市中梁山为例

分析研究了中梁山岩溶山区竹林、灌丛、草地、园地、坡耕地5种土地利用方式的凋落物和土壤的蓄水功能。结果表明,自然利用的竹林地、灌丛地、草地的凋落物蓄积量和最大持水量都远远大于其余两种农耕利用的土地。当自然利用土地改为园地、坡耕地以后,其表层土壤的最大蓄水能力下降31. 2%、非毛管蓄水能力下降65. 5%、坡耕地的毛管蓄水能力下降34. 3%。与此同时由于土地利用方式不同,还使园地整个土壤剖面( 60cm)蓄水潜力增大4. 4% ,坡耕地蓄水潜力减少6.1% ,园地、坡耕地剖面土壤非毛管蓄水能力较自然利用方式土地剖面非毛管蓄水能力下降55. 7%。毛管蓄水量和前期含水量具有极显著的正相关,整个剖面毛管蓄水量和前期含水量都以园地最高。从保水能力上考虑,园地是岩溶山区开垦土地较为理想的利用方式。建议加强园地凋落物的保护;在雨季尽量不让坡耕地空闲裸露,以防止水土流失。      

The role of channel morphology on the mobility and dispersion of bed sediment in a small gravel‐bed stream

This study uses a unique 10‐year tracer dataset from a small gravel‐bed stream to examine bed mobility and sediment dispersion over long timescales and at a range of spatial scales. Seasonal tracer data that captured multiple mobilizing events was examined, while the effects of morphology on bed mobility and sediment dispersion were captured at three spatial scales: within morphological units (unit scale), between morphological units (reach scale) and between reaches with different channel morphologies (channel scale). This was achieved by analyzing both reach‐average mobility and travel distance data, as well as the development of ‘mobility maps’ that capture the spatial variability in tracer mobility within the channel. The tracer data suggest that sediment transport in East Creek remains near critical the majority of the time, with only rare large events resulting in high mobility rates and grain travel distances large enough to move sediment past dominant bedforms. While a variable capturing both the magnitude and frequency of flow events within a season yielded a better predictor to sediment mobility and dispersion than peak discharge alone, the distribution of events of different magnitude within the season played a large role in determining tracer mobility rates and travel distances. The effects of morphology differed depending on the analysis scale, demonstrating the importance of scale, and therefore study design, when examining the effect of morphology on sediment transport. Copyright © 2016 John Wiley & Sons, Ltd.     

On the predictability of the 137Cs distribution in the Severn Estuary

The observed distribution of ¹³⁷Cs resulting from known sources in the Severn Estuary permits the testing of simple predictive models for the one-dimensional distribution of non-conservative substances in an estuary. These models either use a known distribution of salinity to infer corresponding ones for other substances, or else directly solve mass balance equations utilizing previously determined dispersion coefficients. Both methods are shown to previously determined dispersion coefficients. Both methods are shown to provide results comparing favorably with observations.Stokes drift plays an important role in the circulation of the Severn. A modified densimetric Froude number, including this drift, is therefore used to estimate the circulation and stratification of the estuary.A new equation is used for calculating the ¹³⁷Cs distribution from the observed salinity distribution. It generalizes previous formulations to permit variation of the net runoff with position along the estuary.     

Spherical particles as tracers of atmospheric ceramic industry

Castellón province houses the nucleus of ceramics production in Spain (93%). This nucleus, located around in the villages of Castellón, Villarreal, Alcora and Onda, has gone through a special process of industrial expansion. The emissions, most of them of particulate material, can constitute a real environmental problem. A study designed to identify the crystalline and glassy phases in the depositable particulate material has been carried out by SEM/EDX and X-ray diffraction methods. Quartz, calcite, illite, kaolinite, chlorite, and feldspars have been the main crystalline phases identified. The number of spherical morphology particles found in the depositable material is remarkable. The vitreous material found was spherical nodules. Due to the shape, size (1–10 μm), and chemical composition of these particles, they can be excellent tracers of the ceramics industry emissions.The presence of Zn, Ba, or Fe are due to the massive use of these substances as opacifying and pigmentation agents in many ceramics frits and glaze compositions. This fact gives a valuable information that will facilitate the studies guided to obtain important aims such as: toxicology, average size of a particle, formation mechanisms, etc.     

Origine des eaux des émergences karstiques chlorurées du Languedoc-Roussillon

The origin of chloride-rich karstic spring waters representative of the Languedoc-Roussillon region has been investigated with a hydrochemical approach. To this end, the major and trace elements most often used in the study of saline environments have been considered (Cl, SO₄, Br, B, Li). This study allowed distinguishing the different end-members of the various chloride-rich karstic spring waters (evaporitic, marine, geothermal). Associated with the Cl, Br and B contents, the Li/SO₄ ratio appeared as a relevant tracer for the determination of the origin of lithium and by extension of the considered waters. To cite this article: O. Hébrard et al., C. R. Geoscience 338 (2006).     

LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS*

In accordance with a new compensation principle of discrete computations,the traditional meteorological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computational instability and incomplete energy conservation,and raising the computational efficiency of the traditional schemes.As the numerical tests of the new schemes demonstrate,in solving the problem of energy conservation in operational computations,the new schemes can eliminate the (nonlinear) computational instability and,to some extent even the (nonlinear) computational diverging as found in the traditional schemes,Further contrasts between new and traditional schemes also indicate that,in discrete operational computations,the new scheme in the case of nondivergence is capable of prolonging the valid in-tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical computational "climate drift",meanwhile increasing its computational accuracy and reducing its amount of computation.The working principle of this paper is also applicable to the problem concerning baroclinic primitive equations.