Analytical investigation of the exact groundwater divide between rivers beyond the Dupuit–Forchheimer approximation

The groundwater divide is a key feature of river basins and significantly influenced by subsurface hydrological processes. For an unconfined aquifer between two parallel rivers or ditches, it has long been defined as the top of the water table based on the Dupuit–Forchheimer approximation. However, the exact groundwater divide is subject to the interface between two local flow systems transporting groundwater to rivers from the infiltration recharge. This study contributes a new analytical model for two-dimensional groundwater flow between rivers of different water levels. The flownet is delineated in the model to identify groundwater flow systems and the exact groundwater divide. Formulas with two dimensionless parameters are derived to determine the distributed hydraulic head, the top of the water table and the groundwater divide. The locations of the groundwater divide and the top of the water table are not the same. The distance between them in horizontal can reach up to 8.9% of the distance between rivers. Numerical verifications indicate that simplifications in the analytical model do not significantly cause misestimates in the location of the groundwater divide. In contrast, the Dupuit–Forchheimer approximation yields an incorrect water table shape. The new analytical model is applied to investigate groundwater divides in the Loess Plateau, China, with a Monte Carlo simulation process taking into account the uncertainties in the parameters.     

Rainfall intensity affects runoff responses in a semi-arid catchment

The source and hydrochemical makeup of a stream reflects the connectivity between rainfall, groundwater, the stream, and is reflected to water quantity and quality of the catchment. However, in a semi-arid, thick, loess covered catchment, temporal variation of stream source and event associated behaviours are lesser known. Thus, the isotopic and chemical hydrographs in a widely distributed, deep loess, semi-arid catchment of the northern Chinese Loess Plateau were characterized to determine the source and hydrochemical behaviours of the stream during intra-rainfall events. Rainfall and streamflow were sampled during six hydrologic events coupled with measurements of stream baseflow and groundwater. The deuterium isotope (²H), major ions (Cl⁻, SO₄²⁻, NO₃⁻, Ca²⁺, K⁺, Mg²⁺, and Na⁺) were evaluated in water samples obtained during rainfall events. Temporal variation of ²H and Cl⁻ measured in the groundwater and stream baseflow prior to rainfall was similar; however, the isotope compositions of the streamflow fluctuated significantly and responded quickly to rainfall events, likely due to an infiltration excess, overland dominated surface runoff during torrential rainfall events. Time source separation using ²H demonstrated greater than 72% on average, the stream composition was event water during torrential rainfall events, with the proportion increasing with rainfall intensity. Solutes concentrations in the stream had loglinear relationships with stream discharge, with an outling anomaly with an example of an intra-rainfall event on Oct. 24, 2015. Stream Cl⁻ behaved nonconservative during rainfall events, temporal variation of Cl⁻ indicated a flush and washout at the onset of small rainfall events, a dilution but still high concentration pattern in high discharge and old water dominated in regression flow period. This study indicates rainfall intensity affects runoff responses in a semi-arid catchment, and the stored water in the thick, loess covered areas was less connected with stream runoff. Solute transport may threaten water quality in the area, requiring further analysis of the performance of the eco-restoration project.     

Subsurface flow measurements using passive flux meters in variably-saturated cold-regions landscapes

To date, passive flux meters have predominantly been applied in temperate environments for tracking the movement of contaminants in groundwater. This study applies these instruments to reduce uncertainty in (typically instantaneous) flux measurements made in a low-gradient, wetland dominated, discontinuous permafrost environment. This method supports improved estimation of unsaturated and over-winter subsurface flows which are very difficult to quantify using hydraulic gradient-based approaches. Improved subsurface flow estimates can play a key role in understanding the water budget of this landscape.     

High-frequency monitoring of hydrological and biogeochemical fluxes in forested catchments of southern Chile

The variability of rainfall-dependent streamflow at catchment scale modulates many ecosystem processes in wet temperate forests. Runoff in small mountain catchments is characterized by a quick response to rainfall pulses which affects biogeochemical fluxes to all downstream systems. In wet-temperate climates, water erosion is the most important natural factor driving downstream soil and nutrient losses from upland ecosystems. Most hydrochemical studies have focused on water flux measurements at hourly scales, along with weekly or monthly samples for water chemistry. Here, we assessed how water and element flows from broad-leaved, evergreen forested catchments in southwestern South America, are influenced by different successional stages, quantifying runoff, sediment transport and nutrient fluxes during hourly rainfall events of different intensities. Hydrograph comparisons among different successional stages indicated that forested catchments differed in their responses to high intensity rainfall, with greater runoff in areas covered by secondary forests (SF), compared to old-growth forest cover (OG) and dense scrub vegetation (CH). Further, throughfall water was greatly nutrient enriched for all forest types. Suspended sediment loads varied between successional stages. SF catchments exported 455 kg of sediments per ha, followed by OG with 91 kg/ha and CH with 14 kg/ha, corresponding to 11 rainfall events measured from December 2013 to April 2014. Total nitrogen (TN) and phosphorus (TP) concentrations in stream water also varied with rainfall intensity. In seven rainfall events sampled during the study period, CH catchments exported less nutrients (46 kg/ha TN and 7 kg/ha TP) than SF catchments (718 kg/ha TN and 107 kg/ha TP), while OG catchments exported intermediate sediment loads (201 kg/ha TN and 23 kg/ha TP). Further, we found significant effects of successional stage attributes (vegetation structure and soil physical properties) and catchment morphometry on runoff and sediment concentrations, and greater nutrients retention in OG and CH catchments. We conclude that in these southern hemisphere, broad-leaved evergreen temperate forests, hydrological processes are driven by multiple interacting phenomena, including climate, vegetation, soils, topography, and disturbance history.     

Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.     

First evidence of IMF control of Jovian magnetospheric boundary locations: Cassini and Galileo magnetic field measurements compared

The Cassini spacecraft, en route to Saturn, passed close to Jupiter while the Galileo spacecraft was completing its 28th and 29th orbits of Jupiter, thus offering a unique opportunity for direct study of the solar wind-Jovian interaction. Here evidence is given of response of the Jovian magnetopause and bow shock positions to changes of the north-south component of the solar wind magnetic field, a phenomenon long known to occur in equivalent circumstances at Earth. The period analyzed starts with the passage over Cassini of an interplanetary shock far upstream of Jupiter. The shock's arrival at Galileo on the dusk-flank of the magnetosphere caused Galileo to exit into the solar wind. Using inter-spacecraft timing based on the time delay established from the shock arrival at each spacecraft, we point out that Galileo's position with respect to the Jovian bow shock appears to correlate with changes in the disturbed north-south reversing field seen behind the shock. We specifically rule out the alternative of changes in the shape of the bow shock with rotations of the interplanetary magnetic field as the cause.     

青藏高原隆升的非线性动态有限元仿真研究

根据青藏高原的地质特征建立分析模型，采用3维动态有限元方法，在计算仿真板块速度场的基础上，计算在青藏高原的隆升过程中该地区地壳岩石的等效应力和位移随时间的变化，计算仿真得到的速度场与1998年GPS观测的速度场吻合良好；与过去一贯的假设相反，计算结果反映出地壳应力场不是静态的，而是此起彼伏，不断变化的，应力值最大且变化最剧烈的地区在克什米尔地区、鄂尔多斯地区和鲜水河－小江断裂带，与地震多发区域吻合。