This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile–immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection–dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer tests. 相似文献
The relationship between the amplification ratio of earthquake ground motion and geologic conditions at Japan Meteorological Agency (JMA) stations nationwide was examined to propose an estimation method of the amplification ratio that is applicable to entire Japan. The amplification ratios for the instrumental JMA intensity, as well as for the peak ground acceleration and velocity, were obtained from the station coefficients of the attenuation relationships using strong motion records measured at 77 JMA stations over a period of more than 8 years. A combined use of geomorphological land classification and subsurface geology was found to yield the best estimate of the site amplification ratio. This result suggests that these data, and hence the Digital National Land Information, which is a nationwide GIS database, may be conveniently used for the estimation of strong motion distribution over large areas in Japan. 相似文献
In this study, we examine the effects of conditioning spatially variable transmissivity fields using head and/or transmissivity measurements on well-capture zones. In order to address the challenge posed by conditioning a flow model with spatially varying parameters, an innovative inverse algorithm, the Representers method, is employed. The method explicitly considers this spatial variability.
A number of uniform measurement grids with different densities are used to condition transmissivity fields using the Representers method. Deterministic and stochastic analysis of well-capture zones are then examined. The deterministic study focuses on comparison between reference well-capture zones and their estimated mean conditioned on head data. It shows that model performance due to head conditioning on well-capture zone estimation is related to pumping rate. At moderate pumping rates transmissivity observations are more crucial to identify effects arising from small-scale variations in pore water velocity. However, with more aggressive pumping these effects are reduced, consequently model performance, through incorporating head observations, markedly improves. In the stochastic study, the effect of conditioning using head and/or transmissivity data on well-capture zone uncertainty is examined. The Representers method is coupled with the Monte Carlo method to propagate uncertainty in transmissivity fields to well-capture zones. For the scenario studied, the results showed that a combination of 48 head and transmissivity data could reduce the area of uncertainty (95% confidence interval) in well-capture zone location by over 50%, compared to a 40% reduction using either head or transmissivity data. This performance was comparable to that obtained through calibrating on three and a half times the number of head observations alone. 相似文献
A survey of flows was conducted at a river confluence with coarse bed material. Bridges were installed on both tributaries, at the confluence and farther downstream on the receiving stream. At these stations, flow velocities were measured over a dense grid for seven conditions ranging from very low flows to the bankfull stage. Hydraulic geometry relationships established at all four stations revealed that flow is accelerated through the confluence as stage rises. At bankfull discharge, average velocity is 1.6 times higher at the confluence than on either tributary. Flow acceleration occurs at and above intermediate flow stages and is concentrated at the centre of a linear pool located at the confluence. The development of a zone of high shear stress is also associated with the cell of high flow velocity. Flow acceleration is dissipated at the exit of the pool where water surges over boulder ribs. The acceleration is not related to the development of flow separation zones as observed by Best and Reid (1984) for wide junction angles, nor is it explained by the reduction of the friction exerted by the banks. Acceleration is associated with the plan geometry of the confluence, with the lateral slopes which permit water to converge, and with a reduction in grain roughness at the confluence. Owing to the curvature of the tributary and to the acute angle of entry, relative power losses through the confluence decrease with increasing stages. 相似文献
The expected head and standard deviation of the head from the first order Taylor series approximation is compared to Monte Carlo simulation, for steady flow in a confined aquifer with transmissivity as a random variable. Emphasis is on the effect of changes in the covariance structure of the transmissivity, and pumping rates, on the errors in the first order Taylor series approximation. The accuracy of the first order Taylor series approximation is found to be particularly sensitive to pumping rates. With significant pumping the approximation is found to under estimate both the expected drawdown and head variance, and the error increases as the pumping rate increases. This can lead to large errors in probability constraints based on moments from the first order Taylor series approximation. 相似文献