The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

Flow in a single fracture (SF) is an important research subject in groundwater hydrology, hydraulic engineering, radioactive nuclear waste repository and geotechnical engineering. An abruptly changing aperture is a unique type of SF. This study discusses the relation between the values of the critical Reynolds number (Re_c) for the onset of symmetry breaking of flow and the expansion ratio (E) of SF, which is defined as the ratio between the outlet (D) and inlet (d) apertures. This study also investigates the effect of inlet aperture d on Re_c for flow in an SF with abruptly changing apertures (SF‐ACA) using the finite volume method. Earlier numerical and experimental results showed that flow is symmetric in respect to the central plane of the SF‐ACA at small Reynolds number (Re) but becomes asymmetric when Re is sufficiently large. Our simulations show that the value of Re_c decreases with the increasing E, and the relationship between the logarithm of Re_c and E can be described accurately using either a quadratic polynomial function or a logarithmic function. However, the relationship of Re_c and d for a given E value is vague, and Re_c becomes even less sensitive to d when E increases. This study also reveals that the hydraulic gradient (J) and flow velocity (v) follow a super‐linear relationship that can be fitted almost perfectly by the Forchheimer equation. The inertial component (J_i) of J increases monotonically with Re, whereas the viscous component (J_v) of J decreases monotonically with Re. The Re value corresponding to equal inertial and viscous components of J (named as the transitional point Re) decreases when E increases, and such a transitional point Re should be closely related to the critical Reynolds number Re_c, although a rigorous theoretical proof is not yet available. Copyright © 2015 John Wiley & Sons, Ltd.     

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (S_s) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and S_s of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.     

Using stable isotopes to understand seasonal and interannual dynamics in moisture sources and atmospheric circulation in precipitation

Stable isotopes in precipitation are useful tracers to strengthen understanding of climate change and hydrological processes. In this study, the moisture sources of 190 precipitation events in Beijing were analysed using the Hybrid Single‐particle Lagrangian Integrated Trajectory model, based on which we studied the relation between variations in precipitation δ¹⁸O and dynamics in moisture sources and atmospheric circulation in seasonal and interannual timescales. Categorization of 7 groups of moisture sources was performed, among which oceanic moisture sources presented lower δ¹⁸O in precipitation than continental moisture sources. The results show that seasonal variations of precipitation δ¹⁸O were caused by changes of moisture sources. In summer, moisture from proximal oceans dominated vapour transport to Beijing due to increasing monsoon strength and resulted in a relatively small variation of precipitation δ¹⁸O. At the interannual timescale, the variations of δ¹⁸O in summer precipitation were related to dynamics in oceanic moistures, showing depleted values when the contribution of oceanic moistures, especially the proportion of long‐distance oceanic moisture, was high. Further analysis indicated that changes of oceanic moisture sources were controlled by the strength of summer monsoons. These findings address the complexity of moisture sources in midlatitude monsoon areas and suggest that isotopic signals in precipitation have the potential to deduce changes in moisture sources and atmospheric circulation and can therefore serve for palaeoclimate reconstruction.