A spatially and temporally adaptive solution of Richards’ equation

Efficient, robust simulation of groundwater flow in the unsaturated zone remains computationally expensive, especially for problems characterized by sharp fronts in both space and time. Standard approaches that employ uniform spatial and temporal discretizations for the numerical solution of these problems lead to inefficient and expensive simulations. In this work, we solve Richards’ equation using adaptive methods in both space and time. Spatial adaption is based upon a coarse grid solve and a gradient error indicator using a fixed-order approximation. Temporal adaption is accomplished using variable order, variable step size approximations based upon the backward difference formulas up to fifth order. Since the advantages of similar adaptive methods in time are now established, we evaluate our method by comparison with a uniform spatial discretization that is adaptive in time for four different one-dimensional test problems. The numerical results demonstrate that the proposed method provides a robust and efficient alternative to standard approaches for simulating variably saturated flow in one spatial dimension.     

Wave erosion of a massive artificial coastal landslide

The Lone Tree landslide is located on the coast north of San Francisco, California, and is unusual in that it is positioned within the San Andreas fault zone. Its material ranges from mud through to boulders, which makes the slide particularly susceptible to mass movement. Movement of its western half increased following the Loma Prieta earthquake in 1989, closing an important highway for over a year, at which time a large cut-and-fill operation was undertaken to remove the upper portion of the slide so it would create no future disruption. Material cut from the upper slide was dumped below the highway, with the debris extending into the ocean. This created an artificial debris fill that is equivalent to a massive natural landslide, and a unique opportunity to monitor its erosion. Rainfall quickly eroded a series of rills into the face of the artificially created landslide, but the concentration of gravel and cobbles armoured these small channels, greatly reducing the rate of subsequent erosion. Waves cut away the toe, and the focus of this paper is on the development of a model to analyse the frequency of wave attack in terms of tide levels and wave conditions. A beach consisting of cobbles and boulders formed at the toe of the debris, offering partial protection and reducing the rate of continued erosion. In the short term, armouring of the rills and the development of a fronting beach have reduced the overall erosion of the debris and the transfer of sediment to the ocean. In the longer term, the formation of secondary slumps can be expected to renew the erosion. Eventually the morphology of the debris fill should approach the configuration of the natural landslide, an unmodified portion of which remains adjacent to the artificial fill. © 1998 John Wiley & Sons, Ltd.     

A review of the physics and ecological implications of the thermal bar circulation

Following recent applications of numerical modelling and remote sensing to the thermal bar phenomenon, this paper seeks to review the current state of knowledge on the effect of its circulation on lacustrine plankton ecosystems. After summarising the literature on thermal bar hydrodynamics, a thorough review is made of all plankton observations taken in the presence of a thermal bar. Two distinct plankton growth regimes are found, one with production favoured throughout the inshore region and another with a maximum in plankton biomass near the position of the thermal bar. Possible explanations for the observed distributions are then discussed, with reference to numerical modelling studies, and the scope for future study of this interdisciplinary topic is outlined.     

Analytical model for aquifer response incorporating distributed stream leakage

An analytical model of stream/aquifer interaction is proposed that predicts drawdown in an aquifer with leakage from a finite-width stream induced by pumping from a well. The model is formulated based on the assumptions of stream partial penetration, a semipervious streambed, and distributed recharge across a finite-width stream. Advantages of the analytical solution include its simple structure, consisting of the Theis well function with integral modifications. The solution is derived for the semi-infinite domain between the stream and pumping well, which is of primary interest to hydrogeologists. Previous stream/aquifer analytical models are compared to the analytical solution based on dimensionless drawdown profiles. Drawdown in the aquifer near a wide stream was found to be less than that predicted by a solution that ignored stream width. Deviations between the proposed analytical solutions and previous solutions increase as stream width increases. For a hypothetical stream/aquifer system, the proposed analytical solution was equivalent to prior solutions when the ratio of the distance between the stream and aquifer to the stream width was greater than 25. This analytical solution may provide improved estimates of aquifer and streambed leakage parameters by curve fitting experimental field drawdown data.     

Morphology of riffle–pool sequences in the River Severn,England

Despite the occurrence of riffle–pool sequences in many rivers there are few data concerning riffle–pool unit morphology. Of many criteria proposed to identify riffle–pool units, only three methods can be regarded as objective and robust. These are the ‘zero‐crossing’, the ‘spectral analysis’ and the ‘control‐point’ methods. In this paper statistics are developed using the first two of these methods to describe the streamwise morphology of 275 riffles and 285 pools which form a continuous 32·1 km reach of the bed of the River Severn in Shropshire, England. Yalin's theoretical relationship between the average riffle:pool unit length ( λ _p) and channel width ( W ), λ _p = 3 W , applies to the River Severn. Reach‐average riffle height ( H ) is a constant proportion of bankfull depth ( h ); typically H ≅ 0·16 h . Riffle height is a positive function of riffle length. Pool depth is a positive function of pool length. However, both riffle length and pool length increase more rapidly than the bed‐level amplitude, such that long riffles or pools are relatively ‘flat’. As channel gradient reduces, bedforms flatten and become more asymmetric as riffle stoss sides and the proximal slope of pools lengthen at the expense of riffle lee sides and pool distal slopes. The statistical relationships between riffle steepness (H/L) and water depth are similar to those for equilibrium subaqueous dunes. The Severn data are consistent with Yalin's theoretical analysis relating riffle bedform length (L _r) to water depth, i.e. L _r = α2π h, wherein α ≅ 1 for steep near‐equilibrium bedforms but α ≅ 2 to 3 as the relative depth decreases and riffles become long, low features. Theoretical consideration and turbulence data indicate that the frequency of coherent turbulent‐flow structures associated with the riffle–pool mixing length in the Severn should be of the order of 50 to 100 s. The morphological similarity of the steepest River Severn riffles with dunes raises intriguing questions with respect to self‐similar, convergent organization of periodic alluvial bedforms and to bedform dynamic classification particularly. Copyright © 2000 John Wiley & Sons, Ltd.     

The Lower Mantle Minerals in Ophiolite-hosted Diamond

<正>Ophiolites are fragments of ancient ocean lithosphere emplaced on continental margins,in island arcs or in accretionary prisms,and have long been studied to better understand the evolution of ocean basins and collision of tectonic plates,the processes of mountain building and the occurrence of valuable ore bodies,such as podiform