On the well posedness of some wave formulations of the shallow water equations

According to the theory of characteristics, the number of boundary conditions required for the adequate definition of a PDE problem is equal to the number of characteristic half planes entering the domain associated with the PDE problem.This theory was applied to the primitive form of the shallow water equations two decades ago to determine the number of initial and boundary conditions required by these equations. The results of this early study are remembered here. Subsequently, the same theory is applied to some wave formulations of the shallow water equations (the wave continuity and primitive momentum equation model, and the wave continuity and wave momentum equation model).Circumstances under which the number of boundary conditions required by the mathematical model can be reduced to the number of available boundary conditions are discussed for both the primitive and wave formulations of the shallow water equations.     

A methodology to study rain splash and wash processes under natural rainfall

The complex interactions between rainfall‐driven erosion processes and rainfall characteristics, slope gradient, soil treatment and soil surface processes are not very well understood. A combination of experiments under natural rainfall and a consistent physical theory for their interpretation is needed to shed more light on the underlying processes. The present study demonstrates such a methodology. An experimental device employed earlier in laboratory studies was used to measure downslope rain splash and ‘splash‐creep’, lateral splash, upslope splash and rainfall‐driven runoff transport (wash) from a highly aggregated clay‐rich oxisol exposed to natural rainfall in West Java, Indonesia. Two series of measurements were made: the first with the soil surface at angles of 0°, 5°, 15° and 40°; and the second all at an angle of 5° but with different tillage and mulching treatments. A number of rainfall erosivity indices were calculated from rainfall intensity measurements and compared with measured transport components. Overall storm kinetic energy correlated reasonably well with sediment transport, but much better agreement was obtained when a threshold rainfall intensity (20 mm h^?1) was introduced. Rain splash transport measurements were interpreted using a recently developed theory relating detachment to sediment transport. Furthermore, a conceptually sound yet simple wash transport model is advanced that satisfactorily predicted observed washed sediment concentrations. The lack of replication precluded rigorous assessment of the effect of slope and soil treatment on erosion processes, but some general conclusions could still be drawn. The results stress the importance of experiments under conditions of natural rainfall. Copyright © 2002 John Wiley & Sons, Ltd.     

Scale invariance and self‐similarity in kinematic wave overland flow in space and time

Fractals are famous for their self‐similar nature at different spatial scales. Similar to fractals, solutions of scale invariant processes are self‐similar at different space–time scales. This unique property of scale‐invariant processes can be utilized to translate the solution of the processes at a much larger or smaller space–time scale (domain) based on the solution calculated on the original space–time scale. This study investigates scale invariance conditions of kinematic wave overland flow process in one‐parameter Lie group of point transformations framework. Scaling (stretching) transformation is one of the one‐parameter Lie group of point transformations and it has a unique importance among the other transformations, as it leads to the scale invariance or scale dependence of a process. Scale invariance of a process yields a self‐similar solution at different space–time scales. However, the conditions for the process to be scale invariant usually dictate various relationships between the scaling coefficients of the dependent and independent variables of the process. Therefore, the scale invariance of a process does not assure a self‐similar solution at any arbitrary space and time scale. The kinematic wave overland flow process is modelled mathematically as initial‐boundary value problem. The conditions to be satisfied by the system of governing equations as well as the initial and boundary conditions of the kinematic wave overland flow process are established in order for the process to be scale invariant. Also, self‐similarity of the solution of the kinematic wave overland flow under the established invariance conditions is demonstrated by various numerical example problems. Copyright © 2011 John Wiley & Sons, Ltd.     

On the deformations in a general linear substance of a layered media subjected to a body force and a deforming magnetic field

Summary The propagation of disturbances has been studied in a layered media, comprising a liquid and a general linear substance, subject to a body force and permeated by an initial magnetic field acting normal to the plane of the contact. The effect of the body force due to some internal source has been considered in the problem and a set of results has been obtained under two possible extreme variants of the boundary conditions in the form of integral forms, which can be computed to visualize the displacement—time and displacement—depth variations, both in the presence and absence of the body force. The effect of body force on the substance has been, as a sample case, illustrated in the graphs. The stress-strain relation of the general linear substance and the electromagnetic equations of Maxwell have been used in working out the problem.     

Chitosan – A Sizing Agent in Fabric Production – Development and Ecological Evaluation

Chitosan, a natural polymer, was investigated as a possible sizing agent in fabric production by appropriate modification in the textile industry. Based on recipe developments at a laboratory‐scale, the ecological and economical potential of mainly cotton yarns were demonstrated and developed. Subsequent tests within the scope of industrial production confirmed the findings of the basic developments. As an interesting alternative to the conventional sizing process involving the removal of the size after weaving, the use of appropriate processing technologies makes it possible to apply chitosan in the form of a sizing agent resistant to wash‐out processes. Therefore, the wash‐out process and the combined wastewater loading can be avoided and the properties of chitosan can be used beneficially in the later applications of the fabric. The traditional method of sizing and weaving developments as well as the analyses of material recycling showed the possibilities of using closed circuits in textile production involving sizing agent and water. It is possible that a chitosan‐specific enzyme suitable for production conditions, which facilitates the wash‐out process in combination with the biodegradation of the wastewater in a sewage plant, could be developed.     

Rates of surface processes on slopes,slope retreat and denudation

Results taken from 270 publications on rates are summarized, and collated with those from 149 publications reviewed previously (Young, 1969, 1974). The data are classified by major climatic zone, normal or steep relief, and consolidated or unconsolidated rocks. Representative rates and their ranges are given for soil creep, solifluction, surface wash, solution (chemical denudation), rock weathering, slope retreat, cliff (free face) retreat, marine cliff retreat, and denudation, the last being compared with representative rates of uplift. Solifluction is of the order of 10 times faster than soil creep, but both cause only very slow ground loss. Solution is an important cause of ground loss for siliceous rocks, on which it may be half as rapid as on limestones. Total denudation, brought about mainly by surface wash, reaches a maximum in the semi-arid and probably also the tropical savanna zones. Acceleration of natural erosion rates by human activities ranges from 2–3 times with moderately intense land use to about 10 times with intensive land use (and considerably higher still where there is recognized accelerated soil erosion). Where there is active uplift, typical rates are of the order of 10 times faster than denudation, although in some high, steep mountain ranges these may approach equality.     

Creep processes in landslides

Displacement of landslide blocks after initial slope failure can be very slow. In most cases movement of the blocks is attributed to sliding along a well-defined slip surface. It is discussed here whether, in addition to these so-called plastic movements, (continuous) creep processes are involved in the slow displacement. The study was carried out in the downstream part of the Bonne valley in the French Alps, where landslide complexes have developed in varved clay material. Displacements of landslide blocks were measured during a period of three years. Inclinometer measurements in flexible tubes showed that a creep zone developed above the slip surface in a zone about 1 m thick. These field observations on creep processes were supported by soil mechanical analysis. Threshold values for creep found in the laboratory nearly coincide with threshold values calculated from a field creep model developed by Ter-Stepanian. During the measuring period ±15 per cent of the displacement of the blocks possibly occurred via continuous creep.     

Olivine-spinel Phase Boundary Rheology, Strength and Deep Seismicity

In this paper,we discuss (1) whether a significant change in dominant creep mechanism will occur at 400 km discontinuity in some subducting slabs as a result of olivine-spinel phase transition;(2) could the result influence phase boundary strength and deep seismicity? Through this study,we noticed that a transition of creep mechanism from dislocation to diffusion (or superplasticity) could occur at the olivine-spinel phase boundary where temperature effect on phase transition dominates over pressure,which will result in a weakening phase boundary.Triggered by this phase transition weakening,a deep strong earthquake might be generated in the relatively strengthening region above the phase boundary so that the phase boundary is naturally the ceasing boundary of deep seismicity.Contrasting to this,the transition of the creep mechanism from dislocation glide to dislocation climb may be common at the phase boundary where pressure effect on phase transition dominates over temperature.In this case,olivine-spin     

Andrade Creep at the Isostasy Recovering Flows in the Mantle

The laboratory experiments with rock samples show that creep under small strains is transient and can be described by the linear hereditary rheological Andrade model. The flows that recover isostasy (including the postglacial rebound flows) cause the strains in the crust and mantle, which are as low as at most 10^–3 and, hence, demonstrate transient creep. The effective viscosity characterizing the transient creep is lower than that at the steady creep and depends on the characteristic time of the considered process. The characteristic time of restoration of isostatic equilibrium (isostatic rebound) after the initial perturbation of the Earth’s surface topography is at most 10 kyr and, therefore, the distribution of the rheological properties along the depth of the mantle and the crust differs from the distribution that corresponds to the slow geological processes. When considering the process of isostatic rebound, the upper crust can be modeled by a thin elastic plate, whereas the underlying crust and the mantle can be modeled by the halfspace with transient creep in which the rheological parameter is inhomogeneous with depth. For this system, the continuum mechanics equations are solved by means of the Fourier and Laplace transforms. The vertical displacements that violate the isostasy propagate from the area of the initial perturbation along the Earth’s surface and can be considered as the mechanism of the present-day vertical movements of the crust. Comparing the obtained results with the observation data allows estimating the Andrade parameter. The use of the Andrade rheological model makes it possible to quantify the relationship between the effective viscosity of the asthenosphere corresponding to the postglacial flows and the seismic Q-factor of this layer.     

中国东部地区断裂的缜奏性活动

对中国东部地区断裂的节奏性活动进行了探讨,认为这种节奏性活动主要根据构造地貌进行鉴别,并可分为六种型式:稳定—蠕滑错动;稳定—急速错动;蠕滑—急速错动;交替型蠕滑错动;交替型急速错动和复式错动。地震活动周期与断裂的节奏性活动相关联。断裂活动产生强震的型式有单发式、对偶式和连发式,这三种形式分别出现在不同的断裂中,并取决于不同区域、不同断裂的活动特征。     

Crusting effects on erosion processes under simulated rainfall on a tropical Alfisol

Sealing and crusting of soil surfaces have dramatic effects on water infiltration into and runoff from soils, thereby greatly influencing erosion processes. This study focused on the effect of the initial stage of crusting on inter-rill erosion processes for a crust-prone Alfisol sampled from south-central India. Soil aggregates ranging from 2·4 to 8 mm collected from ploughed (PL) and naturally vegetated (NV) treatments were subjected to rainfall simulation under laboratory conditions. Runoff from PL soil aggregates was 2–2·5 times higher, while percolation was 20–100% lower, than for NV aggregates. Soil wash and splash losses were 0·5–3 times greater for PL than for NV soil. Runoff and inter-rill erosion were significantly higher during the wet simulation run compared with the dry run. The results indicated that NV soil aggregates were more resistant to breakdown from raindrop impact and slaking, and subject to less rapid sealing, than PL soil. Total soil loss was influenced most by initial aggregate stability and the extent of seal development. Splash and wash losses of soil both increased as a result of surface sealing regardless of soil condition for short (30–60 min) rainfall durations. High drying rates resulted in the highest crust bulk densities. Increased crust strength for PL soil compared with NV soil reflected the greater susceptibility of cultivated soil to surface sealing and crusting. © 1998 John Wiley & Sons, Ltd.     

Scaling and self‐similarity in one‐dimensional unsteady open channel flow

The conditions under which the Saint Venant equations system for unsteady open channel flow, as an initial–boundary value problem, becomes self‐similar are investigated by utilizing one‐parameter Lie group of point scaling transformations. One of the advantages of this methodology is that the self‐similarity conditions due to the initial and boundary conditions can also be investigated thoroughly in addition to the conditions due to the governing equation. The obtained self‐similarity conditions are compared with the scaling relationships that are derived through the Froude similitude. It is shown that the initial–boundary value problem of a one‐dimensional unsteady open channel flow process in a prototype domain can be self‐similar with that of several different scaled domains. However, the values of all the flow variables (at specified time and space) under different scaled domains can be upscaled to the same values in the prototype domain (at the corresponding time and space), as shown in this study. Distortion in scales of different space dimensions has been implemented extensively in physical hydraulic modelling, mainly because of cost, space and time limitations. Unlike the traditional approach, the distinction is made between the longitudinal–horizontal and transverse–horizontal length scales in this study. The scaled domain obtained by the proposed approach, when scaling ratios of channel width and water depth are equal, is particularly important for the similarity of flow characteristics in a cross‐section because the width‐to‐depth ratio and the inclination angles of the banks are conserved in a cross‐section. It is also shown that the scaling ratio of the roughness coefficient under distorted channel conditions depends on that of hydraulic radius and longitudinal length. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal and economical flexibility in setting up physical hydraulic models. Copyright © 2013 John Wiley & Sons, Ltd.     

Slope flows governed by diffusion effects in seas, lakes, and reservoirs

The hydrodynamics of slope flows governed by heat and salt diffusion near a rigid sloping impermeable boundary in stratified water bodies is studied. The physics of this phenomenon consists in that, because of the impermeability of the shore slope, the fluxes of heat and salt normal to the slope surface must be zero. Since the background stratification does not meet this condition, diffusion boundary layers appear along the shore slope. It is shown that, depending on the ratio between diffusion coefficients of heat and salt and the parameters of stratification by temperature and salinity, of convection the slope flows can be either ascending or descending. Moreover, under some conditions, a finger-type regime can form in boundary layers, though the background stratification is stable. The appearing slope flows, though they are local, initiate global transverse ventilation of water in the entire water body.     

On a power series solution to the Boussinesq equation

For certain initial and boundary conditions the Boussinesq equation, a nonlinear partial differential equation describing the flow of water in unconfined aquifers, can be reduced to a boundary value problem for a nonlinear ordinary differential equation. Using Song et al.'s (2007) [7] approach, we show that for zero head initial condition and power-law flux boundary condition at the inlet boundary, the solution in the form of power series can be obtained with Barenblatt's (1990) [2] rescaling procedure applied to the power series solution obtained in Song et al. (2007) [7] for the power-law head boundary condition. Polynomial approximations can then be obtained by taking terms from the power series. Although for a small number of terms the newly obtained approximations may be worse than polynomial approximations obtained by other techniques, any desired accuracy can be achieved by taking more terms from the power series.     

Simultaneous identification of parameter,initial condition,and boundary condition in groundwater modelling

In this paper, we perform an inverse method to simultaneously estimate aquifer parameters, initial condition, and boundary conditions in groundwater modelling. The parameter estimation is extended to a complete inverse problem that makes the calibrated groundwater flow model more realistic. The adjoint state method, the gradient search method, and the least square error algorithm are combined to build the optimization procedure. Horizontal two‐dimensional groundwater flow in a confined aquifer is exemplified to demonstrate the correlation between unknowns, the contribution of observation, as well as the suitability of applying the inverse method. The correlation analysis shows the connection between storage coefficient and initial condition. Besides, transmissivity and boundary conditions are also highly correlated. More observations at different location and time are necessary to provide sufficient information. A time series of unsteady head is requested for estimation of storage coefficient and initial condition. Observation near boundary is very effective for boundary condition estimation. The observation at pumping well mostly contributes to the estimation of transmissivity. According to all observations, it is possible to identify parameters, initial condition, and boundary condition simultaneously. Furthermore, the results not only illustrate the traditional assumption of known boundary condition but also initial condition, which may cause an incorrect estimation. Copyright © 2009 John Wiley & Sons, Ltd.     

The differential impact of some soil loss factors on flow,runoff creep and rainwash

The Hortonian model of runoff flow which had been thought to be applicable in arid areas has previously been shown not to be valid, notably in Israel, where inverse relations have been observed between slope angle, and runoff discharge and slope erosion. The paper discusses laboratory experiments on simulated slope conditions in a rather arid environment. It is shown by rain simulation on granite grus that infiltration capacity is a function of rainfall intensity, slope angle and runoff discharge. The infiltration capacity f can equal the rainfall intensity beyond a critical distance x(m) so that discharge becomes constant. Debris covers affect runoff hydraulics, especially on poorly cohesive soils, and both slow downslope and upslope movements which correspond to the process of so-called runoff creep can occur. Coarse debris and grass covers, as roughness factors, induce hydraulic discontinuities and activate local turbulent flow and slope erosion. Instead of being merely protective elements these factors tend to catalyze the slope wash, in comparison with naked surfaces, if the Reynolds number of the flow exceeds a certain critical value.     

波浪作用下成层海床孔隙水压力响应的简化分析

采用不排水条件下孔隙水压力发展模式,作为Terzagh i一维固结方程中考虑波浪循环作用所引起的孔隙水压力源项,对于成层海床建立了推广的一维动力固结方程,运用数理方程中的分离变量法与G reen函数求解了成层海床在波浪作用下残余孔隙水压力的发展规律,进而对成层海床的液化势进行了评判。对比计算与分析表明,海床表层土的渗透性及其厚度对于海床的整体抗液化性能具有显著的影响,低渗透性的表层导致海床孔隙水压力的显著积累,此时表层置换法是防治液化的有效途径。     

Two-dimensional mantle flow beneath a rigid accreting lithosphere

This study considers two-dimensional mantle flow beneath a rigid lithosphere. The lithosphere which forms the upper boundary of a convecting region moves with a prescribed uniform horizontal velocity, and thickens with distance from the accreting plate boundary as it cools. Beneath the lithosphere, the mantle deforms viscously by diffusion creep and is heated radiogenically from within. Solutions for thermal convection beneath the lithosphere are obtained by finite-difference methods. Two important conclusions have resulted from this study: (1) convective patterns of large aspect ratio are stable beneath a rigid moving lithosphere; (2) even for a lithosphere velocity as small as 3 cm/yr. and a Rayleigh number as large as 10⁶, mantle circulation with large aspect ratio is driven dominantly by the motion of the lithosphere rather than by temperature gradients within the flow. Gravity, topography and heat flow are determined and implications for convection in the upper mantle are discussed.     

The subsurface–land surface–atmosphere connection under convective conditions

The dynamics of the free groundwater table influence land surface soil moisture and energy balance components, and are therefore also linked to atmospheric processes. In this study, the sensitivity of the atmosphere to groundwater table dynamics induced heterogeneity in land surface processes is examined under convective conditions. A fully coupled subsurface–land surface–atmosphere model is applied over a 150 km × 150 km study area located in Western Germany and ensemble simulations are performed over two convective precipitation events considering two separate model configurations based on groundwater table dynamics. Ensembles are generated by varying the model atmospheric initial conditions following the prescribed ensemble generation method by the German Weather Service in order to account for the intrinsic, internal atmospheric variability. The results demonstrate that especially under strong convective conditions, groundwater table dynamics affect atmospheric boundary layer height, convective available potential energy, and precipitation via the coupling with land surface soil moisture and energy fluxes. Thus, this study suggests that systematic uncertainties may be introduced to atmospheric simulations if groundwater table dynamics are neglected in the model.     

Quantification of uncertainty in design water levels due to uncertain bed form roughness in the Dutch river Waal

Hydrodynamic river models are applied to design and evaluate measures for purposes such as safety against flooding. The modelling of river processes involves numerous uncertainties, resulting in uncertain model results. Knowledge of the type and magnitude of these uncertainties is crucial for a meaningful interpretation of the model results. Uncertainty in the hydraulic roughness due to bed forms is one of the main contributors to the uncertainty in the modelled water levels. The aim of this study was to quantify the uncertainty in the bed form roughness under design conditions and quantify the effect on the design water levels in the Dutch river Waal. Five roughness models that predict bed form roughness based on measured bed form and flow characteristics were extrapolated to design conditions. The results show that the 95% confidence interval of the predicted Nikuradse roughness values under design conditions ranges from 0.32 to 1.03 m. This uncertainty was propagated through the two‐dimensional hydrodynamic model, WAQUA, by means of a Monte Carlo simulation for an idealized schematization of the Dutch river Waal. The uncertain bed form roughness results in an uncertainty in the design water levels, with a 95% confidence interval of 0.53 m, which is significant for Dutch river management practice. The uncertainty in the bed form roughness was mainly caused by a lack of knowledge about the physical process of bed form evolution that causes roughness. An improved estimation of bed form roughness can significantly reduce the uncertainty in the design water levels. Copyright © 2012 John Wiley & Sons, Ltd.