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Singularities of Taylor's power law in the analysis of aggregation measures
Get PDFTaylor's law is a well-known power law (TPL) for analysing the scaling behaviour of many fluctuating physical phenomena in nature. The scaling exponent of this law forms the basis of the aggregation process to which a precise probability density function corresponds. In some phenomena, TPL behavior with periodic components of the aggregates has been observed for small partitions, especially for physical processes characterized by values of where fluctuation-related aggregation processes are supported by Poissonian distributions. We intend to show that for values of very close to unity it is possible to find a trend, in the double logarithmic scale, of the TPL that there are `periodic patterns' (components) between variance and mean. This behaviour is found in other binomial-type distributions, of which the Poissonian is a particular case, with mappings characterised by a variance close to 1
Stochastic analysis of steady seepage underneath a water-retaining wall through highly anisotropic porous media
No full textSteady seepage is determined by a head drop upstream/downstream of a water-retaining wall. Due to its erratic variations, hydraulic log-conductivity is modelled as a stationary random space function (RSF). We deal with a highly anisotropic porous formation, i.e. an axisymmetric medium where the horizontal correlation integral scale of is much larger than the vertical one. The goal of computing the resulting flow field within a stochastic framework is complicated by non-uniformity of the mean flow. Simple (closed-form) expressions for the correlation functions of the flow variables as well as the mean head are derived. We use these results to quantify the impact of spatial variability of upon the probability that the exit volumetric flow rate downstream of the wall is greater than that obtained by regarding the formation as homogeneous (with constant hydraulic conductivity). In particular, we show that the spatial variability of may lead to predictions (and consequently to design choices) which significantly differ from those achieved by regarding the porous formation as homogeneous
A scale-invariant property of the water retention curve in weakly heterogeneous vadose zones
No full textAdvances in River Hydraulic Characterization
Get PDFThe characterization of river hydraulics is very important for the definition of many problems connected with flood and morphodynamical models, including the stability of banks, slopes and sediments transport. These physical aspects are often closely related to the observation scale of hydraulic phenomena. The latter has significant value both for the channel and basin scale. This coupling of scales is now possible due to, for example, modern LiDAR detection techniques, in which topographic surveys (DEMs) are predominant, as well as other topographical survey techniques. River scale hydraulic phenomena and their field measurements represent a new paradigm towards the development of computational procedures for the spatio-temporal scale representation of complex hydraulic phenomena.
This Special Issue aims to emphasize new numerical techniques and physical measurements in the field of hydraulic observations at laboratory, channel, and basin scale.
Applying channel scale, He et al. [1] analyzed the effect of physical factors on the growth of Chlorella vulgaris on enriched media by the use of orthogonal analysis and response surface methodology. In this context, rivers are also viewed as biological coupled systems, and in particular, this study shows that the growth of C. vulgaris can be regulated by changing physical conditions simultaneously, and the optimization of physical conditions can be applied to biomass production, algae prediction, and acid water treatment in rivers [1].
By the use of channel scale, Licciardello et al. [2] introduced a stream hydro-morphological evaluation, analysis, and monitoring system procedure called IDRAIM, which allows us, on the basis of a number of physically based geomorphological descriptors, us to determine the overall state of physical ’equilibrium’ of a river. This is a study case of Dittaino River (Eastern Sicily, Italy). It is very important, because the assessment of a river’s ecological status, including its hydro-morphological and morphological dynamics, which can be used for the implementation of design models and interventions integrating protection and environmental requalification, requires the evaluation of hydro-morphological state changes. As such, the IDRAIM procedure could help in sustainable river management [2].
Rivers also affect urban drainage scales. The transition from confluence situations can highlight critical elements for an adequate design and management. In this context, Zhang and Lin [3] conducted an experimental study on the influence of drastically varying discharge ratios on bed topography and flow structure at urban channel confluences. This study showed that the drastic change in discharge ratio causes secondary scouring to the equilibrium bed topography in the confluence area. The bed surface in the sand hole, a sand bar drops, and the sediment are transported downstream. In this experiment, although local sand hole and sand ridge were formed in the flow recovery zone downstream, the results may be more suitable for urban channel confluence with relatively large width–depth ratio and small- and medium-sized natural channel confluences [3].
At basin scale, Primavera and Florio [4] introduced a new fixed mass algorithm that allows direct determination of the multi-fractal spectrum of a river network. The hybrid procedure, based on parallel computation, makes possible the direct estimation of the multifractal spectrum and the exponents of the singularities, without going through the Legendre transforms. By correctly estimating the scale exponents, i.e., the right-hand side of a spectrum, the maximum singularity index to be used in flood prediction models can be correctly estimated. MIUH (multifractal instantaneous unit hydrograph) is based exclusively on this parameter, so a technique that drastically reduces the computation time of multifractal spectra allows to validate real-time prediction flood procedures based on geomorphological descriptors [4].
Costabile et al. [5] investigated the effects of DEM depression filling on river drainage patterns and surface runoff generated by 2D rain-on-grid scenarios. The analysis, which is interesting from the point of view of morphological scaling, offers criteria for defining scaling effects from the transition of grid-channels to hydraulically active channels. The core of these transitions is based on models characterized by shallow water equations [5]
A note on the fractal behavior of hydraulic conductivity and effective porosity for experimental values in a confined aquifer
Get PDFHydraulic conductivity and effective porosity values for the confined sandy loam aquifer of the Montalto Uffugo (Italy) test field were obtained by laboratory and field measurements; the first ones were carried out on undisturbed soil samples and the others by slug and aquifer tests. A direct simple-scaling analysis was performed for the whole range of measurement and a comparison among the different types of fractal models describing the scale behavior was made. Some indications about the largest pore size to utilize in the fractal models were given. The results obtained for a sandy loam soil show that it is possible to obtain global indications on the behavior of the hydraulic conductivity versus the porosity utilizing a simple scaling relation and a fractal model in coupled manner. © 2013 Samuele De Bartolo et al
Average steady flow toward a drain through a randomly heterogeneous porous formation
Get PDFWe consider the problem of steady pumping of water from a line drain on the surface of a wet ground. Unlike the classical formulation, which regards the conductivity parameter K as uniformly distributed in the domain, the problem here is solved within a stochastic framework in order to account for the irregular (random), and more realistic, spatial variability of K. Due to the linearity of the problem at stake, we focus on the derivation of the mean Green function G. This is computed by means of an asymptotic expansion. The fundamental result is an analytical (closed form) expression of G which generalizes the classical solution. Based on this, we develop an equivalent conductivity Keq which enables one to tackle the problem similarly to the classical one. In particular, it is shown that the equivalent conductivity grows monotonically with the radial distance r from the drain, and it lies within the range Keq(0) ≤ Keq(r) ≤ Keq(∞) < ∞
Simple scaling analysis of active channel patterns in Fiumara environment
No full textA simple scaling analysis was performed on experimental data relative to a riverbed reach of the Allaro Fiumara, a fluvial environment typical of Southern Italy. For this purpose, a simplified geometrical approach was followed to determine the spatial distribution of the number of active channels for the river stretch considered. In particular, the section lines crossing the braided network skeleton with distance ranging from 5 to 200. m were considered. Firstly, a probabilistic analysis of the experimental data was carried out by using a truncated Poisson distribution to characterize the examined river morphologically. Afterward, a scaling analysis was performed to investigate the existence of a possible multimodal behaviour of the number of active channels and to identify the corresponding cutoff values. For this second approach by the so-called standard coarse graining analysis, we defined a power law usable to give the probability distribution of the active channels number with varying spatial partition (distance between consecutive sections). In this way, verifying the existence of a bimodal scaling behaviour was possible. Moreover, the cutoff limits that characterize the bimodal behaviour of the active channels were found for all the partition distances from 5 to 100. m, while the corresponding shape and scale parameters were also determined. A comparison of the results obtained by the statistical approach and the scaling analysis was carried out. The variability of the characteristic parameters of the Poisson and power type laws with scale was also investigated
Approximations on the Peano river network: Application of the Horton-Strahler hierarchy to the case of low connections
No full textA network analysis is used to investigate the low connections of natural river channels. At the basin scale, the river networks are analyzed according to the Horton-Strahler hierarchy. We propose a quantitative criterion for the average junction degree as a function of a fixed hierarchical order of the network and independent of the usual scaling laws. The numerical results of this analysis are compared with exact results of the Peano river network, showing differences of the order of 10-3. This aspect is especially relevant for the characterization of transport and diffusion processes at the basin scale. © 2009 The American Physical Society
A fractal analysis of the water retention curve
No full textThe dependence of the soil water content θ upon the matric potential ψ is studied within a fractal approach that regards the water retention curve as a sequence of well defined fractal regimes. Each of such regimes accounts for a given functional dependence θ≡θ(ψ), which in turn is characterized by a fractal dimension. The difference between the double fractal (observed into sandy soils) and multifractal (observed into clay soils) regime is explained by recalling that, for a sandy soil, the transition from saturated to dry conditions is driven by a steep reduction of ψ. To the contrary, for a clay (where the change from the highest water contents to the smallest ones is characterized by a large range of the matric potential), the multifractal behaviour is observed. These results are also confirmed by the analysis of experimental data. In particular, we show that the intermediate regime, generally accounting for the fractal multimodality, is due to the sandy nature of the soil at stake, practically immaterial. Finally, we demonstrate that our model can be also regarded as the straightforward generalization of that of Millán and González-Posada (2005)
Sensitivity analysis of bridge pier scour depth predictive formulae
No full textSensitivity analysis is an approach to recognising the behaviour of models and relative importance of causative factors. In this paper, behaviours of six pier scour depth empirical formulae are evaluated on the basis of an analytical method. The sensitivity of predicted scour depth is analysed with respect to the following independent parameters: approach flow depth, riverbed slope and median sediment size. Also their combined influence is studied examining the relative importance of each parameter with respect to the total variation of the maximum scour depth. Results show that: (1) sensitivity significantly depends on flow intensity for most of the selected formulae, whereas for the others it is a constant value or depends on other influencing parameters; (2) different formulae demonstrate various level of sensitivity to the input variables, so that, for a certain error in the input variables, the error in the results may vary consistently; (3) some formulae are very sensitive to the input parameters under some conditions, hence an error in an input variable may be amplified in the output results; and (4) most of the formulae are more sensitive to the variations of the influencing parameters in clear-water than in live-bed conditions. © IWA Publishing 2013
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