Elpidio Caroni

Solute Concentration Statistics in Heterogeneous Aquifers for Finite Péclet Values

A Lagrangian framework is used for analysing the concentration fields associated with transport of nonreactive solutes in heterogeneous aquifers. This is related to two components: advection by the random velocity field v(x) and pore-scale dispersion, characterized by the dispersion tensor Dd; the relative effect of the two components is quantified by the Péclet number. The principal aim of this paper is to define the probability density function (pdf) of a nonreactive solute concentration and its relevant moments >C< and σ2c as sampled on finite detection volumes. This problem could be relevant in technical applications such as risk analysis, field monitoring and pollution control. A method to compute the concentration statistical moments and pdf is developed in the paper on the basis of the reverse formulation widely adopted to study solute dispersion in turbulent flows. The main advantages of this approach are: (i) a closed form solution for concentration mean and variance is attained, in case of small size of the sampling volume; (ii) a numerically efficient estimate of the concentration pdf can be derived. The relative effects of injection and sampling volume size and Péclet number on concentration statistics are assessed. The analysis points out that the concentration pdf can be reasonably fitted by the beta function. These results are suitable to be employed in practical applications, when the estimate of probability related to concentration thresholds is required.

Stability Analysis of Plunge Pool Linings

AbstractIn the paper, the stability of a plunge pool bottom under the impact of an impinging jet is theoretically analyzed, with reference to the mean characteristics of the flow field: pressure and velocity. In cases when the mean components are relevant in respect to the fluctuating ones, this analysis is exhausting. In other cases, a separate evaluation of the fluctuation effects in lining design is treated by means of experimental evidence. The mean dynamic pressure at the bottom depends strongly on the impingement angle, which assumes a relevant role in the design of floor protections. In plunge pools, which are confined upstream by the presence of the drop structure, the impingement angle is theoretically determined by mass balance and momentum conservation, resulting independent of the jet entrance angle at the plunge pool water surface. The theoretical results are compared with literature, experimental evidence, and numerical simulations. This highlights the capability of the proposed theoretical ...

Unsteady Seepage Applied to Lining Design in Stilling Basins

AbstractCases of damages experienced in stilling basins and on the toe of chute spillways are recognized to be due to global instantaneous uplift force resulting from imbalance between the instantaneous pressure distribution both above and below slabs. The latter is due to pressure fluctuation propagation forced though unsealed slab joints. In the past, several theoretical approaches were developed to estimate the uplift contribution due to pressure transmission underneath the slabs. In the paper, a model is presented, based on unsteady flow analysis of seepage through porous media, that shows that the propagation models proposed in literature are particular cases of this more comprehensive formulation. In addition, the use of the unsteady seepage model makes it possible to account for finite thickness foundation layers, typical in the cases of earth dams, rock-fill dams, and in other dam types, whenever the slabs are posed on alluvial substrates. Experimental results obtained in laboratory facilities, as...

A new approach to master recession curve analysis

Abstract The analysis of drought discharge is of utmost relevance in the design of water intake structures, management of water resources, and in coping with environmental issues. In this context, the master recession curve represents a tool in hydrological analysis, giving integrated information on long period drought flow rates. In this paper, a technique is developed for deriving a master recession curve directly from daily discharge series that takes into account the high variability in the behaviour of individual recession segments. The statistical framework developed allows us to explicitly represent uncertainty, and hence a novel interpretation of the master recession curve is derived. The method is successfully applied to three important Italian basins draining the southern slopes of the eastern Alps. Citation Fiorotto, V. and Caroni, E., 2013. A new approach to master recession curve analysis. Hydrological Sciences Journal, 58 (5), 966–975.

Spillway Stilling Basins Lining Design via Taylor Hypothesis

AbstractThe paper presents the results from detailed experiments of the statistical structure of turbulence pressure fluctuations at the bottom of hydraulic jumps, with special reference to the spillway stilling basins lining design. Here, the whole spatial correlation structure of the fluctuating pressure field is required in order to evaluate slab stability. This is computed via simultaneous acquisition of the point pressure fluctuations on a dense grid in the hydraulic jump region, requiring a severe experimental work. As an alternative, one can evaluate the pressure spatial correlation structure via autocorrelation using one point pressure acquisition and applying the Taylor hypothesis. To adopt the Taylor hypothesis, one must know the pressure propagation celerity in space that can be obtained by comparing the whole spatial pressure correlation with the pivot point pressure autocorrelation. The experiments were performed by simultaneous pressure acquisitions at the bottom of a hydraulic jump for Frou...

Supercritical Flow over a Dentated Sill

Experimental analysis concerning supercritical flow over a dentated sill in nonsubmerged conditions and the local scour downstream of this sill is presented. In this case, the energy dissipation is incomplete so that a scour control downstream of the hydraulic structure could be required. The use of this type of dissipation device could be needed in cases where the maximum flow depth upstream of the sill must be limited to satisfy physical or structural conditions. This could happen, for instance, in the restoration of stilling basin in gravity dams and at the outlet of diversion systems. Experimental and theoretical results, useful in the design of this type of stilling basin and scour control, are presented in the paper, with an application to the case of the Molato Dam in Italy.

Design of Stilling Basin Linings with Sealed and Unsealed Joints

AbstractOne of the main causes of lining damage in stilling basins and at the toe of chute spillways is the global instantaneous uplift forces due to the difference in pressure acting on the upper and the lower surface of protection slabs or rock elements. Spillway stilling basin linings can be built according to two different techniques: using sealed joints or unsealed joints. In the case of sealed joints, the pressure underneath the slab is constant and the uplift force results from the pressure fluctuations acting on the slab. In the case of unsealed joints, the pressure propagation at the lower surface of the slab, being transferred through the joints, should also be considered. The aim of the paper is to study, define, and compare the design criteria in these two cases. In the present study, the pressure field on the slab is evaluated according to a recent method based on the Taylor hypothesis, whereas the pressure propagation under the slab is computed by a new 3D model based on unsteady flow analys...

Analysis of concentration under non-ergodic transport as sampled in natural aquifers

Groundwater is probably the major source of water supply in the world, and the predictive ability in describing the fate of chemical contaminants in soils is of great importance when performing risk assessment and designing effective and efficient techniques to mitigate such problems. Most of environmental regulations (e.g., U.S. EPA, 1988; European Union, Directive 80/778/EEC) define water quality standards and acceptability in terms of concentration thresholds, and thus the prediction in natural aquifers must be performed with reference to the concentration probability of excess relative to the relevant threshold value. Natural porous formation are inherently heterogeneous, and solute plumes transported exhibit irregular shapes. Transport of an inert solute in heterogeneous porous formation is determined by large-scale advection and pore-scale dispersion, the relative importance given by the Peclet number. The first is mainly controlled by the spatial variability of hydraulic conductivity while the second, acting at scales lower than the heterogeneity characteristic length, is usually neglected. The prediction of the concentration field, due to the irregular variation of permeability, is affected by uncertainty, which has been set in a theoretical framework by regarding the permeability as a random space function. Several investigations have been conducted, for small values of the log-conductivity variance, in order to define the first and second moment of concentration, both in Eulerian and in Lagrangian framework. These analyses have been carried out under the ergodic hypothesis (satisfied when the solute initial characteristic lengths are much larger than the heterogeneity correlation scale), in which case the position of the barycenter of the plume can be regarded as deterministic. Moreover, these approaches give only an estimate of mean concentration and variance, while no consideration has been made about the underlying pdf. Recently, Fiorotto and Caroni (Trans. Porous Media, 48, 2002), and Caroni and Fiorotto (Trans. Porous Media, 59, 2005), analyzed, under ergodic conditions, the statistical properties of solute concentration in natural aquifers as sampled in observation wells. The aim of the present paper is to extend such previous research, in particular investigating to which extent the ergodic hypothesis may be assumed valid, and analyzing the statistical properties of the position of the barycenters of the solute plume, thus giving an estimate of the uncertainty in the prediction. The calculations, in Lagrangian framework, take advantage of the reverse formulation where, instead of considering the destination of the injected particles, the origin of the particle being sampled is sought. The advantage is that the concentration can be simulated using a reduced number of particles, while the accurate forward computation of the concentration requires a large number of particles, increasing up to prohibitive levels as long as the sampling area tends to shrink into a point. The analyses, have considered different sizes of the solute initial plume, and have been carried out varying the log-conductivity variance and the Peclet number, to quantify the relative role of the macro and the pore scale dispersion processes. In the case of small values of the log-conductivity variance, the methodology allows the derivation of an analytical expression for concentration mean, variance and pdf, while for high values, a Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer, characterized by log-normally distributed trasmissivity with an exponential covariance, has been developed. In the last case, the adoption of the Beta function to fit the concentration pdf proves valid for practical application, under the ergodic hypothesis (Caroni and Fiorotto, Trans. Porous Media, 59, 2005). Simulations show that, under non-ergodic transport, the uncertainty in the prediction of the barycenters of the plumes may be described by a multinormal random variate: this allows an estimate of the overall concentration pdf, which may be obtained by the convolution between the two distributions (in this case reducing to the mere product, being the processes uncorrelated).