Marilena Pannone

Transient Hydrodynamic Dispersion in Rough Open Channels: Theoretical Analysis of Bed-Form Effects

A stochastic Lagrangian approach is proposed to describe dispersion in a two-dimensional low-regime river flow past random bed undulations characterized by the superposition of periodical and stationary exponential correlations, through a suitable time-dependent coefficient. The resulting dimensionless expression depends on the overall resistance factor, which is proportional to the average Peclet number of the process. A graphical analysis shows that the oscillatory transient originating from the periodic component of the bottom elevation pattern is enhanced by reduced global flow resistance, while relatively more intense tracer spreading is associated with wavelike profiles affected by persistent trendless random noise, which also determines the characteristic time needed by the plume to achieve the asymptotic domain. Numerical simulations, validating the first-order analytical approach in a wide range of heterogeneous bed geometries, are also discussed. A semianalytical procedure is finally suggested for the study of depth-averaged transport processes in real three-dimensional streams, based on the use of the derived dispersion coefficient.

Stochastic numerical analysis of anomalous longitudinal dispersion and dilution in shallow decelerating stream flows

The paper deals with the numerical analysis of solute dispersion and dilution within shallow stream flows which are characterized by a low gradient and undergo a downstream deceleration, near the confluence into large reservoirs or upstream from fluvial barrages. The main purpose of the study consists in investigating the effect that the size and the slope of the channel induce on solute transport in the presence of backwaters. The analysis, performed by a numerical stochastic Lagrangian approach, detects a characteristic travel time beyond which the longitudinal hydrodynamic dispersion, jointly with dilution, undergoes a drastic decline. One of the key results of the simulations is indeed represented by the possibility to estimate the large-time section-averaged concentration resorting to the classic Gaussian distribution characterized by the actual first- and second-order particle moments and, therefore, by increasing and asymptotically constant values. In addition, the assessment of dilution at cloud scale, performed through the entropic evaluation of the total volume occupied by the solute and a closed-form expression of the geometric mean of the reactor ratio, reveals that, after a transient characterized by the earlier tendency to the cross-sectional mixing, the backwater flows induce a global re-densification of the cloud and a permanent transverse non-uniformity.

An Entropic Model for the Assessment of Streamwise Velocity Dip in Wide Open Channels

The three-dimensional structure of river flow and the presence of secondary currents, mainly near walls, often cause the maximum cross-sectional velocity to occur below the free surface, which is known as the “dip” phenomenon. The present study proposes a theoretical model derived from the entropy theory to predict the velocity dip position along with the corresponding velocity value. Field data, collected at three ungauged sections located along the Alzette river in the Grand Duchy of Luxembourg and at three gauged sections located along three large rivers in Basilicata (southern Italy), were used to test its validity. The results show that the model is in good agreement with the experimental measurements and, when compared with other models documented in the literature, yields the least percentage error.

A Mathematical Model for the Flow Resistance and the Related Hydrodynamic Dispersion Induced by River Dunes

Present work is aimed at the derivation of a simply usable equation for the total flow resistance associated with river bedforms, by a unifying approach allowing for bypassing some of the limiting restrictions usually adopted in similar types of studies. Specifically, we focused on the effect induced by the out-of-phase free surface undulations appearing in presence of sand dunes. The proposed expression, obtained by combining the balance of momentum referred to the control volume whose longitudinal dimension coincides with the dune wavelength and the energy balance integrated between its extreme sections, was tested by comparison with some laboratory experimental measurements available in the literature and referred to steady flow past fixed, variably rough bedforms. In terms of shear stress or friction factor, the proposed theory provides estimates in good agreement with the real data, especially if evaluated against the performances provided by other classical similar approaches. Moreover, when analyzed in terms of hydrodynamic dispersive properties as a function of the skin roughness on the basis of a previously derived analytical solution, the dune-covered beds seem to behave like meandering channels, responsible for a globally enhanced fluid particles longitudinal spreading, with a relatively reduced effect in the presence of less pronounced riverbed modelling.

Analytical Solution for the Pressure Oscillations Caused by Trains of Solitary Waves within Confined Coastal Aquifers

An exact analytical solution is proposed for the pressure oscillations within deep coastal aquifers under the action of tidal level time-variations attributable to train of solitary waves originating off-shore. The purpose of the study is to relate the characteristics of the response of the system to amplitude, steepness, and asymmetry of the soliciting waves, in order to assess its vulnerability to events like violent seaquakes and consequent tsunamis. The time needed by the forcing perturbations, approximated by consecutive triangular impulses, to attain their maximum is assumed to be always smaller than the aquifer diffusive time, in order to evaluate the consequences of the sudden raise of water level along the shoreline, typical of those quite extreme phenomena.