Stability Analysis of Gravity Currents of a Power-Law Fluid in a Porous Medium

We analyse the linear stability of self-similar shallow, two-dimensional and axisymmetric gravity currents of a viscous power-law non-Newtonian fluid in a porous medium. The flow domain is initially saturated by a fluid lighter than the intruding fluid, whose volume varies with time astα. The transition between decelerated and accelerated currents occurs atα= 2 for two-dimensional and atα= 3 for axisymmetric geometry. Stability is investigated analytically for special values ofαand numerically in the remaining cases; axisymmetric currents are analysed only for radially varying perturbations. The two-dimensional currents are linearly stable forα 2 (two-dimensional accelerated currents) andα> 3 (axisymmetric accelerated currents) the linear stability analysis is of limited value since the hypotheses of the model will be violated

Experimental study on radial gravity currents flowing in a vegetated channel

We present an experimental study of gravity currents in a cylindrical geometry, in the presence of vegetation. Forty tests were performed with a brine advancing in a fresh water ambient fluid, in lock release, and with a constant and time-varying flow rate. The tank is a circular sector of angle $30^circ$ with radius equal to 180 cm. Two different densities of the vegetation were simulated by vertical plastic rods with diameter $D=1.6; extrm{cm}$. We marked the height of the current as a function of radius and time and the position of the front as a function of time. The results indicate a self-similar structure, with lateral profiles that after an initial adjustment collapse to a single curve in scaled variables. The propagation of the front is well described by a power law function of time. The existence of self-similarity on an experimental basis corroborates a simple theoretical model with the following assumptions: (i) the dominant balance is between buoyancy and drag, parameterized by a power law of the current velocity $sim |u|^{lambda-1}u$; (ii) the current advances in shallow-water conditions; (iii) ambient-fluid dynamics is negligible. In order to evaluate the value of ${lambda}$ (the only tuning parameter of the theoretical model), we performed two additional series of measurements. We found that $lambda$ increased from 1 to 2 while the Reynolds number increased from 100 to approximately $6cdot10^3$, the drag coefficient and the transition from $lambda=1$ to $lambda=2$ are quantitatively affected by $D$, but the structure of the model is not

Interaction of Swell and Sea Waves with Partially Reflective Structures for Possible Engineering Applications

In this work, we investigate the interaction between the combination of wind-driven and regular waves and a chamber defined by a rigid wall and a thin vertical semi-submerged barrier. A series of laboratory experiments were performed with different values of incident wave height, wave period, and wind speed. The analysis focuses on the effect of the geometry of the system characterized in terms of its relative submergence d/h and relative width B/L. Results show that for the case of d/h = 0.58 a resonant effect takes place inside the chamber regardless of the wind speed. Wind-driven waves have a higher influence on the variation of the wave period of the waves seaward and leeward of the plate, as well as on the phase lag. Results show that the amplification or reduction of the wave energy inside the chamber is closely related to the wave period as compared to the 1st order natural period of the chamber.A.L.L. is supported by the research group TEP-209 (Junta de Andalucía) and project AQUACLEW. Project AQUACLEW is part of ERA4CS, an ERA-NET initiated by JPI Climate, and funded by FORMAS (SE), DLR (DE), BMWFW (AT), IFD (DK), MINECO (ES), ANR (FR) with co-funding by the European Union (Grant 690462). During the preparation of the manuscript, A.L.L. was doing a research stay at the University of Parma (PhD cotutelle agreement) funded by the Campus of International Excellence of the Sea (CEIMAR) and the University of Granada

Shear-Thinning Fluid Flow in Variable-Aperture Channels

Non-Newtonian fluid flow in a single fracture is a 3-D nonlinear phenomenon that is often averaged across the fracture aperture and described as 2-D. To capture the key interactions between fluid rheology and spatial heterogeneity, we adopt a simplified geometric model to describe the aperture variability, consisting of adjacent one-dimensional channels with constant aperture, each drawn from an assigned aperture distribution. The flow rate is then derived under the lubrication approximation for the two limiting cases of an external pressure gradient that is parallel/perpendicular to the channels; these two arrangements provide upper and lower bounds to the fracture conductance. The fluid rheology is described by the Prandtl–Eyring shear-thinning model. Novel closed-form results for the flow rate and hydraulic aperture are derived and discussed; different combinations of the parameters that describe the fluid rheology and the variability of the aperture field are considered. The flow rate values are very sensitive to the applied pressure gradient and to the shape of the distribution; in particular, more skewed distribution entails larger values of a dimensionless flow rate. Results for practical applications are compared with those valid for a power-law fluid and show the effects on the fracture flow rate of a shear stress plateau

PROPAGATION OF GRAVITY CURRENTS OF NON-NEWTONIAN POWER-LAW FLUIDS IN POROUS MEDIA

A comprehensive analytical and experimental framework is presented to describe gravity-driven motions of rheologically complex fluids through porous media. These phenomena are relevant in geophysical, environmental, industrial and biological applications. The fluid is characterized by an Ostwald-DeWaele constitutive equation with behaviour index n. The flow is driven by the release of fluid at the origin of an infinite porous domain. In order to represent several possible spreading scenarios, we consider: i) different domain geometries: plane, radial, and channelized, with the channel shape parameterized by ; ii) instantaneous or continuous injection, depending on the time exponent of the volume of fluid in the current, ; iii) horizontal or inclined impermeable boundaries. Systematic heterogeneity along the streamwise and/or transverse direction is added to the conceptualization upon considering a power-law permeability variation governed by two additional parameters  and . Scalings for current length and thickness are derived in self similar form coupling the modified Darcy’s law accounting for the fluid rheology with the mass balance equation. The speed, thickness, and aspect ratio of the current are studied as a function of model parameters; several different critical values of  emerge and govern the type of dependency, as well as the tendency of the current to accelerate or decelerate and become thicker or thinner at a given point. The asymptotic validity of the solutions is limited to certain ranges of model parameters. Experimental validation is performed under constant volume, constant and variable flux regimes in tanks/channels filled with transparent glass beads of uniform or variable diameter, using shear-thinning suspensions and Newtonian mixtures. The experimental results for the length and profile of the current agree well with the self-similar solutions at intermediate and late times

Porous gravity currents: A survey to determine the joint influence of fluid rheology and variations of medium properties

We develop a model to grasp the combined effect of rheology and spatial stratifications on two- dimensional non-Newtonian gravity-driven flow in porous media. We consider a power-law constitutive equation for the fluid, and a monomial variation of permeability and porosity along the vertical direction (transverse to the flow) or horizontal direction (parallel to the flow). Under these assumptions, similar- ity solutions are derived in semi-analytical form for thin gravity currents injected into a two-dimensional porous medium and having constant or time-varying volume. The extent and shape of the porous domain affected by the injection is significantly influenced by the interplay of model parameters. These describe the fluid (flow behaviour index n ), the spatial heterogeneity (coefficients β, γ, δ, ω for variations of per- meability and porosity in the horizontal or vertical direction), and the type of release (volume exponent α). Theoretical results are validated against two sets of experiments with α= 1 (constant inflow) con- ducted with a stratified porous medium (simulated by superimposing layers of glass beads of different diameter) and a Hele-Shaw analogue for power-law fluid flow, respectively. In the latter case, a recently established Hele-Shaw analogy is extended to the variation of properties parallel to the flow direction. Comparison with experimental results shows that the proposed model is able to capture the propagation of the current front and the current profile

Invariants of Turbulence Reynolds Stress and of Dissipation Tensors in Regular Breaking Waves

A series of measurements in a flume with a particle-tracking system in three dimensions applied to breaking waves is used to analyse the structure of turbulence with a full set of variables that usually are available only in numerical simulations. After extracting turbulence, in addition to the standard analysis aiming to quantify the fluxes, i.e., the time-average and the phase-average levels of turbulence and vorticity (details are given in two former papers), a more in-depth description of the structure of turbulence Reynolds stress tensor is given, focussing on the invariants evolution in time and in the vertical. A relation between the components of the Reynolds stress tensor and of the dissipation tensor is depicted. This relation is finalised to possible models of turbulence in breaking waves

Wave-current interaction in the Porto di Lido entrance of the Venice Lagoon

Water Qualit

Buoyancy transfer in a two-layer system in transient and steady state. Experiments in a wave flume

Presentation in a conferenc

Characterization of breast tissues in density and effective atomic number basis via spectral X-ray computed tomography

Differentiation of breast tissues is challenging in X-ray imaging because tissues might share similar or even the same linear attenuation coefficients $\mu$. Spectral computed tomography (CT) allows for more quantitative characterization in terms of tissue density and effective atomic number by exploiting the energy dependence of $\mu$. In this work, 5 mastectomy samples and a phantom with inserts mimicking breast soft tissues were evaluated in a retrospective study. The samples were imaged at three monochromatic energy levels in the range of 24 - 38 keV at 5 mGy per scan using a propagation-based phase-contrast setup at SYRMEP beamline at the Italian national synchrotron Elettra. A custom-made algorithm incorporating CT reconstructions of an arbitrary number of spectral energy channels was developed to extract the density and effective atomic number of adipose, fibro-glandular, pure glandular, tumor, and skin from regions selected by a radiologist. Preliminary results suggest that, via spectral CT, it is possible to enhance tissue differentiation. It was found that adipose, fibro-glandular and tumorous tissues have average effective atomic numbers (5.94 $\pm$ 0.09, 7.03 $\pm$ 0.012, and 7.40 $\pm$ 0.10) and densities (0.90 $\pm$ 0.02, 0.96 $\pm$ 0.02, and 1.07 $\pm$ 0.03 g/cm$^{3}$) and can be better distinguished if both quantitative values are observed together.Comment: 26 pages, 7 figures, submitted to Physics in Medicine and Biolog