Experimental study on radial gravity currents flowing in a vegetated channel

2022 ◽  
Vol 933 ◽  
Author(s):  
D. Petrolo ◽  
M. Ungarish ◽  
L. Chiapponi ◽  
S. Longo
Keyword(s):  
Experimental Study ◽  
Theoretical Model ◽  
Power Law ◽  
Gravity Currents ◽  
Tuning Parameter ◽  
Ambient Fluid ◽  
Self Similarity ◽  
Circular Sector ◽  
Power Law Function ◽  
Self Similar

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 $D=1.6\ \textrm{cm}$ . 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; and (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 $6\times10^3$ , and 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.

Converging gravity currents over a permeable substrate

2015 ◽  
Vol 778 ◽  
pp. 669-690 ◽  
Author(s):  
Zhong Zheng ◽  
Sangwoo Shin ◽  
Howard A. Stone
Keyword(s):  
Power Law ◽  
Gravity Current ◽  
Gravity Currents ◽  
Numerical Predictions ◽  
Front Position ◽  
Dependent Position ◽  
Self Similar ◽  
Vertical Leakage ◽  
Similar Solutions ◽  
Lock Gate

We study the propagation of viscous gravity currents along a thin permeable substrate where slow vertical drainage is allowed from the boundary. In particular, we report the effect of this vertical fluid drainage on the second-kind self-similar solutions for the shape of the fluid–fluid interface in three contexts: (i) viscous axisymmetric gravity currents converging towards the centre of a cylindrical container; (ii) viscous gravity currents moving towards the origin in a horizontal Hele-Shaw channel with a power-law varying gap thickness in the horizontal direction; and (iii) viscous gravity currents propagating towards the origin of a porous medium with horizontal permeability and porosity gradients in power-law forms. For each of these cases with vertical leakage, we identify a regime diagram that characterizes whether the front reaches the origin or not; in particular, when the front does not reach the origin, we calculate the final location of the front. We have also conducted laboratory experiments with a cylindrical lock gate to generate a converging viscous gravity current where vertical fluid drainage is allowed from various perforated horizontal substrates. The time-dependent position of the propagating front is captured from the experiments, and the front position is found to agree well with the theoretical and numerical predictions when surface tension effects can be neglected.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Sandro Longo ◽  
Vittorio Di Federico
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Power Law ◽  
Gravity Currents ◽  
Two Dimensional ◽  
Continuum Spectrum ◽  
Fluid Behavior ◽  
Self Similar ◽  
Flow Domain

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 (decelerated currents) with a continuum spectrum of eigenvalues and unstable forα= 2, with a growth rate proportional to the square of the fluid behavior index. The axisymmetric currents are linearly stable for anyα< 3 (decelerated currents) with a continuum spectrum of eigenvalues, while forα= 3 no firm conclusion can be drawn. 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.

scholarly journals Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents

2014 ◽  
Vol 747 ◽  
pp. 218-246 ◽  
Author(s):  
Zhong Zheng ◽  
Ivan C. Christov ◽  
Howard A. Stone
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Gravity Currents ◽  
Similar Solution ◽  
Phase Plane Analysis ◽  
Plane Analysis ◽  
Self Similar Solution ◽  
Theoretical Predictions ◽  
Self Similar ◽  
Similar Solutions

AbstractWe report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.

scholarly journals Lubricated viscous gravity currents

2015 ◽  
Vol 766 ◽  
pp. 626-655 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
M. Grae Worster
Keyword(s):  
Gravity Current ◽  
Gravity Currents ◽  
Singular Limit ◽  
Vertical Shear ◽  
Surface Films ◽  
Viscous Coupling ◽  
Self Similarity ◽  
Transient Behaviour ◽  
Fingering Instability ◽  
Self Similar

AbstractWe present a theoretical and experimental study of viscous gravity currents lubricated by another viscous fluid from below. We use lubrication theory to model both layers as Newtonian fluids spreading under their own weight in two-dimensional and axisymmetric settings over a smooth rigid horizontal surface and consider the limit in which vertical shear provides the dominant resistance to the flow in both layers. There are contributions from Poiseuille-like flow driven by buoyancy and Couette-like flow driven by viscous coupling between the layers. The flow is self-similar if both fluids are released simultaneously, and exhibits initial transient behaviour when there is a delay between the initiation of flow in the two layers. We solve for both situations and show that the latter converges towards self-similarity at late times. The flow depends on three key dimensionless parameters relating the relative dynamic viscosities, input fluxes and density differences between the two layers. Provided the density difference between the two layers is bounded away from zero, we find an asymptotic solution in which the front of the lubricant is driven by its own gravitational spreading. There is a singular limit of equal densities in which the lubricant no longer spreads under its own weight in the vicinity of its nose and ends abruptly with a non-zero thickness there. We explore various regimes, from thin lubricating layers underneath a more viscous current to thin surface films coating an underlying more viscous current and find that although a thin film does not greatly influence the more viscous current if it forms a surface coating, it begins to cause interesting dynamics if it lubricates the more viscous current from below. We find experimentally that a lubricated gravity current is prone to a fingering instability.

scholarly journals Self-Similarity in Abrasiveness of Hard Carbon-Containing Coatings

2002 ◽  
Vol 125 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Feodor M. Borodich ◽  
Leon M. Keer ◽  
Stephen J. Harris
Keyword(s):  
Power Law ◽  
Contact Region ◽  
Self Similarity ◽  
Hard Carbon ◽  
Flat Disk ◽  
Abrasion Rate ◽  
Flat Steel ◽  
Self Similar ◽  
Number Of Cycles ◽  
Experimental Scatter

The abrasiveness of hard carbon-containing thin films such as diamond-like carbon (DLC) and boron carbide (nominally B4C) towards steel is considered here. First, a remarkably simple experimentally observed power-law relationship between the abrasion rate of the coatings and the number of cycles is described. This relationship remains valid over at least 4 orders of magnitude of the number of cycles, with very little experimental scatter. Then possible models of wear are discussed. It is assumed that the dominant mechanism of steel wear is its mechanical abrasion by nano-scale asperities on the coating that have relatively large attack angles, i.e. by the so-called sharp asperities. Wear of coating is assumed to be mainly due to physical/chemical processes. Finally, models of the abrasion process for two basic cases are presented, namely a coated ball on a flat steel disk and a steel ball on a coated flat disk. The nominal contact region can be considered as constant in the former case, while in the latter case, the size of the region may be enlarged due to wear of the steel. These models of the abrasion process are based on the assumption of self-similar changes of the distribution function characterizing the statistical properties of patterns of scattered surface sharp asperities. It is shown that the power-law relationship for abrasion rate follows from the models.

Critical regime of gravity currents flowing in non-rectangular channels with density stratification

2018 ◽  
Vol 840 ◽  
pp. 579-612
Author(s):  
L. Chiapponi ◽  
M. Ungarish ◽  
S. Longo ◽  
V. Di Federico ◽  
F. Addona
Keyword(s):  
Cross Section ◽  
Power Law ◽  
Rectangular Cross Section ◽  
Gravity Current ◽  
Gravity Currents ◽  
Critical Conditions ◽  
Uniform Density ◽  
Ambient Fluid ◽  
Real Numbers ◽  
Positive Real

We present theoretical and experimental analyses of the critical condition where the inertial–buoyancy or viscous–buoyancy regime is preserved in a uniform-density gravity current (which propagates over a horizontal plane) of time-variable volume ${\mathcal{V}}=qt^{\unicode[STIX]{x1D6FF}}$ in a power-law cross-section (with width described by $f(z)=bz^{\unicode[STIX]{x1D6FC}}$, where $z$ is the vertical coordinate, $b$ and $q$ are positive real numbers, and $\unicode[STIX]{x1D6FC}$ and $\unicode[STIX]{x1D6FF}$ are non-negative real numbers) occupied by homogeneous or linearly stratified ambient fluid. The magnitude of the ambient stratification is represented by the parameter $S$, with $S=0$ and $S=1$ describing the homogeneous and maximum stratification cases respectively. Earlier theoretical and experimental results valid for a rectangular cross-section ($\unicode[STIX]{x1D6FC}=0$) and uniform ambient fluid are generalized here to a power-law cross-section and stratified ambient. Novel time scalings, obtained for inertial and viscous regimes, allow a derivation of the critical flow parameter $\unicode[STIX]{x1D6FF}_{c}$ and the corresponding propagation rate as $Kt^{\unicode[STIX]{x1D6FD}_{c}}$ as a function of the problem parameters. Estimates of the transition length between the inertial and viscous regimes are also derived. A series of experiments conducted in a semicircular cross-section ($\unicode[STIX]{x1D6FC}=1/2$) validate the critical values $\unicode[STIX]{x1D6FF}_{c}=2$ and $\unicode[STIX]{x1D6FF}_{c}=9/4$ for the two cases $S=0$ and $1$. The ratio between the inertial and viscous forces is determined by an effective Reynolds number proportional to $q$ at some power. The threshold value of this number, which enables a determination of the regime of the current (inertial–buoyancy or viscous–buoyancy) in critical conditions, is determined experimentally for both $S=0$ and $S=1$. We conclude that a very significant generalization of the insights and results from two-dimensional (rectangular cross-section channel) gravity currents to power-law cross-sections is available.

THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050054
Author(s):  
KUN CHENG ◽  
DIRONG CHEN ◽  
YUMEI XUE ◽  
QIAN ZHANG
Keyword(s):  
Power Law ◽  
Path Length ◽  
Small World ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Scale Free ◽  
Power Law Exponent ◽  
Self Similar ◽  
Encoding Method

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be [Formula: see text] and the average clustering coefficients are shown to be larger than [Formula: see text]. Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.

SCALING LAWS IN A TURBULENT BAROCLINIC INSTABILITY

Fractals ◽  
1995 ◽  
Vol 03 (02) ◽  
pp. 297-314 ◽  
Author(s):  
C. SERIO ◽  
V. TRAMUTOLI
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Spatial Scales ◽  
Baroclinic Instability ◽  
Satellite Image ◽  
Horizontal Resolution ◽  
Turbulent Motion ◽  
Self Similarity ◽  
Wavelet Transform Analysis ◽  
Self Similar

This work provides an empirical investigation of scaling laws in a cloud system generated and advected by a strong baroclinic instability. An infrared satellite image with a spatial (horizontal) resolution of about 1 km has been analyzed. The presence of two sizeable and unmistakable scaling regions, one extending from 1 to 15 km and characterized by a power law with an exponent close to 1, the other stretching from 20 km up to 100 km and characterized by a power law with exponent close to 1/3, have been revealed by variogram analysis. These two scaling laws are in agreement with the idea of scale invariance of the turbulent motion and also suggest the presence of a self-similar structure. To explore this possibility, wavelet transform analysis at different spatial scales has been used. Our findings are that self-similarity is present at the smallest scales, but this universal characteristic may be masked by non-universal effects which influence the homogeneity of the underlying turbulent motion. The implications of the two scaling exponents, 1 and 1/3, are also discussed.

Self-similar gravity currents with variable inflow revisited: plane currents

1994 ◽  
Vol 258 ◽  
pp. 77-104 ◽  
Author(s):  
Julio Gratton ◽  
Claudio Vigo
Keyword(s):  
Density Ratio ◽  
Gravity Currents ◽  
Type I ◽  
Type Ii ◽  
Ambient Fluid ◽  
Discontinuous Solutions ◽  
Continuous Solutions ◽  
Self Similar ◽  
Similar Solutions ◽  
Transition Type

We use shallow-water theory to study the self-similar gravity currents that describe the intrusion of a heavy fluid below a lighter ambient fluid. We consider in detail the case of currents with planar symmetry produced by a source with variable inflow, such that the volume of the intruding fluid varies in time according to a power law of the type tα. The resistance of the ambient fluid is taken into account by a boundary condition of the von Kármán type, that depends on a parameter β that is a function of the density ratio of the fluids. The flow is characterized by β, α, and the Froude number [Fscr ]0 near the source. We find four kinds of self-similar solutions: subcritical continuous solutions (Type I), continuous solutions with a supercritical-subcritical transition (Type II), discontinuous solutions (Type III) that have a hydraulic jump, and discontinuous solutions having hydraulic jumps and a subcritical-supercritical transition (Type IV). The current is always subcritical near the front, but near the source it is subcritical ([Fscr ]0 < 1) for Type I currents, and supercritical ([Fscr ]0 > 1) for Types II, III, and IV. Type I solutions have already been found by other authors, but Type II, III, and IV currents are novel. We find the intervals of parameters for which these solutions exist, and discuss their properties. For constant-volume currents one obtains Type I solutions for any β that, when β > 2, have a ‘dry’ region near the origin. For steady inflow one finds Type I currents for O < β < ∞ and Type II and III Currents for and β, if [Fscr ]0 is sufficiently large.

scholarly journals SELF-SIMILARITY IN THE TAXONOMIC CLASSIFICATION OF HUMAN LANGUAGES

2001 ◽  
Vol 04 (02n03) ◽  
pp. 281-286 ◽  
Author(s):  
DAMIAN H. ZANETTE
Keyword(s):  
Long Range ◽  
Power Law ◽  
Biological Species ◽  
Statistical Properties ◽  
Taxonomic Classification ◽  
Self Similarity ◽  
Self Similar ◽  
Evolutionary Foundation ◽  
Language Classification

Statistical properties of the taxonomic classification of human languages are studied. It is shown that, at the highest levels of the taxonomic hierarchy, the frequency of taxon members as a function of the number of languages belonging to each member decays as a power law. This feature reveals that a self-similar structure underlies the taxonomy of languages, exactly as observed in the taxonomic classification of biological species. Such an analogy is a clue to the evolutionary foundation of language classification based on long-range comparison.

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