scholarly journals Propagation of viscous gravity currents inside confining boundaries: the effects of fluid rheology and channel geometry

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150070 ◽  
Author(s):  
S. Longo ◽  
V. Di Federico ◽  
L. Chiapponi
Keyword(s):  
Cross Sections ◽  
Rheological Behaviour ◽  
Gravity Currents ◽  
Channel Cross Section ◽  
Rigid Boundary ◽  
Cross Sectional ◽  
Self Similar ◽  
Similar Solutions ◽  
Fluid Rheology ◽  
Asymptotic Validity

A theoretical and experimental investigation of the propagation of free-surface, channelized viscous gravity currents is conducted to examine the combined effects of fluid rheology, boundary geometry and channel inclination. The fluid is characterized by a power-law constitutive equation with behaviour index n . The channel cross section is limited by a rigid boundary of height parametrized by k and has a longitudinal variation described by the constant b ≥0. The cases k ⋛ 1 are associated with wide, triangular and narrow cross sections. For b >0, the cases k ≷ 1 describe widening channels and squeezing fractures; b =0 implies a constant cross-sectional channel. For a volume of released fluid varying with time like t α , scalings for current length and thickness are obtained in self-similar forms for horizontal and inclined channels/fractures. The speed, thickness and aspect ratio of the current jointly depend on the total current volume ( α ), the fluid rheological behaviour ( n ), and the transversal ( k ) and longitudinal ( b ) geometry of the channel. The asymptotic validity of the solutions is limited to certain ranges of parameters. Experimental validation was performed with different fluids and channel cross sections; experimental results for current radius and profile were found to be in close agreement with the self-similar solutions at intermediate and late times.

scholarly journals On the effect of cross sectional shape on incipient motion and deposition of sediments in fixed bed channels

2014 ◽  
Vol 62 (1) ◽  
pp. 75-81 ◽  
Author(s):  
Mir-Jafar-Sadegh Safari ◽  
Mirali Mohammadi ◽  
Golezar Gilanizadehdizaj
Keyword(s):  
Cross Sections ◽  
Research Work ◽  
Fixed Bed ◽  
Deposition Condition ◽  
Incipient Motion ◽  
Rigid Boundary ◽  
Cross Sectional ◽  
Motion Equations ◽  
Sectional Shape ◽  
Minimum Velocity

Abstract The condition of incipient motion and deposition are of the essential issues for the study of sediment transport. This phenomenon is of great importance to hydraulic engineers for designing sewers, drainage, as well as other rigid boundary channels. This is a study carried out with the objectives of describing the effect of cross-sectional shape on incipient motion and deposition of particles in rigid boundary channels. In this research work, the experimental data given by Loveless (1992) and Mohammadi (2005) are used. On the basis of the critical velocity approach, a new incipient motion equation for a V-shaped bottom channel and incipient deposition of sediment particles equations for rigid boundary channels having circular, rectangular, and U-shaped cross sections are obtained. New equations were compared to the other incipient motion equations. The result shows that the cross-sectional shape is an important factor for defining the minimum velocity for no-deposit particles. This study also distinguishes incipient motion of particles from incipient deposition for particles. The results may be useful for designing fixed bed channels with a limited deposition condition.

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.

Self-similar viscous gravity currents: phase-plane formalism

1990 ◽  
Vol 210 ◽  
pp. 155-182 ◽  
Author(s):  
Julio Gratton ◽  
Fernando Minotti
Keyword(s):  
Scaling Laws ◽  
Phase Plane ◽  
Gravity Current ◽  
Classical Problem ◽  
Gravity Currents ◽  
Steady Flows ◽  
Two Phase ◽  
Integral Curves ◽  
Self Similar ◽  
Similar Solutions

A theoretical model for the spreading of viscous gravity currents over a rigid horizontal surface is derived, based on a lubrication theory approximation. The complete family of self-similar solutions of the governing equations is investigated by means of a phase-plane formalism developed in analogy to that of gas dynamics. The currents are represented by integral curves in the plane of two phase variables, Z and V, which are related to the depth and the average horizontal velocity of the fluid. Each integral curve corresponds to a certain self-similar viscous gravity current satisfying a particular set of initial and/or boundary conditions, and is obtained by solving a first-order ordinary differential equation of the form dV/dZ = f(Z, V), where f is a rational function. All conceivable self-similar currents can thus be obtained. A detailed analysis of the properties of the integral curves is presented, and asymptotic formulae describing the behaviour of the physical quantities near the singularities of the phase plane corresponding to sources, sinks, and current fronts are given. The derivation of self-similar solutions from the formalism is illustrated by several examples which include, in addition to the similarity flows studied by other authors, many other novel ones such as the extension to viscous flows of the classical problem of the breaking of a dam, the flows over plates with borders, as well as others. A self-similar solution of the second kind describing the axisymmetric collapse of a current towards the origin is obtained. The scaling laws for these flows are derived. Steady flows and progressive wave solutions are also studied and their connection to self-similar flows is discussed. The mathematical analogy between viscous gravity currents and other physical phenomena such as nonlinear heat conduction, nonlinear diffusion, and ground water motion is commented on.

The Influence of Boundaries on Gravity Currents and Thin Films: Drainage, Confinement, Convergence, and Deformation Effects

2022 ◽  
Vol 54 (1) ◽  
pp. 27-56
Author(s):  
Zhong Zheng ◽  
Howard A. Stone
Keyword(s):  
Thin Film ◽  
Oil And Gas ◽  
Gravity Currents ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Self Similar ◽  
Similar Solutions ◽  
Film Flows ◽  
Gravity Surface

Thin film flows, whether driven by gravity, surface tension, or the relaxation of elastic boundaries, occur in many natural and industrial processes. Applications span problems of oil and gas transport in channels to hydraulic fracture, subsurface propagation of pollutants, storage of supercritical CO2 in porous formations, and flow in elastic Hele–Shaw configurations and their relatives. We review the influence of boundaries on the dynamics of thin film flows, with a focus on gravity currents, including the effects of drainage into the substrate, and the role of the boundaries to confine the flow, force its convergence to a focus, or deform, and thus feedback to alter the flow. In particular, we highlight reduced-order models. In many cases, self-similar solutions can be determined and describe the behaviors in canonical problems at different timescales and length scales, including self-similar solutions of both the first and second kind. Additionally, the time transitions between different solutions are summarized. Where possible, remarks about various applications are provided.

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.

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 Dynamics of non-circular finite-release gravity currents

2015 ◽  
Vol 783 ◽  
pp. 344-378 ◽  
Author(s):  
N. Zgheib ◽  
T. Bonometti ◽  
S. Balachandar
Keyword(s):  
Aspect Ratio ◽  
Density Ratio ◽  
Front Propagation ◽  
Gravity Currents ◽  
Box Model ◽  
Wall Friction ◽  
Cross Sectional ◽  
Initial Shape ◽  
Box Models ◽  
Self Similar

The present work reports some new aspects of non-axisymmetric gravity currents obtained from laboratory experiments, fully resolved simulations and box models. Following the earlier work of Zgheib et al. (Theor. Comput. Fluid Dyn., vol. 28, 2014, pp. 521–529) which demonstrated that gravity currents initiating from non-axisymmetric cross-sectional geometries do not become axisymmetric, nor do they retain their initial shape during the slumping and inertial phases of spreading, we show that such non-axisymmetric currents eventually reach a self-similar regime during which (i) the local front propagation scales as $t^{1/2}$ as in circular releases and (ii) the non-axisymmetric front has a self-similar shape that primarily depends on the aspect ratio of the initial release. Complementary experiments of non-Boussinesq currents and top-spreading currents suggest that this self-similar dynamics is independent of the density ratio, vertical aspect ratio, wall friction and Reynolds number $\mathit{Re}$, provided the last is large, i.e. $\mathit{Re}\geqslant O(10^{4})$. The local instantaneous front Froude number obtained from the fully resolved simulations is compared to existing models of Froude functions. The recently reported extended box model is capable of capturing the dynamics of such non-axisymmetric flows. Here we use the extended box model to propose a relation for the self-similar horizontal aspect ratio ${\it\chi}_{\infty }$ of the propagating front as a function of the initial horizontal aspect ratio ${\it\chi}_{0}$, namely ${\it\chi}_{\infty }=1+(\ln {\it\chi}_{0})/3$. The experimental and numerical results are in good agreement with the proposed relation.

Gender determination of caucasoid hair using image analysis

1993 ◽  
Vol 51 ◽  
pp. 216-217
Author(s):  
T.B. Ball ◽  
W.M. Hess
Keyword(s):  
Image Analysis ◽  
Cross Sections ◽  
Scalp Hair ◽  
The Body ◽  
Equivalent Diameter ◽  
Cross Sectional ◽  
Hair Samples ◽  
Length Width ◽  
Morphological Differences

It has been demonstrated that cross sections of bundles of hair can be effectively studied using image analysis. These studies can help to elucidate morphological differences of hair from one region of the body to another. The purpose of the present investigation was to use image analysis to determine whether morphological differences could be demonstrated between male and female human Caucasian terminal scalp hair.Hair samples were taken from the back of the head from 18 caucasoid males and 13 caucasoid females (Figs. 1-2). Bundles of 50 hairs were processed for cross-sectional examination and then analyzed using Prism Image Analysis software on a Macintosh llci computer. Twenty morphological parameters of size and shape were evaluated for each hair cross-section. The size parameters evaluated were area, convex area, perimeter, convex perimeter, length, breadth, fiber length, width, equivalent diameter, and inscribed radius. The shape parameters considered were formfactor, roundness, convexity, solidity, compactness, aspect ratio, elongation, curl, and fractal dimension.

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