scholarly journals Viscous sheets advancing over dry beds

1977 ◽  
Vol 81 (4) ◽  
pp. 735-756 ◽  
Author(s):  
J. Buckmaster
Keyword(s):  
Open Channel ◽  
Retaining Wall ◽  
Thin Sheet ◽  
Circular Cross Section ◽  
Leading Edge ◽  
Inclined Plane ◽  
Extreme Sensitivity ◽  
Bed Slope ◽  
Fall Line ◽  
Creeping Motion

The unsteady creeping motion of a thin sheet of viscous liquid as it advances over a gently sloping dry bed is examined. Attention is focused on the motion of the leading edge under various influences and four problems are discussed. In the first problem the fluid is travelling down an open channel formed by two straight parallel retaining walls placed perpendicular to an inclined plane. When the channel axis is parallel to the fall line there is a progressive-wave solution with a straight leading edge, but inclination of the axis generates distortions and these are calculated. In the second problem a sheet with a straight leading edge travelling over an inclined plane penetrates a region where the bed is uneven, and the subsequent deformation of the leading edge is followed. The third problem considers the flow down an open channel of circular cross-section (a partially filled pipe) and the time-dependent shape of the leading edge is calculated. The fourth problem is that of flow down an inclined plane with a single curved retaining wall. These problems are all analysed by assuming that a length characteristic of the geometry is large compared with the fluid depth divided by the bed slope, and all the solutions display extreme sensitivity to the data.

Spreading and instability of a viscous fluid sheet

1990 ◽  
Vol 211 ◽  
pp. 373-392 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Related Problem ◽  
Numerical Solutions ◽  
Thin Sheet ◽  
Leading Edge ◽  
Small Disturbance ◽  
Inclined Plane ◽  
Moving Contact Line ◽  
Moving Contact

Experiments by Huppert (1982) have demonstrated that a finite volume of fluid placed on an inclined plane will elongate into a thin sheet of fluid as it slides down the plane. If the fluid is initially placed uniformly across the plane, the sheet retains its two-dimensionality for some time, but when it has become sufficiently long and thin, the leading edge develops a spanwise instability. A similarity solution for this motion was derived by Huppert, without taking account of the edge regions where surface tension is important. When these regions are examined, it is found that the conditions at the edges can be satisfied, but only when the singularity associated with the moving contact line is removed. When the sheet is sufficiently elongated, the profile of the free surface shows an upward bulge near the leading edge. It is suggested that the observed instability of the shape of the leading edge is a result of the dynamics of the fluid in this bulge. The related problem of a ridge of fluid sliding down the plane is examined and found to be linearly unstable. The spanwise lengthscale of this instability is, however, dependent on the width of the channel occupied by the fluid, which is at variance with the observed nature of the instability. Preliminary numerical solutions for the nonlinear development of a small disturbance to the position of a straight leading edge show the incipient development of a finger of fluid with a width that does not depend on the channel size, in accordance with the observations.

1. On a New Formula for the Pressure of Earth Against a Retaining Wall

1888 ◽  
Vol 14 ◽  
pp. 85-97
Author(s):  
A. C. Elliott ◽  
Armstrong
Keyword(s):  
Retaining Wall ◽  
Resultant Force ◽  
Chronological Order ◽  
Inclined Plane ◽  
The Earth ◽  
New Formula ◽  
Mutual Action

There are two main distinct methods of attacking the problem of the retaining wall. The first in chronological order is due to Coulomb, and is variously named, perhaps most commonly as the method of the Wedge of Least Eesistance. Briefly characterised, it might be said to depend upon the mathematical artifice of finding the resultant force due to the mutual action of the earth mass, and the wall a maximum, the earth being supposed to yield incipiently under the action of its weight, and in opposition to friction and the reaction in question, along an inclined plane determined so as to fulfil that imposed condition. Coulomb's method has been developed by various writers, and may be regarded as complete.

Physical and Mathematical Modeling of Solid-Liquid Flow at High Bed Shear in Steep Flume

2015 ◽  
Author(s):  
Václav Matoušek ◽  
Štěpán Zrostlík ◽  
Jan Krupička ◽  
Tomáš Picek ◽  
Vojtěch Bareš
Keyword(s):  
Mathematical Modeling ◽  
Flow Rate ◽  
Open Channel ◽  
Bed Load ◽  
Flow Depth ◽  
Load Transport ◽  
Bed Load Transport ◽  
Bed Slope ◽  
Solid Liquid ◽  
Bed Friction

The paper discusses new results of our experimental- and mathematical modeling of sediment-laden open-channel flows in the upper plane bed regime associated with intense transport of sediment. Our recent studies showed that bed-load transport and bed friction are interrelated and classical formulae for bed friction (Nikuradse formula) and bed-load transport (Meyer-Peter and Muller formula) need to be modified to account for the intense transport of sediment. The new results of our laboratory experiments in a tilting flume are presented and analyzed for different sediment fractions. The analysis is focused on the effect of solids density and size on the solid-liquid flow characteristics as the solids flow rate, flow depth, and bed slope for certain flow rate of water in a channel of given geometry. The experimental results are compared with outputs of our mathematical model simulating the observed phenomena. The simple 1-D model combines hydrodynamic- and sediment-transport equations and enables to use different transport- and friction formulae to predict the solids transport, flow depth and bed slope under the condition of (pseudo-) uniform flow of solid-water mixture in the open channel.

scholarly journals How do glaciers respond to climate? Perspectives from the simplest models

2013 ◽  
Vol 59 (217) ◽  
pp. 949-960 ◽  
Author(s):  
W.D. Harrison
Keyword(s):  
Climate Change ◽  
Fast Response ◽  
Equilibrium Line ◽  
Stability Characteristic ◽  
Inclined Plane ◽  
Macroscopic Theory ◽  
Basic Properties ◽  
Response Change ◽  
Increased Sensitivity ◽  
Bed Slope

AbstractWe study the approximations underlying the macroscopic theory of glacier response to climate, and illustrate some basic properties of glacier response using two simple examples, a block on an inclined plane and a block with a more realistic terminal region. The properties include nonlinearity and the usefulness of linear approximations, sensitivity to bed slope, timescale, stability, characteristic elevations of the equilibrium line at which the properties of the response change, the limit of fast response in a changing climate, the minimum sustainable size, increased sensitivity to climate change as a glacier retreats, and finally the similarity in the responses of simple glaciers with the same product of length and square of bed slope.

scholarly journals An analytical study on a flow field in an open channel with gradually varied bed slope.

1990 ◽  
pp. 63-71 ◽  
Author(s):  
Keita FURUKAWA ◽  
Tomoya ICHIMURA ◽  
Masato SEKINE ◽  
Hideo KIKKAWA
Keyword(s):  
Flow Field ◽  
Analytical Study ◽  
Open Channel ◽  
Bed Slope

scholarly journals On the ridging of a thin sheet of lead ice

1991 ◽  
Vol 15 ◽  
pp. 81-86 ◽  
Author(s):  
M. A. Hopkins ◽  
W. D. Hibler
Keyword(s):  
Potential Energy ◽  
Sea Ice ◽  
Simulation Model ◽  
Total Energy ◽  
Numerical Experiments ◽  
Thin Sheet ◽  
Leading Edge ◽  
Particle Simulation ◽  
Two Dimensional ◽  
Ridge Structure

A two-dimensional particle simulation model of the sea-ice ridging process is developed. In this model, ridges are formed from an intact layer of newly frozen lead ice colliding with a thick multi-year floe. Blocks broken from the leading edge of the lead ice collect above and beneath the multi-year floe to form the characteristic ridge structure seen in the central Arctic. The total energy consumed in ridging ice, which is converted into the potential energy of the ridge structure and dissipated by the frictional and inelastic contacts between blocks of ice, is calculated explicitly. The results of preliminary numerical experiments using this model indicate that the amount of energy required to ridge ice may be much larger than previous estimates.

Influence of Leading Edge and Spacing on the Near Wake of Cylinder Pairs

2009 ◽  
Author(s):  
Jonathan M. Tsikata ◽  
Samuel S. Paul ◽  
Chris Katopodis ◽  
Mark F. Tachie
Keyword(s):  
Open Channel ◽  
Particle Image ◽  
Leading Edge ◽  
Particle Image Velocimetry System ◽  
Turbulence Level ◽  
Near Wake ◽  
Mean Velocity ◽  
Rectangular Cylinder ◽  
Image Velocimetry ◽  
The Mean

An experimental study of the effects of the shape of rectangular cylinder leading edge and the cylinder spacing on the wake dynamics in an open channel turbulent flow is reported. The shapes of the rectangular cylinder leading edges were square and round with each having a square trailing edge. In each experiment, measurements were conducted for a pair of cylinders that have identical leading edge shape. Three centre-to-centre spacing (b = 30 mm, 50 mm and 75 mm) were investigated for each cylinder leading edge shape. Particle image velocimetry system was used to conduct measurements around each cylinder pair. The results show that the mean velocity and the turbulence level increases with decreasing spacing. The turbulence levels downstream of a cylinder pair with a round leading edge are relatively higher than the corresponding cylinder pair with square leading edge.

scholarly journals On the ridging of a thin sheet of lead ice

1991 ◽  
Vol 15 ◽  
pp. 81-86 ◽  
Author(s):  
M. A. Hopkins ◽  
W. D. Hibler
Keyword(s):  
Potential Energy ◽  
Sea Ice ◽  
Simulation Model ◽  
Total Energy ◽  
Numerical Experiments ◽  
Thin Sheet ◽  
Leading Edge ◽  
Particle Simulation ◽  
Two Dimensional ◽  
Ridge Structure

A two-dimensional particle simulation model of the sea-ice ridging process is developed. In this model, ridges are formed from an intact layer of newly frozen lead ice colliding with a thick multi-year floe. Blocks broken from the leading edge of the lead ice collect above and beneath the multi-year floe to form the characteristic ridge structure seen in the central Arctic. The total energy consumed in ridging ice, which is converted into the potential energy of the ridge structure and dissipated by the frictional and inelastic contacts between blocks of ice, is calculated explicitly. The results of preliminary numerical experiments using this model indicate that the amount of energy required to ridge ice may be much larger than previous estimates.

Open Channel Boundary Layer Relaxation Behind a Forward Facing Step at Low Reynolds Numbers

2001 ◽  
Vol 123 (3) ◽  
pp. 539-544 ◽  
Author(s):  
Mark F. Tachie ◽  
Ram Balachandar ◽  
D. J. Bergstrom
Keyword(s):  
Open Channel ◽  
Mean Field ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Low Reynolds Numbers ◽  
Channel Boundary ◽  
Self Similar ◽  
Forward Facing Step ◽  
Upstream Flow

This paper reports laser-Doppler anemometer measurements of mean velocity and turbulence statistics upstream and downstream of a 3-mm forward facing step in a shallow open channel flow. The Reynolds numbers based on the momentum thickness (θ) of the approaching upstream flow and step height (h) are in the range 1010⩽Reθ⩽2240 and 960⩽Reh⩽1890, respectively. Measurements are obtained at 50 step heights upstream of the leading edge of the step and 1⩽x/h⩽162 downstream of the step. The results show that the overlap region develops more slowly than the inner and outer regions. The mean field recovers at x/h=50. Distributions of the turbulence intensity tend to become self-similar for x/h>100 but the profiles do not necessarily collapse onto the upstream profiles.

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