Solution of two-dimensional problems of unsteady heavy-fluid seepage into unsaturated porous soil on the basis of an instantaneous saturation model

1992 ◽  
Vol 27 (1) ◽  
pp. 64-70 ◽  
Author(s):  
A. N. Kraiko ◽  
Sh. Salomov
Keyword(s):  
Two Dimensional ◽  
Heavy Fluid ◽  
Saturation Model ◽  
Fluid Seepage ◽  
Porous Soil

scholarly journals Accumulation of a light non-aqueous phase liquid on a flat barrier baffling a descending groundwater flow

2012 ◽  
Vol 468 (2147) ◽  
pp. 3667-3684 ◽  
Author(s):  
A. R. Kacimov ◽  
Yu. V. Obnosov
Keyword(s):  
Two Dimensional ◽  
Heavy Fluid ◽  
Cross Sectional ◽  
Free Surfaces ◽  
New Class ◽  
Impermeable Barrier ◽  
Two Dimensional Flow ◽  
Phase Liquid ◽  
The Given ◽  
Vertical Height

The pioneering solution of Zhukovskii for a steady two-dimensional flow of an ideal heavy fluid with a nonlinear free boundary condition is extended to a Darcian flow of groundwater encumbered by an impermeable barrier. The stoss or/and lee sides of the barrier are covered by a macrovolume of a liquid contaminant. Explicit parametric equations of the sharp interface are obtained by inversion of the hodograph domain. Zhukovskii's gas-finger shape is shown to be a particular case of our new class of free surfaces. For a cap of a light liquid, partially covering the roof, from the given cross-sectional area of the cap, the affixes of the conformal mapping are found as a solution of a system of two nonlinear equations. The horizontal width and vertical height of the cap are determined. If the dimensionless incident velocity is higher than the density contrast, then the interface (cap boundary) cusps at its apex. For a relatively small velocity, the interface spreads to the vertices of the barrier, the apex zone remaining blunt shaped. We depict all the relevant domains and plot the flow nets using computer algebra routines.

scholarly journals Two-Dimensional Soil Geometric Tortuosity Model Based on Porosity and Particle Arrangement

Minerals ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 43
Author(s):  
Jin Gan ◽  
Zhiquan Yang ◽  
Zhiwei Zhang ◽  
Chaoyue Li ◽  
Yi Yang ◽  
...  
Keyword(s):  
Functional Relationship ◽  
Geometric Analysis ◽  
Anisotropy Parameter ◽  
Two Dimensional ◽  
Soil Permeability ◽  
Theoretical Derivation ◽  
Permeability Characteristics ◽  
Physical Mechanisms ◽  
Particle Arrangement ◽  
Fluid Seepage

Porosity and particle arrangement are important parameters affecting soil tortuosity, so it is of great significance to determine the intrinsic relationship between them when studying soil permeability characteristics. Theoretical derivation and geometric analysis methods are used to derive a two-dimensional geometric tortuosity model. The model is a function of particle arrangement parameters (m and θ) and porosity. An analysis of the model and its parameters shows that: (1) The arrangement of particles is one of the reasons for the different functional relationship between tortuosity and porosity, which proved that the tortuosity is not only related to the porosity but also affected by the particle arrangement. (2) The greater the anisotropy parameter m is, the greater the tortuosity is, indicating m varies when fluid passes through the soil from different sides resulting in different values of permeability. (3) The tortuosity increases with the increase in the blocking parameters θ. (4) With increasing porosity, the influence of the parameters m and θ on the tortuosity gradually decreases, suggesting that the influence of particle arrangement on tortuosity gradually decreases. The results presented here increase the understanding of the physical mechanisms controlling tortuosity and, hence, the process of fluid seepage through soil.

Stressed horizontal convection

2012 ◽  
Vol 692 ◽  
pp. 317-331 ◽  
Author(s):  
J. Hazewinkel ◽  
F. Paparella ◽  
W. R. Young
Keyword(s):  
Surface Stress ◽  
Numerical Solutions ◽  
Interesting Case ◽  
Two Dimensional ◽  
Uniform Temperature ◽  
Heavy Fluid ◽  
Driving Mechanisms ◽  
Horizontal Convection ◽  
Scaling Argument ◽  
Boussinesq Fluid

AbstractWe consider the problem of a Boussinesq fluid forced by applying both non-uniform temperature and stress at the top surface. On the other boundaries the conditions are thermally insulating and either no-slip or stress-free. The interesting case is when the direction of the steady applied surface stress opposes the sense of the buoyancy driven flow. We obtain two-dimensional numerical solutions showing a regime in which there is an upper cell with thermally indirect circulation (buoyant fluid is pushed downwards by the applied stress and heavy fluid is elevated), and a second deep cell with thermally direct circulation. In this two-cell regime the driving mechanisms are competitive in the sense that neither dominates the flow. A scaling argument shows that this balance requires that surface stress vary as the horizontal Rayleigh number to the three-fifths power.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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