Flow in soils underlain by a highly permeable pressure horizon

The seepage of water from a system of channels and irrigation furrows and its interaction with the ground water are investigated in relation to such factors as the capillarity of the soil and the evaporation from the free surface, and their combined effect on the flow structure is evaluated. On the basis of the results of computer calculations the dependence of the seepage rate and the capillary spread on the profile and width of the sources and the distance between them, the head, and the thickness of the soil layer is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 98–104, March–April, 1991.The authors wish to thank P. Ya. Kochina and N. N. Verigin for useful advice and comments.     

Effect of an impermeable inclusion in an irrigated soil layer on seepage from a channel

In [1] plane steady seepage from a channel through a soil layer into an underlying unpressurized formation with an impermeable inclusion at the top was investigated in the case of constant uniform infiltration to the free surface. The results of numerical calculations are presented and the effect of the physical parameters of the model on the principal seepage characteristics is analyzed. The limiting cases of flow in the absence of the following factors are considered: inclusion [2], channel [3], channel and backwater [4], and backwater and infiltration [5]. A related scheme, the solution for which is obtained from the relations established, but outside the range of the limitation for one of the mapping parameters, is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 71–76, September–October, 1990.The author wishes to thank P. Ya. Kochina for her interest and useful advice.     

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

Two-dimensional problems of the unsteady seepage of a heavy fluid into a uniform unsaturated porous soil from a single channel and from an infinite periodic system of identical channels are solved. The fluid level in the channel is a known function of timet, which simulates the propagation of the fluid along a furrow normal to the plane of the problem. Seepage into the soil, which occupies the space outside (mainly below) the channel, takes place under the influence of the force of gravity and begins at the momentt=0 after it is instantaneously filled with fluid. On the interval 0 <t < t₁ the height of the fluid in the channel is constant, and whent=t ₁ it falls instantaneously to some other level, also constant. This may be the zero level, which coincides with the bottom of the channel. The problem in which the fluid level in the channel rises is also considered.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 86–94, January–February, 1992.In conclusion the authors wish to thank V. A. Vostretsov for his assistance.     

Ground water regime in an irrigated soil layer with lower lying strongly permeable pressure level

A solution is found to the problem of planar pressureless steady filtration from a system of equidistance channels of the same thickness through a soil layer to a lower lying pressure level in the case of uniform infiltration (evaporation) to the free surface. The unique solvability of the system of equations for the two unknown transformation parameters is established. The filtration flow rate from a channel is investigated analytically as a function of the infiltration intensity and the magnitude of the backwater.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 168–174, March–April, 1979.I thank N. S. Kolodei for assistance in the calculations and the simulation.     

Seepage-limitation optimization of the shape of an irrigation channel by the inverse boundary-value problem method

A study is made of the problem of finding the optimal shape of the section of an irrigation channel from the point of view of minimizing the seepage loss; the inverse boundary-value problem method [1] is used.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–80, May–June, 1984.     

Estimates of backwater and drying levels in a hydrodynamic model

The form of an irrigation system is determined from the condition of an extremal value of the backwater or water-table lowering subject to isoperimetric constraints. The unknown functionals and equations of the extremals are written down in explicit form on the basis of the method of Lagrangian multipliers. Seepage in the region of irrigation systems can have both a negative effect on the adjacent territory (water-table elevation, swamping, salination near large canals and reservoirs) and improve the water regime of the soil (regulation of the drying norms by drainage). From the practical point of view, it is important to know how to find the distortions of the natural level of ground water introduced by such systems, and also to determine the influence of the resulting flows on artificial (foundations, screens to prevent seepage) and natural (troughs, slopes) objects. For known hydrogeological conditions, regimes of pressure variation, and disposition of the supply and discharge regions, these problems can be solved either in the framework of a hydraulic [1] or hydrodynamic [2] flow model. In this paper, a hydrodynamic model is used to estimate the raising of the ground-water level due to seepage from a channel, its lowering by a drain, and the seepage pressure force on the foundation near a reservoir. It is important that these estimates are obtained by solving problems of constructive type, i.e., problems in which the arrangement of the system (supply, water receiving, or topping-up contour) is not specified in advance but is found as an extremal of an isoperimetric problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 82–90, March–April, 1991.     

Effect of an impermeable inclusion in the underlying highly permeable pressurized horizon on the conditions of ground water in an irrigated layer of soil

The problem of plane, nonpressurized, steady-state filtration through a layer of soil into an underlying pressurized horizon, which contains an impermeable section at the top, with uniform infiltration on the free surface is solved in a hydro-dynamic formation. A constructive solution of the problem is given with the help of the method of P. Ya. Polubarinova-Kochina; representations are obtained for the characteristic dimensions of the flow scheme and the depression. The case of limiting flow — no head in the bottom, highly permeable layer — studied in [1] is noted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–5, May–June, 1986.The author thanks V. N. Emikh for useful remarks and discussions.     

Transient motion of groundwater (subsurface water) in the presence of evaporation

The spread of a mound of groundwater in the region between two parallel channels with different water levels (H₁ at x = 0 and H₂ at x = L) during irrigation is studied with due allowance for evaporation. Evaporation is taken into account in relation to the depth of the groundwater h(x, t); its intensity is regarded as zero when h < h₀ (where h₀ is the critical level of the ground-water), while varying linearly or remaining constant when h > h₀. The intensity or irrigation is regarded as constant. This problem is solved by using the thermal potentials of a double layer and reduces to the solution of a nonlinear integral equation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 176–182, March–April, 1975.     

Gas flow in cylindrical capillaries under intermediate conditions

At present, there are sufficient solutions of the problem of free-molecular gas flow through a short cylindrical channel, for example, [1–3]. In intermediate flow conditions, for Knudsen number Kn 1, solutions have been obtained for the limiting cases: an infinitely long channel [4] and a channel of zero length (an aperture) [5]. However, no solution is known for short channels for Kn 1. The present work reports a calculation by the Monte Carlo method of the macroscopic characteristics of the gas flow through a short cylindrical channel (for various length—radius ratios), taking into account intermolecular collisions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–190, January–February, 1977.     

Electric field in the transverse cross section of the channel of an MHD generator

During the motion of a partially ionized gas in magnetohydrodynamic channels the distribution of the electrical conductivity is usually inhomogeneous due to the cooling of the plasma near the electrode walls. In Hall-type MHD generators with electrodes short-circuited in the transverse cross section of the channel the development of inhomogeneities results in a decrease of the efficiency of the MHD converter [1]. A two-dimensional electric field develops in the transverse section. Numerical computations of this effect for channels of rectangular cross section have been done in [2, 3], At the same time it is advisable to construct analytic solutions of model problems on the potential distribution in Hall channels, which would permit a qualitative analysis of the effect of the inhomogeneous conductivity on local and integral characteristics of the generators. In the present work an exact solution of the transverse two-dimensional problem is given for the case of a channel with elliptical cross section stretched along the magnetic field. The parametric model of the distribution of the electrical conductivity of boundary layer type has been used for obtaining the solution. The dependences of the electric field and the current and also of the integral electrical characteristics of the generator on the inhomogeneity parameters are analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 3–10, January–February, 1973.     

Propagation of a flush wave in a prismatic channel

By a water flush there is generally understood an unsteady-state flow of water, arising in millraces, with the breaching (rupture) of a dam. The special characteristics of a flush wave are also possessed by a flow in a lower millrace at some distance from the dam, with the overflow of water arising in the reservoir over the crest of the dam. Usually, the necessary information on the parameters of a flush wave with its motion in natural channels is obtained by numerical solution, in a digital computer, of the equations of not fully established one-dimensional flow [1–3]. These calculations are very labor-consuming and require rather detailed information on the channel. Therefore, it is of practical importance to clarify the overall laws governing the propagation of flush waves in schematized, in particular, in prismatic channels. In some cases, on the basis of such laws, it is possible to make a preliminary diagnosis of the expected scales of the phenomenon.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 39–44, January–February, 1975.     

Approximate models of salt transfer with washings of soils with water-impermeable base

On the basis of an approximate model of filtration with drainage washings of a soil layer with a water-impermeable base [1], shown schematically in Fig. 1, an investigation is made of the desalinization process of soils for several forms of the equations of salt transfer between the moving solution and the fixed phase. Neglect of the external diffusion makes it possible to reduce the investigation to the solution of one-dimensional boundary-value problems, characterizing salt transfer along fixed streamlines. Analogous problems were discussed in [2] with application to the one-dimensional filtration of wash waters in a dry soil.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 44–51, January–February, 1978.The author thanks V. N. Émikh and V. I. Pen'kovskii for their repeated and useful evaluations of the work.     

Oscillatory thermocapillary instability of a liquid layer in the presence of a surfactant

The effect of capillarity and a surfactant on the stability of a liquid layer in the presence of a vertical temperature gradient is investigated. It is found that the surfactant leads to the appearance of both monotonic and oscillatory instability, the presence of a surface concentration destabilizing the equilibrium in the case of heating from below. When the free surface is heated, the surfactant stabilizes the capillary instability.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 6–10, January–February, 1993.     

Thermocapillary instability of a liquid layer in the presence of a soluble surfactant

The effect of capillarity on the stability of a plane layer of viscous heat-conducting liquid in the presence of a soluble surfactant is investigated. It is found that an increase in surfactant solubility has a stabilizing effect on equilibrium. Monotonic instability is the most dangerous mode in the case of long-wave perturbations, whereas in the short-wave region loss of stability is induced by oscillatory perturbations.Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–8, January–February, 1996.     

Some cases of unsteady flow in porous media associated with irrigation

The results of an earlier study [1] are used to consider the motion of underground water flowing from an irrigation channel. The surface of the ground flow usually has an uneven shape, since in some sections there is stripwise irrigation, while at others evaporation may occur or rain may fall. The variations of the water level in the channel are assumed known. The subsequent variation of the ground water level is determined. If the level rises appreciably there can be salinization or swamped ground can form.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 130–137, May–June, 1988.     

Interaction of a laminar boundary layer with external turbulence

Transition in the boundary layer on a flat plate in a turbulent flow is investigated experimentally and theoretically. It is established that over a broad range of flow conditions (variation of the intensity and scale of the external turbulence, the angle of attack, the shape of the leading edge, etc.) transition takes place without the formation of Tollmien-Schlichting waves, and its initial stages, including the amplification of disturbances, are described by the linearized unsteady three-dimensional boundary layer equations without a pressure gradient.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 55–65, September–October, 1989.The authors are grateful to N. F. Polyakov, V. S. Kosorygin, and O. S. Ryzhov for useful discussions and to N. N. Bychkov and O. N. Konstantinovskii for assisting with the experiments.     

Asymptotic drag formulas for rapidly rotating radial channels of rectangular cross section

Taking, as an example, the solution of the drag problem of a slitlike channel, the change in flow characteristics with increase in intensity of rotation is shown. The form of the asymptotic drag formulas is determined for rapidly rotating channels with sides in a finite ratio, at Rossby numbers of the order of unity. Good agreement with experimental data is found. The final form of the asymptotic solution, valid at small Rossby numbers, is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 42–49, November–December, 1978.This considerably restricts the range of permissible values of E for channels elongated in the direction of the axis of rotation.     

Determination of the shape of the downstream slope of an earth-fill dam from the seepage strength conditions at the face

Inverse boundary-value problems of determining the slope of an earth-fill dam (or its core) for which the local seepage strength conditions are exactly satisfied over the entire face, with no unnecessary margin, are formulated. Variants of these conditions are examined for cases of suffosion (undermining), local slip and contact suffosion. The shape of the boundary of the region in the velocity hodograph plane is established and the possibility of using it to construct a solution is demonstrated. Analytical and numerical methods of solution are proposed and justified. It is shown that problems with a condition similar to that associated with slip can be solved by Polubarinova-Kochina's analytical method [5]. For a number of special cases solutions are obtained in explicit form and the results of numerical calculations are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, 101–107, May–June, 1987.     

Kinematic analysis of disturbed flow past a plate in a channel with porous walls

Analytic expressions for the complex flow potential are obtained in the linear formulation in the neighborhood of a plate at a small angle of incidence and near porous channel walls. The general solution includes the limiting cases of a plate in a channel with impermeable walls and in a jet. Numerical results concerning the effect of porosity on the flow geometry in the neighborhood of the plate and the channel walls are presented. The disturbed-flow velocity distributions along the channel walls and the flow rate of the fluid sinking at infinity are obtained.Cheboksary. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 13–19, July–August, 1995.     

Rotational inviscid flow with circulation zones in a channel of variable cross section

The development of the theory of rotational motion of inviscid fluids for the purposes of describing channel flow encounters certain difficulties in connection with the appearance of viscosity effects near the walls. In the potential-rotational model [1], in which the vorticity is nonzero only in a closed circulation zone surrounded by potential flow, it is assumed that the separation and attachment points are known in advance. For example, for flow around a cavity these points coincide with the extreme corner points of the contour. The problem of determining the vorticity in a closed zone for the potential-rotational model has been investigated in a number of studies [2, 3], etc. In the case of an incompressible fluid the vorticity in the circulation zone is constant for two-dimensional flow and proportional to the distance from the axis for axisymmetric flow. The value of the constant is found from the steady-state condition for the adjoining viscous layers. If the channel walls have a smooth profile without corner points, then for determining the boundaries of the circulation zones additional conditions must be used. This study employs another scheme, in which the vorticity is formed outside the region of flow and in a particular problem is specified in the form of a boundary condition. An analytic solution describing the rotational flow of an inviscid fluid in a channel with a slightly varying cross section is obtained. Three types of entrance flow nonuniformity are considered: 1) uniform shear flow, 2) wake-type flow, and 3) potential flow with a narrow wall boundary layer. Streamline patterns with circulation zones are constructed for flows in diffuser channels with the above-mentioned types of entrance nonuniformity. A model of flow separation in a channel with a turbulent boundary layer on the walls is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 31–37, March–April, 1985.In conclusion the author wishes to thank E. Yu. Shal'man, A. N. Kraiko, and A. B. Vatazhin for useful discussions and advice.