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Yu. V. Obnosov - One of the best experts on this subject based on the ideXlab platform.

  • infiltration induced Phreatic Surface flow to periodic drains vedernikov engelund vasil ev s legacy revisited
    Applied Mathematical Modelling, 2021
    Co-Authors: A R Kacimov, Yu. V. Obnosov
    Abstract:

    Abstract An explicit analytical solution is obtained to an old problem of a potential steady-state 2-D saturated Darcian flow in a homogeneous isotropic soil towards systematic drains modeled as line sinks (submerged drains under an overhanging of a Phreatic Surface), placed on a horizontal impervious substratum, with a constant-rate infiltration from the vadose zone. The corresponding boundary-value problem brings about a quarter-plane with a circular cut. A mathematical clue to solving the Hilbert problem for a two-dimensional holomorphic vector-function is found by engaging a hexagon, which has been earlier used in analytical solution to the problem of Phreatic flow towards Zhukovsky’s drains (slits) on a horizontal bedrock. A hodograph domain is mapped on this hexagon, which is mapped onto a reference plane where derivatives of two holomorphic functions are interrelated via a Polubarinova-Kochina type analysis. HYDRUS2D numerical simulations, based on solution of initial and boundary value problems to the Richards equation involving capillarity of the soil, concur with the analytical results. The position of the water table, isobars, isotachs, and streamlines are analyzed for various infiltration rates, sizes of the drains, boundary conditions imposed on them (empty drains are seepage face boundaries; full drains are constant piezometric head contours with various backpressures).

  • Steady Flow from an Array of SubSurface Emitters: Kornev’s Irrigation Technology and Kidder’s Free Boundary Problems Revisited
    Transport in Porous Media, 2018
    Co-Authors: A R Kacimov, Yu. V. Obnosov, J. Šimůnek
    Abstract:

    Kornev’s (SubSurface irrigation, Selhozgiz, Moscow-Leningrad, 1935 ) subSurface irrigation with a periodic array of emitting porous pipes is analytically modeled as a steady potential Darcian flow from a line source generating a Phreatic Surface. The hodograph method is used. The complex potential strip is mapped onto the triangle of the inverted hodograph. An analogy with the Deemter (Theoretische en numerieke behandeling van ontwaterings-en infiltratie stromings problemen (in Dutch). Theoretical and numerical treatment of flow problems connected to drainage and irrigation. Ph.D. dissertation, Delft University of Technology, 1950 ) drainage problem and Kidder (J Appl Phys 27(8):867–869, 1956 ) free-Surface flow toward an array of oil wells underlain by a “wavy” oil–water interface is drawn. For a half-period of Kornev’s flow, the “wavy” Phreatic Surface has an inflection point. The “waviness” of the Phreatic Surface is controlled by the spacing between emitters, the strength of line sources, and the pipe pressure and radius. Numerical modeling with HYDRUS involved two factors which constrained the saturated–unsaturated flow: the positive pressure head at the outlet of the modeled domain and lateral no-flow boundaries, with a qualitative corroboration of analytical solutions for potential (fully saturated) and purely unsaturated flows. HYDRUS is also applied to a generalized Philip’s regime of an unsaturated flow past a subterranean hole, which is impermeable at its top and leaks at the bottom.

  • Strip-focused Phreatic Surface flow driven by evaporation: Analytical solution by the Riesenkampf function
    Advances in Water Resources, 2006
    Co-Authors: Anvar Kacimov, Yu. V. Obnosov
    Abstract:

    Steady free-Surface seepage in a homogeneous porous aquifer is studied by a conformal mapping of the inversed hodograph (angle) onto the domain in the Riesenkampf plane (slanted-face half-strip or trapezium). Seepage from the water table is caused by evaporation uniformly distributed with a horizontal coordinate. This distributed sink forms a regional trough on the Phreatic Surface with groundwater moving from the flanks to the trough center on the regional scale and from the water table to the soil Surface locally. The free Surfaces, streamlines of marked particles, travel times, and Darcian velocity are presented.

  • Phreatic Surface flow from a near-reservoir saturated tongue
    Journal of Hydrology, 2004
    Co-Authors: Anvar Kacimov, Yu. V. Obnosov, Johan Perret
    Abstract:

    Steady and transient 2D Darcian flows in a saturated ‘tongue’ adjacent to a reservoir are studied analytically. First, a stable tongue receiving water from an inclined equipotential reservoir bed and losing moisture through a Phreatic Surface is considered. The hydraulic head is governed by the Laplace equation and the complex potential and complex coordinate are determined explicitly by the Polubarinova-Kochina method at an arbitrary bank slopes and evapotranspiration rates. In a particular case of a vertical slope, the tongue becomes a right-angled triangle extending into the layer for the same distance as the Dupuit-Forchheimer model predicts. Second, a saturated Dupuit-Forchheimer flow in the tongue is analyzed under the assumption of evaporation exponentially and linearly decreasing with the depth of a Phreatic Surface. The corresponding non-linear ordinary differential equation is integrated twice and predicts the length of the tongue as a function of the reservoir water level. Third, a transient regime is modelled by the Boussinesq equation with evaporation uniform in space, but varying cyclostationary with time. A straight-line water table translating upward–downward is found to be located always below the water table for steady regimes with an average evaporation.

  • Infiltration-Induced Phreatic Surface Flow to Periodic Drains: Vedernikov-Engelund-Vasil’ev’s Legacy Revisited
    Applied Mathematical Modelling, 1
    Co-Authors: Anvar Kacimov, Yu. V. Obnosov
    Abstract:

    Abstract An explicit analytical solution is obtained to an old problem of a potential steady-state 2-D saturated Darcian flow in a homogeneous isotropic soil towards systematic drains modeled as line sinks (submerged drains under an overhanging of a Phreatic Surface), placed on a horizontal impervious substratum, with a constant-rate infiltration from the vadose zone. The corresponding boundary-value problem brings about a quarter-plane with a circular cut. A mathematical clue to solving the Hilbert problem for a two-dimensional holomorphic vector-function is found by engaging a hexagon, which has been earlier used in analytical solution to the problem of Phreatic flow towards Zhukovsky’s drains (slits) on a horizontal bedrock. A hodograph domain is mapped on this hexagon, which is mapped onto a reference plane where derivatives of two holomorphic functions are interrelated via a Polubarinova-Kochina type analysis. HYDRUS2D numerical simulations, based on solution of initial and boundary value problems to the Richards equation involving capillarity of the soil, concur with the analytical results. The position of the water table, isobars, isotachs, and streamlines are analyzed for various infiltration rates, sizes of the drains, boundary conditions imposed on them (empty drains are seepage face boundaries; full drains are constant piezometric head contours with various backpressures).

Anvar Kacimov - One of the best experts on this subject based on the ideXlab platform.

  • How much floating light nonaqueous phase liquid can a Phreatic Surface sustain? Riesenkampf's scheme revisited
    Water Resources Research, 2011
    Co-Authors: Anvar Kacimov, Yurii Obnosov, Ali Al-maktoumi, Mohammed S. Al-balushi
    Abstract:

    [1] Steady, Darcian, one-phase, Phreatic Surface flow of groundwater into a horizontal well with a pancake lens of light nonaqueous phase liquid (LNAPL) accumulated in the water table trough is studied by the method of complex analysis. A sharp interface model assumes groundwater capped by two isobaric limbs (groundwater–vadose zone interfaces) of a free Surface with an in-between cambered segment of an immiscible LNAPL-water interface, along which pressure is hydrostatically increasing with the depth of the LNAPL “channel.” The complex potential polygon is mapped onto an auxiliary half plane where the complex physical coordinate of the flow domain is represented in terms of singular integrals as a solution of the Keldysh-Sedov problem. The shapes of semi-infinite “wings” of the water table contacting the vadose zone gas and of a finite length LNAPL-groundwater interface are found from parametric equations that involve the sink strength and location with respect to the pancake Surface, the ordinate of the lowest trough point, and the volume of LNAPL accreted in the lens. Critical conditions, corresponding to the lens contour cusping toward the sink, are found. The Riesenkampf solution contains a free parameter, which is fixed by specifying either a point on the free Surface or the volume of the trough-intercepted LNAPL.

  • Strip-focused Phreatic Surface flow driven by evaporation: Analytical solution by the Riesenkampf function
    Advances in Water Resources, 2006
    Co-Authors: Anvar Kacimov, Yu. V. Obnosov
    Abstract:

    Steady free-Surface seepage in a homogeneous porous aquifer is studied by a conformal mapping of the inversed hodograph (angle) onto the domain in the Riesenkampf plane (slanted-face half-strip or trapezium). Seepage from the water table is caused by evaporation uniformly distributed with a horizontal coordinate. This distributed sink forms a regional trough on the Phreatic Surface with groundwater moving from the flanks to the trough center on the regional scale and from the water table to the soil Surface locally. The free Surfaces, streamlines of marked particles, travel times, and Darcian velocity are presented.

  • Phreatic Surface flow from a near-reservoir saturated tongue
    Journal of Hydrology, 2004
    Co-Authors: Anvar Kacimov, Yu. V. Obnosov, Johan Perret
    Abstract:

    Steady and transient 2D Darcian flows in a saturated ‘tongue’ adjacent to a reservoir are studied analytically. First, a stable tongue receiving water from an inclined equipotential reservoir bed and losing moisture through a Phreatic Surface is considered. The hydraulic head is governed by the Laplace equation and the complex potential and complex coordinate are determined explicitly by the Polubarinova-Kochina method at an arbitrary bank slopes and evapotranspiration rates. In a particular case of a vertical slope, the tongue becomes a right-angled triangle extending into the layer for the same distance as the Dupuit-Forchheimer model predicts. Second, a saturated Dupuit-Forchheimer flow in the tongue is analyzed under the assumption of evaporation exponentially and linearly decreasing with the depth of a Phreatic Surface. The corresponding non-linear ordinary differential equation is integrated twice and predicts the length of the tongue as a function of the reservoir water level. Third, a transient regime is modelled by the Boussinesq equation with evaporation uniform in space, but varying cyclostationary with time. A straight-line water table translating upward–downward is found to be located always below the water table for steady regimes with an average evaporation.

  • Estimation and Optimization of Transient Seepage with Free Surface
    Journal of Irrigation and Drainage Engineering, 1993
    Co-Authors: Anvar Kacimov
    Abstract:

    Single sink depths providing maximum ground-water table decrease during a fixed time interval within a selected area are found for the 2-D and 3-D cases. The curve of the maximal Phreatic Surface position (underflooding curve) in the aquifer from flood induced variation in water level of the ground-water reservoir is calculated. Well-known analytical solutions based on nonlinear and linear potential theories and the Dupuit-Forchheimer approximation are applied to calculate the objective function, decision variables, and boundary of the fully saturated zone. In the linear case, an explicit analytic solution gives the unique maximum of the water table decrease at the compliance point for a given pumping duration. For small values of sink depth, the linear approach is invalid. In the nonlinear case, complex analysis and series expansions are used. For small values of drain depth, the series technique becomes untenable. For the reservoir-aquifer problem the spreading Phreatic Surface is a rotating straight line and the underflooding curve is a parabola.

  • Infiltration-Induced Phreatic Surface Flow to Periodic Drains: Vedernikov-Engelund-Vasil’ev’s Legacy Revisited
    Applied Mathematical Modelling, 1
    Co-Authors: Anvar Kacimov, Yu. V. Obnosov
    Abstract:

    Abstract An explicit analytical solution is obtained to an old problem of a potential steady-state 2-D saturated Darcian flow in a homogeneous isotropic soil towards systematic drains modeled as line sinks (submerged drains under an overhanging of a Phreatic Surface), placed on a horizontal impervious substratum, with a constant-rate infiltration from the vadose zone. The corresponding boundary-value problem brings about a quarter-plane with a circular cut. A mathematical clue to solving the Hilbert problem for a two-dimensional holomorphic vector-function is found by engaging a hexagon, which has been earlier used in analytical solution to the problem of Phreatic flow towards Zhukovsky’s drains (slits) on a horizontal bedrock. A hodograph domain is mapped on this hexagon, which is mapped onto a reference plane where derivatives of two holomorphic functions are interrelated via a Polubarinova-Kochina type analysis. HYDRUS2D numerical simulations, based on solution of initial and boundary value problems to the Richards equation involving capillarity of the soil, concur with the analytical results. The position of the water table, isobars, isotachs, and streamlines are analyzed for various infiltration rates, sizes of the drains, boundary conditions imposed on them (empty drains are seepage face boundaries; full drains are constant piezometric head contours with various backpressures).

Kacimov A. - One of the best experts on this subject based on the ideXlab platform.

  • Moving Phreatic Surface in a porous slab: An analytical solution
    2020
    Co-Authors: Kacimov A., Yakimov N.
    Abstract:

    Transient Darcian flow in an inclined rigid fully saturated porous layer is studied. A Phreatic Surface of fixed shape driven by uniformly increasing (but generally not equal) water levels in the contiguous reservoirs moves upward with a constant velocity. In a system of coordinates travelling with the reservoir water level the real and imaginary parts of the complex potential (an analytic function) and complex coordinate are linearly interconnected along the boundary of the flow domain that allows implementing the Polubarinova-Kochina method. An explicit analytic equation of the free Surface is derived and shown to result in non-trivial configurations including the saturated zone overhanging dry areas

  • Phreatic Surface flow from a near-reservoir saturated tongue
    2020
    Co-Authors: Kacimov A., Obnosov Y., Perret J.
    Abstract:

    Steady and transient 2D Darcian flows in a saturated 'tongue' adjacent to a reservoir are studied analytically. First, a stable tongue receiving water from an inclined equipotential reservoir bed and losing moisture through a Phreatic Surface is considered. The hydraulic head is governed by the Laplace equation and the complex potential and complex coordinate are determined explicitly by the Polubarinova-Kochina method at an arbitrary bank slopes and evapotranspiration rates. In a particular case of a vertical slope, the tongue becomes a right-angled triangle extending into the layer for the same distance as the Dupuit-Forchheimer model predicts. Second, a saturated Dupuit-Forchheimer flow in the tongue is analyzed under the assumption of evaporation exponentially and linearly decreasing with the depth of a Phreatic Surface. The corresponding non-linear ordinary differential equation is integrated twice and predicts the length of the tongue as a function of the reservoir water level. Third, a transient regime is modelled by the Boussinesq equation with evaporation uniform in space, but varying cyclostationary with time. A straight-line water table translating upward-downward is found to be located always below the water table for steady regimes with an average evaporation. © 2004 Elsevier B.V. All rights reserved

  • Strip-focused Phreatic Surface flow driven by evaporation: Analytical solution by the Riesenkampf function
    2020
    Co-Authors: Kacimov A., Obnosov Y.
    Abstract:

    Steady free-Surface seepage in a homogeneous porous aquifer is studied by a conformal mapping of the inversed hodograph (angle) onto the domain in the Riesenkampf plane (slanted-face half-strip or trapezium). Seepage from the water table is caused by evaporation uniformly distributed with a horizontal coordinate. This distributed sink forms a regional trough on the Phreatic Surface with groundwater moving from the flanks to the trough center on the regional scale and from the water table to the soil Surface locally. The free Surfaces, streamlines of marked particles, travel times, and Darcian velocity are presented. © 2006 Elsevier Ltd. All rights reserved

  • How much floating light nonaqueous phase liquid can a Phreatic Surface sustain? Riesenkampf's scheme revisited
    2020
    Co-Authors: Kacimov A., Obnosov Y., Al-maktoumi A., Al-balushi M.
    Abstract:

    Steady, Darcian, one-phase, Phreatic Surface flow of groundwater into a horizontal well with a pancake lens of light nonaqueous phase liquid (LNAPL) accumulated in the water table trough is studied by the method of complex analysis. A sharp interface model assumes groundwater capped by two isobaric limbs (groundwater-vadose zone interfaces) of a free Surface with an in-between cambered segment of an immiscible LNAPL-water interface, along which pressure is hydrostatically increasing with the depth of the LNAPL "channel." The complex potential polygon is mapped onto an auxiliary half plane where the complex physical coordinate of the flow domain is represented in terms of singular integrals as a solution of the Keldysh-Sedov problem. The shapes of semi-infinite "wings" of the water table contacting the vadose zone gas and of a finite length LNAPL-groundwater interface are found from parametric equations that involve the sink strength and location with respect to the pancake Surface, the ordinate of the lowest trough point, and the volume of LNAPL accreted in the lens. Critical conditions, corresponding to the lens contour cusping toward the sink, are found. The Riesenkampf solution contains a free parameter, which is fixed by specifying either a point on the free Surface or the volume of the trough-intercepted LNAPL. Copyright 2011 by the American Geophysical Union

  • Steady Flow from an Array of SubSurface Emitters: Kornev’s Irrigation Technology and Kidder’s Free Boundary Problems Revisited
    2020
    Co-Authors: Kacimov A., Obnosov Y., Šimůnek J.
    Abstract:

    © 2017 Springer Science+Business Media B.V., part of Springer Nature Kornev’s (SubSurface irrigation, Selhozgiz, Moscow-Leningrad, 1935) subSurface irrigation with a periodic array of emitting porous pipes is analytically modeled as a steady potential Darcian flow from a line source generating a Phreatic Surface. The hodograph method is used. The complex potential strip is mapped onto the triangle of the inverted hodograph. An analogy with the Deemter (Theoretische en numerieke behandeling van ontwaterings-en infiltratie stromings problemen (in Dutch). Theoretical and numerical treatment of flow problems connected to drainage and irrigation. Ph.D. dissertation, Delft University of Technology, 1950) drainage problem and Kidder (J Appl Phys 27(8):867–869, 1956) free-Surface flow toward an array of oil wells underlain by a “wavy” oil–water interface is drawn. For a half-period of Kornev’s flow, the “wavy” Phreatic Surface has an inflection point. The “waviness” of the Phreatic Surface is controlled by the spacing between emitters, the strength of line sources, and the pipe pressure and radius. Numerical modeling with HYDRUS involved two factors which constrained the saturated–unsaturated flow: the positive pressure head at the outlet of the modeled domain and lateral no-flow boundaries, with a qualitative corroboration of analytical solutions for potential (fully saturated) and purely unsaturated flows. HYDRUS is also applied to a generalized Philip’s regime of an unsaturated flow past a subterranean hole, which is impermeable at its top and leaks at the bottom

Henk M. Haitjema - One of the best experts on this subject based on the ideXlab platform.

  • Approximate Analytic Solutions to 3D Unconfined Groundwater Flow Within Regional 2D Models
    Journal of Hydrology, 2000
    Co-Authors: K. Luther, Henk M. Haitjema
    Abstract:

    Abstract We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the Phreatic Surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the Phreatic Surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the Phreatic Surface.

  • An analytic element solution to unconfined flow near partially penetrating wells
    Journal of Hydrology, 1999
    Co-Authors: K. Luther, Henk M. Haitjema
    Abstract:

    An analytic element solution for steady-state unconfined flow near one or more partially penetrating wells in an ambient flow field has been developed. The Phreatic Surface is modeled using a three-dimensional version of the Zhukovski function. Boundary conditions at control points on the Phreatic Surface and seepage face at the well are maintained by use of distributed singularities outside the flow domain. The Phreatic Surface and seepage face for a single well is compared with two different numerical solutions and a laboratory experiment found in the literature. A sample case showing flow near two wells in an ambient flow field is presented.

A R Kacimov - One of the best experts on this subject based on the ideXlab platform.

  • infiltration induced Phreatic Surface flow to periodic drains vedernikov engelund vasil ev s legacy revisited
    Applied Mathematical Modelling, 2021
    Co-Authors: A R Kacimov, Yu. V. Obnosov
    Abstract:

    Abstract An explicit analytical solution is obtained to an old problem of a potential steady-state 2-D saturated Darcian flow in a homogeneous isotropic soil towards systematic drains modeled as line sinks (submerged drains under an overhanging of a Phreatic Surface), placed on a horizontal impervious substratum, with a constant-rate infiltration from the vadose zone. The corresponding boundary-value problem brings about a quarter-plane with a circular cut. A mathematical clue to solving the Hilbert problem for a two-dimensional holomorphic vector-function is found by engaging a hexagon, which has been earlier used in analytical solution to the problem of Phreatic flow towards Zhukovsky’s drains (slits) on a horizontal bedrock. A hodograph domain is mapped on this hexagon, which is mapped onto a reference plane where derivatives of two holomorphic functions are interrelated via a Polubarinova-Kochina type analysis. HYDRUS2D numerical simulations, based on solution of initial and boundary value problems to the Richards equation involving capillarity of the soil, concur with the analytical results. The position of the water table, isobars, isotachs, and streamlines are analyzed for various infiltration rates, sizes of the drains, boundary conditions imposed on them (empty drains are seepage face boundaries; full drains are constant piezometric head contours with various backpressures).

  • Steady Flow from an Array of SubSurface Emitters: Kornev’s Irrigation Technology and Kidder’s Free Boundary Problems Revisited
    Transport in Porous Media, 2018
    Co-Authors: A R Kacimov, Yu. V. Obnosov, J. Šimůnek
    Abstract:

    Kornev’s (SubSurface irrigation, Selhozgiz, Moscow-Leningrad, 1935 ) subSurface irrigation with a periodic array of emitting porous pipes is analytically modeled as a steady potential Darcian flow from a line source generating a Phreatic Surface. The hodograph method is used. The complex potential strip is mapped onto the triangle of the inverted hodograph. An analogy with the Deemter (Theoretische en numerieke behandeling van ontwaterings-en infiltratie stromings problemen (in Dutch). Theoretical and numerical treatment of flow problems connected to drainage and irrigation. Ph.D. dissertation, Delft University of Technology, 1950 ) drainage problem and Kidder (J Appl Phys 27(8):867–869, 1956 ) free-Surface flow toward an array of oil wells underlain by a “wavy” oil–water interface is drawn. For a half-period of Kornev’s flow, the “wavy” Phreatic Surface has an inflection point. The “waviness” of the Phreatic Surface is controlled by the spacing between emitters, the strength of line sources, and the pipe pressure and radius. Numerical modeling with HYDRUS involved two factors which constrained the saturated–unsaturated flow: the positive pressure head at the outlet of the modeled domain and lateral no-flow boundaries, with a qualitative corroboration of analytical solutions for potential (fully saturated) and purely unsaturated flows. HYDRUS is also applied to a generalized Philip’s regime of an unsaturated flow past a subterranean hole, which is impermeable at its top and leaks at the bottom.