Influence of broken ice on the propagation of surface waves over a bottom shelf

The influence of drifting broken ice on the propagation of small-amplitude plane surface waves from an infinitely deep region of a basin to a region of finite depth over a bottom shelf is analyzed on the basis of wave source theory. The variations in the characteristics of the reflected and transmitted waves and the fluid surface perturbation profile due to the drifting ice are estimated as functions of the distance from the shelf. Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 106–115, November–December, 1998.     

Numerical simulation of the interaction of gravity waves with elastic ice floes

The self-consistent motion of a fluid and elastically oscillating plates partially covering the fluid is simulated numerically in the linear approximation. The problem is reduced to the simultaneous solution of the Laplace equation for the fluid and the equation of elastic plate oscillations for the ice. The numerical and analytical solutions, the latter obtained from an integral equation containing the Green’s function, are compared. To solve the problem numerically, the boundary element method for the Laplace equation and the finite element method for the equation describing the elastic plate are proposed. The coefficients of transmission and reflection of surface gravity waves from the floating plates are calculated. It is shown that the solution may be quasi-periodic with characteristics determined by the initial values of the wave and ice-floe parameters. The ice floes may exert a filtering effect on the surface wave spectrum, essentially reducing its most reflectable components. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 123–131, May–June, 2000.     

Derivation of a Darcy’s Law for a Porous Medium Composed of Two Solid Phases Saturated by a Single- Phase Fluid: A Homogenization Approach

The objective of this article is to derive a macroscopic Darcy’s law for a fluid-saturated moving porous medium whose matrix is composed of two solid phases which are not in direct contact with each other (weakly coupled solid phases). An example of this composite medium is the case of a solid matrix, unfrozen water, and an ice matrix within the pore space. The macroscopic equations for this type of saturated porous material are obtained using two-space homogenization techniques from microscopic periodic structures. The pore size is assumed to be small compared to the macroscopic scale under consideration. At the microscopic scale the two weakly coupled solids are described by the linear elastic equations, and the fluid by the linearized Navier–Stokes equations with appropriate boundary conditions at the solid–fluid interfaces. The derived Darcy’s law contains three permeability tensors whose properties are analyzed. Also, a formal relation with a previous macroscopic fluid flow equation obtained using a phenomenological approach is given. Moreover, a constructive proof of the existence of the three permeability tensors allows for their explicit computation employing finite elements or analogous numerical procedures.     

Effect of the viscosity properties of ICE on the deflection of an ICE sheet subjected to a moving load

Steady-state rectilinear motion of a load on an ice sheet modeled by a viscoelastic plate is considered. The viscoelastic properties of ice are described using the linear Maxwell and Kelvin-Voigt models and a generalized Maxwell-Kelvin model. Calculated vertical displacements and strains of the ice plate are compared with available experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 147–157, May–June, 2009.     

Numerical solution of the problem of an ice sheet under a moving load

A method for analyzing the bending of an ice sheet subjected to a moving load is proposed. The problem is solved in a dynamic formulation. The algorithm of solution is based on the finiteelement method and the finite-difference method. The method proposed allows one to determine the stress-strain state of an ice sheet for any law of motion of a load over ice. Two versions of initial conditions are considered. Examples of calculations are given. Komsomol’sk-on-Amur State Technical University, Komsomol’sk-on-Amur 681013. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 243–248, July–August, 1999.     

Numerical solution of the problem of motion of a load on a cracked ice sheet

A mathematical model is constructed for the motion of a load on a cracked ice sheet. Examples of calculation of ice deflections are given, and the calculation results are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 151–156, May–June, 2008.     

Wave resistance of an air-cushion vehicle in unsteady motion over an ice sheet

Unsteady rectilinear motion of an air-cushion vehicle over an ice sheet at various speeds is considered. Ice is modeled by a viscoelastic ice plate. The effects of the basin depth, the thickness and relaxation time of ice, vehicle length, acceleration, deceleration, and speed of uniform motion on the wave resistance of the vehicle are analyzed. Maneuvering methods for increasing or lowering the wave resistance of the vehicle are proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 89–99, January–February, 2008.     

Stress-strain state of an ice sheet subjected to a moving load under shallow-water conditions

The following two classes of problems of determining the stress-strain state of an ice sheet under a moving load are considered: determination of the resonant velocity for a load moving over a continuous ice field and calculation of the deflections of an ice field with a bounded ice-free zone subjected to a moving load. The problems are solved in a dynamic formulation. The algorithm of solution is based on the finite-clement method and finite-difference methods. Examples of calculations are given. Komsomol'sk-on-Amur State Technical University, Komsomol'sk-on-Amur 681013. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol 41, No. 4, pp. 206–210, July–August, 2000.     

Hydraulic jump structures in the presence of an ice sheet

Jumps of the bore type arising in a fluid layer with an ice sheet are investigated. These jump structures are considered for a determining mechanism in the form of dispersion due to the presence of an ice sheet. For this purpose a generalized Korteweg-de Vires equation [1] is used. The structure of these jumps consists of a wave zone that expand with time. On the boundary of the wave zone there are transitions between uniform and periodic states which can be locally considered as jumps. Among them are jumps which can be regarded as steady in the coordinate system moving with the boundary of the wave zone. These are jumps between a sequence of solitons and a uniform state (jumps of soliton type) on the boundary of the wave zone and jumps between periodic and uniform states (jumps with radiation). In addition, there are jumps which are unsteady even from the standpoint of a local analysis. In order to investigate the effect of dissipation processes on the jumps considered a system of generalized Boussinesq equations is derived with allowance for bottom slope and bottom and ice friction. The jump damping process is investigated numerically. This system of equations also makes it possible to investigate undamped jumps of the floodwater wave type. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 139–146. July–August, 2000.     

Evolution of the ice breaking process

The spatial problem of the stress-strain state of an ice sheet of finite thickness broken by a patented method is solved using the theory of small elastic strains and a proven numerical method. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 114–119, January–February, 2008.     

Mathematical Modeling for One New Method of Breaking Ice Cover

The spatial problem of determining the stress-strain state of an ice plate of finite thickness broken by a patented method is solved using the theory of small elastoplastic strains and a proven numerical method. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 139–146, March–April, 2006.     

Motion of a system of seismic sources over ice on a body of water under the action of a pulse

The vertical motion of a system of two identical seismic sources and a spring truck tractor on ice under the action of a shock pulse from the seismic sources is studied to estimate the strength of ice. It is shown that during the pulse time, the interaction of the masses of the seismic sources and the tractor is small and the compressibility effect of the liquid can be ignored. Calculations show that for the seismic sources, the dynamic load far exceeds the static load and for the tractor, the static load is maximal. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 147–155, March–April, 2007.     

Pressure growth dynamics during freezing of a closed volume of water with dissolved gases

A model for the freezing of a closed volume of water with dissolved gases is proposed and studied numerically. It is shown that gas release during ice formation leads to a considerable time delay in the time of a sudden pressure increase. In the freezing process, the pressure depends not only on the volume of ice formed but also on the freezing rate, which is determined by the cooling rate and the geometry and dimensions of the freezing volume. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 85–92, November–December, 2006.     

Effect of broken ice on the wave resistance of an amphibian air-cushion vehicle in nonstationary motion

The uniformly accelerated motion of an amphibian air-cushion vehicle on the surface of a basin covered by finely small ice floes is considered. Institute of Machine Science and Metallurgy, Far-Eastern Division, Russian Academy of Sciences, Komsomol'sk-on-Amur 681005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 48–53, November–December, 1999.     

Numerical solution of the problem of the effect of a shock pulse on an ice sheet

A mathematical formulation of the problem is given. A method is proposed to determine the initial velocities of points of an ice sheet subjected to a point shock pulse. An example of calculation of ice-sheet deflections is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 152–159, March–April, 2008.     

Nonlinear parametric vibrations of orthotropic cylindrical shells interacting with a pulsating fluid flow

The paper addresses the dynamic interaction of an orthotropic cylindrical shell with the fluid flowing inside. Its velocity has a constant component and low-amplitude pulsations. A method to calculate the characteristics of the parametric vibrations of the shell when the velocity of the fluid is close to critical is proposed. The amplitude–frequency characteristics of the shell–fluid system at fundamental parametric resonance are determined     

Convective mass transfer across fluid interfaces in straight angular pores

Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated. This situation is relevant to a variety of mass transport process in porous media, including the fate of residual non-aqueous phase liquid ganglia and gas bubbles. The model incorporates the essential physics of capillarity and solute mass transfer by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid–fluid contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface shear (‘perfect-slip’) and infinite surface shear (‘no-slip’) at the fluid–fluid interface are considered. The governing equations for laminar flow within the corner filament and convective diffusion to or from the fluid–fluid interface are solved using finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance of corner filaments against recent numerical solutions by Patzek and Kristensen (J. Colloid Interface Sci 236, 305–317 2001). Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical equations appropriate for implementation in pore network models. Finally, a previously published “2D-slit” approximation to the problem at hand is checked and found to be in considerable error.     

Explicit Rate–Time Solutions for Modeling Matrix–Fracture Flow of Single Phase Gas in Dual-Porosity Media

One of the widely used methods for modeling matrix–fracture fluid exchange in naturally fractured reservoirs is dual porosity approach. In this type of modeling, matrix blocks are regarded as sources/sinks in the fracture network medium. The rate of fluid transfer from matrix blocks into fracture medium may be modeled using shape factor concept (Warren and Root, SPEJ 3:245–255, 1963); or the rate–time solution is directly derived for the specific matrix geometry (de Swaan, SPEJ 16:117–122, 1976). Numerous works have been conducted to study matrix–fracture fluid exchange for slightly compressible fluids (e.g. oil). However, little attention has been taken to systems containing gas (compressible fluid). The objective of this work is to develop explicit rate–time solutions for matrix–fracture fluid transfer in systems containing single phase gas. For this purpose, the governing equation describing flow of gas from matrix block into fracture system is linearized using pseudopressure and pseudotime functions. Then, the governing equation is solved under specific boundary conditions to obtain an implicit relation between rate and time. Since rate calculations using such an implicit relation need iterations, which may be computationally inconvenient, an explicit rate–time relation is developed with the aid of material balance equation and several specific assumptions. Also, expressions are derived for average pseudopressure in matrix block. Furthermore, simplified solutions (originated from the complex general solutions) are introduced applicable in infinite and finite acting flow periods in matrix. Based on the derived solutions, expressions are developed for shape factor. An important observation is that the shape factor for gas systems is the same as that of oil bearing matrix blocks. Subsequently, a multiplier is introduced which relates rate to matrix pressure instead of matrix pseudopressure. Finally, the introduced equations are verified using a numerical simulator.     

Nanoscale Poiseuille flow and effects of modified Lennard–Jones potential function

Numerical simulation of Poiseuille flow of liquid Argon in a nanochannel using the non-equilibrium molecular dynamics simulation (NEMD) is performed. The nanochannel is a three-dimensional rectangular prism geometry where the concerned numbers of Argon atoms are 2,700, 2,550 and 2,400 at 102, 108 and 120 K. Poiseuille flow is simulated by embedding the fluid particles in a uniform force field. An external driving force, ranging from 1 to 11 PN (Pico Newton), is applied along the flow direction to inlet fluid particles during the simulation. To obtain a more uniform temperature distribution across the channel, local thermostating near the wall are used. Also, the effect of other mixing rules (Lorenthz–Berthelot and Waldman–Kugler rules) on the interface structure are examined by comparing the density profiles near the liquid/solid interfaces for wall temperatures 108 and 133 K for an external force of 7 PN. Using Kong and Waldman–Kugler rules, the molecules near the solid walls were more randomly distributed compared to Lorenthz–Berthelot rule. These mean that the attraction between solid–fluid atoms was weakened by using Kong rule and Waldman–Kugler rule rather than the Lorenthz–Berthelot rule. Also, results show that the mean axial velocity has symmetrical distribution near the channel centerline and an increase in external driving force can increase maximum and average velocity values of fluid. Furthermore, the slip length and slip velocity are functions of the driving forces and they show an arising trend with an increase in inlet driving force and no slip boundary condition is satisfied at very low external force (<1 PN).