Internal waves induced by moving periodic perturbations applied to the surface of a stratified fluid

Investigations of internal wave generation by moving perturbations are of considerable interest for submarine navigation, hydroacoustics, ocean seismology, etc. The main results for perturbations of constant intensity were published in [1–3]. In the present paper we continue the investigations and study moving perturbations whose intensity varies periodically in time. The perturbations are approximated by surface shape variations or an external pressure on the surface. The vertical displacement of the water particles relative to the equilibrium position is obtained in the form of a series in terms of waves modes for a given density stratification. A calculation algorithm and a program for computing each of the wave modes have been compiled. The boundaries of the wave regions and constant-phase lines are constructed and the displacement amplitudes are calculated. It is shown that there are resonance relations between the oscillation frequency and the perturbation velocity for which the displacement for a given mode becomes infinite (in the linear theory). Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 130–135, July–August, 1994.     

Axisymmetric equilibrium shapes of a fluid in a toroidal vessel under conditions of weightlessness

The axisymmetric problem of the evolution of the free surface of a fluid during the filling of a toroidal vessel under conditions of weightlessness is considered. Despite its interest [1, 2], this topical problem of the hydrodynamics of weightlessness remains unsolved for lack of an effective method of solution. This paper employs the iteration-difference approach proposed in [3–5] for calculating simply and doubly connected axisymmetric equilibrium figures. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 154–156, November–December, 1986.     

Steady-state conditions of a nonisothermal film with a heat-insulated free boundary

The equilibrium shapes of a nonisothermal liquid film with a heat-insulated free surface for large Marangoni numbers are investigated in the long-wave approximation using a combination of analytical and numerical methods. It is proved that the two-dimensional problem of the equilibrium of a strip-shaped film has a steady-state solution for an arbitrary large temperature gradient on the boundaries of the strip. An increase in this gradient leads to an abrupt thinning of the film near the heated boundary, which can result in instability and rupture of the film. In the equilibrium problem for a film fixed on a circular contour, the nonuniform distribution of the heat flux on the contour was found to have a significant influence on the free-surface shape. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 59–73, July–August, 2008.     

Stress state of a transversely isotropic magnetoelectroelastic body with a plane crack under antisymmetric loads

The static equilibrium of a transversely isotropic magnetoelectroelastic body with a plane crack of arbitrary shape in the isotropy plane under antisymmetric mechanical loading is studied. The relationships between the stress intensity factors (SIFs) for an infinite magnetoelectroelastic body and the SIFs for a purely elastic body with the same crack and under the same antisymmetric loading are established. This enables the SIFs for a magnetoelectroelastic body to be found directly from the analogous problem of elasticity. As an example of using this result, the SIFs for penny-shaped, elliptic, and parabolic cracks in a magnetoelectroelastic body under antisymmetric mechanical loading are found Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 37–51, October 2008.     

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech 26(4):470–475 2005a, IMA J Appl Math, pp 1–8, 2005). The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and ramp-type heating). The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters.     

Heat transfer to blunt-edged swept wings at angle of attack in hypersonic flow

An approximate analytic solution is obtained for the relative heat fluxes on the lateral surface of swept wings of infinite span in a hypersonic viscous gas flow at angles of attack and yaw. The accuracy of the relations obtained is estimated on the basis of a comparison with numerical solutions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 170–179, July–August, 1994.     

Determination of the shape of the shocks ahead of a transverse jet injected into a supersonic flow

The three-dimensional shape of the shock wave formed ahead of a sonic jet flowing out into a supersonic flow through the surface of a sharp cone is determined. The shape of the wave in the longitudinal and transverse cross-sections of the model is constructed using schlieren photographs taken for various angles of rotation and freestream Mach numbers M=1.75–3. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 41–44, March–April, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 95-01-00709a).     

On the stress state of a piezoceramic body with a flat crack under symmetric loads

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005.     

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.     

Effect of scattering of elastic harmonic waves in the far zone by a spatial crack

A three-dimensional wave field formed owing to diffraction of low-frequency waves on a curved crack in an infinite elastic solid at a large distance from the defect is studied by the method of boundary integral equations. Direction diagrams of the scattered field versus the excentricity of the crack surface and wavenumber are obtained for different directions of incidence of planar longitudinal waves onto a gently sloping spheroidal crack. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 115–123, July–August, 2006.     

Scattering of nonspherical particles rebounding from a smooth and a rough surface in a high-speed gas-particle flow

Scattering indicatrices of nonspherical particles rebounding from a smooth and a rough surface are obtained by direct Monte Carlo simulations. Particles shaped as ellipsoids of revolution, rectangular prisms, and prisms with truncated vertices are considered. Surface roughness is defined as a two-dimensional profile whose scattering characteristics are close to those of real roughness induced by abrasive erosion of the surface in a high-speed gas-particle flow. Impact interaction of an individual particle with the surface is considered in a three-dimensional formulation. The scattering indicatrices of reflected particles are found to depend substantially on the particle shape in the case of rebound from a smooth surface and to be almost independent of the particle shape if the particles rebound from a rough surface. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 79–88, March–April, 2008.     

Equilibrium self-polarization of clay

A condition of equilibrium between charged clay particle surfaces and the solution contained in the pore space of the rock is derived using electrical double layer theory. This condition is the relation linking the cation concentration in the middle surface of the pores with the exchange capacity of the clay, the total ion charges, and the specific surface area of the particles. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 96–103, September–October, 2007.     

Two-dimensional problem of periodic loading of an elastic plate floating on the surface of an infinitely deep fluid

The action of external periodic pressure on an elastic plate floating on the surface of a fluid assumed to be ideal and incompressible is examined by the method of normal modes in the linear formulation. The behavior of the matrix of coefficients of the hydrodynamic load on the plate is considered in detail for different frequencies. The behavior of the plate under localized periodic loading is compared for the cases of a heavy fluid with a finite or infinite depth and for a weightless infinite-depth fluid. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 61–72, May–June, 2005.     

Transitive flows on orientable surfaces

We consider smooth vector fields on closed orientable surfaces with a fixed collection of singularities and a finite number of separatrices none of which connects the equilibrium states. We prove that, on an orientable surface of arbitrary genus g ≥ 2, there exists a vector field with an admissible set of singularities (degenerate saddles) whose trajectory is everywhere dense on the surface. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 178–186, April–June, 2006.     

Equilibrium thermodynamics of pseudoelasticity and quasiplasticity

Motivated by recent experimental results by Glasauer [1], a thermodynamic theory of shape memory alloys is proposed, which includes not only the high temperature – pseudoelastic – behavior but also the low temperature range of quasiplasticity. Due to the occurance of three different phases – austenite and two martensitic variants – several cases of two-phase equilibria and a three-phase equilibrium have to be taken into account. Their relevance is determined by minimization of the total free energy and subsequently illustrated by the construction of phase charts. A special point of interest is the influence of interfacial energy effects on these phase charts, resulting in phenomena like, for example, the apparent violation of Gibbs' phase rule. Furthermore, the role of interfacial energies in the hysteretic load-displacement behavior is discussed in the light of the additional quasiplastic case. Received June 12, 1996     

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.     

Rayleigh-Benard problem for an anomalous fluid

The stability of the state of rest of a heated infinite horizontal layer of a viscous heat-conducting fluid (the Rayleigh-Benard problem) is considered. The equation of state for the fluid takes into account the nonmonotonic temperature and pressure dependence of water density. Instability of the mechanical equilibrium with respect to small monotonic perturbations is studied. The effect of the problem parameters on the Rayleigh numbers and their corresponding critical motions is investigated numerically using linear theory. Numerical investigation of the spectral problem is based on the Godunov-Abramov orthogonalization method. The calculation results are compared with the well-known results for the limiting case where the density is considered a quadratic function of temperature and does not depend on pressure. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 27–38, March–April, 2007.     

Unsteady behavior of an elastic articulated beam floating on shallow water

The unsteady behavior of an elastic beam composed of hinged homogeneous sections, which freely floats on the surface of an ideal incompressible fluid, is studied within the framework of the linear shallow water theory. The unsteady behavior of the beam is due to incidence of a localized surface wave or initial deformation. Beam deflection is sought in the form of an expansion with respect to eigenfunctions of oscillations in vacuum with time-dependent amplitudes. The problem is reduced to solving an infinite system of ordinary differential equations for unknown amplitudes. The beam behavior with different actions of the medium and hinge positions is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 54–65, July–August, 2009.     

Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape

We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization, provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency conditions.      

Oscillating thermocapillary convection regimes driven by a point heat source

The stability of an axisymmetric thermocapillary flow driven by a point heat source located in the neighborhood of the free surface of a fluid filling a deep tank is investigated theoretically and experimentally. It is shown that for certain values of the depth and power of the heat source thermocapillary convection becomes unstable with respect to oscillating perturbations of the surface shape. Perm’, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 92–103, March–April, 2000.