Plane waves in a heavy two-layer liquid excited by a cylinder moving at an angle to the horizontal

A solution of an initial-boundary-value problem for a system of integrodifferential equations which describes the plane waves excited in an initially stationary heavy two-layer ideal fluid by a cylinder moving at an angle to the horizontal is investigated. The homogeneous fluid fractions of different densities are assumed to be separated by an evolving fluid interface (horizontal plane, if the liquid is at rest). An approximate solution of two problems for the waves excited by a cylinder moving with a constant acceleration and an oscillating cylinder is constructed analytically. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–152, July–August, 1998.     

Waves excited by variable pressure on the free surface of a heavy liquid

An approximate solution of the initial and boundary value problem is constructed for a system of nonlinear integrodifferential equations describing the process of formation and evolution of axisymmetric waves excited on the unbounded free surface of an ideal liquid by pressure varying with time and in space in accordance with laws of a fairly general form. For a pressure force of limited power distributed over a fairly large area, formulas describing the free surface evolution on the semi-axist>0 (t is time) are obtained. Using the passage to the limit ast , the shape of the standing nonlinear wave excited by near-periodic pressure with a fairly wide frequency spectrum is found and its energy properties are studied.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 97–108, May–June, 1996.     

The acoustic field in a rigid cylindrical vessel excited by a sphere oscillating by a definite law

The problem on the interaction between a spherical body oscillating by a definite law and a rigid cylinder filled with an ideal compressible liquid is formulated. The geometrical center of the sphere is located on the cylinder axis. The solution is based on the possibility of representing the particular solutions of the Helmholtz equation in cylindrical coordinates in terms of particular solutions in spherical coordinates, and vice versa. As a result of satisfaction of the boundary conditions on the surfaces of the sphere and cylinder, an infinite system of linear algebraic equations is obtained to determine the coefficients of expansion of the potential of liquid velocities into a Fourier series in terms of Legendre polynomials. The use of the reduction technique for solving the infinite system obtained is substantiated. The hydrodynamic characteristics of the liquid filling the cylindrical cavity are determined and compared with the case of a sphere vibrating in an infinite liquid. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 88–97, June, 2000.     

The secondary flow induced around a sphere in an oscillating stream of elastico-viscous liquid

The present paper is devoted to the theoretical study of the secondary flow induced around a sphere in an oscillating stream of an elastico-viscous liquid. The boundary layer equations are derived following Wang's method and solved by the method of successive approximations. The effect of elasticity of the liquid is to produce a reverse flow in the region close to the surface of the sphere and to shift the entire flow pattern towards the main flow. The resistance on the surface of the sphere and the steady secondary inflow increase with the elasticity of the liquid.Nomenclature a radius of the sphere - b ^ik contravariant components of a tensor - e contravariant components of the rate of strain tensor - F() see (47) - G total nondimensional resistance on the surface of the sphere - g _ik covariant components of the metric tensor - f, g, h secondary flow components introduced in (34) - k ₀ measure of relaxation time minus retardation time (elastico-viscous parameter) - K =k ₀ ²/V ₀ ² , nondimensional parameter characterizing the elasticity of the liquid - n measure of the ratio of the boundary layer thickness and the oscillation amplitude - N, T defined in (44) - p arbitrary isotropic pressure - p _ik covariant components of the stress tensor - p ^ik contravariant components of the stress tensor associated with the change of shape of the material - R =V ₀ a/v, the Reynolds number - S =a/V ₀, the Strouhall number - r, , spherical polar coordinates - u, v, w r, , component of velocity - t time - V(, t) potential velocity distribution around the sphere - V ₀ characteristic velocity - u, v, t, y, P nondimensional quantities defined in (15) - reciprocal of s - density - defined in (32) - defined in (42) - ₀ limiting viscosity for very small changes in deformation velocity - complex conjugate of - oscillation frequency - = ₀/, the kinematic coefficient of viscosity - , defined in (52) - (, y) stream function defined in (45) - =(NT/2n)^1/2 y - /t convective time derivative (1) _ik      

Internal waves excited in a two-layer liquid by a moving region of reduced pressure

The excitation of two-dimensional wave motions at the interface of two liquids by a raoving region of reduced pressure has been studied theoretically and experimentally.Translated from Isvestiya Akadeiaii Nauk SSSR, Mekhanika Zhidkpsti i Gaza, No. 5, pp. 109–116, September–October, 1984.     

Nonlinear waves in a heavy two-layer liquid generated by an initial disturbance of the horizontal interface

Nonlinear waves in a heavy two-layer liquid generated by an initial disturbance of the horizontal interface are considered. The generalized velocity potential for certain kinds of flows with nonzero circulation (along a closed contour) and a relative parameter associated with the geometry of the initial disturbance of the interface are introduced. On this basis the integrodifferential equations of the problem are formulated and solved approximately for extended disturbances with a small ratio of the initial amplitude to a characteristic horizontal dimension.     

Drop in an oscillating liquid

At the present time there is a complete lack of studies devoted to the forced motion of a drop located in an oscillating liquid. However, this problem is of considerable interest. For example, it represents simulation of hydrodynamic processes occurring during the irradiation of drops of one liquid located in another liquid by longwave sound. The stationary flows occurring in this case may have a significant influence on the heat- and mass-transfer processes. In the present article we investigate the velocity field in the interior and exterior of a drop executing forced oscillatory motion as a result of its interaction with the ambient liquid. At a sufficiently large distance from the drop the ambient liquid oscillates in a specified way, where s/R ? 1 (s is the amplitude of displacement of the liquid particles, and R is the radius of the drop).     

Experimental study of the velocity field of parametrically excited waves in a two-layer liquid

The results of measuring the velocities of the particles of a two-layer liquid in standing parametrically excited waves are presented. The horizon on which the vertical harmonic components of the velocity are equal to zero is determined. It is established that the oscillatory motion of the particles is accompanied by a system of slow circulating flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 161–166, September–October, 1991.     

Radiation of waves by a sphere harmonically oscillating to-and-fro in a viscous medium

The theory of the radiation of sound by a sphere in an ideal medium is presented in detail in [1–3]. The emission of waves by a sphere oscillating to-and-fro in a viscous incompressible liquid is analyzed in [4, 5]. The present paper gives a precise solution to the problem of the radiation of sound by a sphere oscillating in a viscous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–106, September–October, 1970.     

Couple on a rotary oscillating sphere in a dusty gas

Rotary oscillations of a sphere about its vertical diameter in an infinite expanse of viscous, incompressible fluid with imbedded identical spherical particles are studied. The problem is solved by the method of separation of variables and explicit expressions for the velocity of fluid particles and the couple experienced by the sphere due to fluid stresses are obtained. The couple is expressed in terms of two parameters and graphs have been drawn to represent the variation in these parameters and some interesting conclusions are made.Nomenclature u ⁵ velocity of fluid particles - v ⁶ velocity of dust particles - P ⁵ pressure - ⁶ fluid density - t ⁹ time - m mass of a dust particle - N number density of dust particles - k ⁵ Stokes resistance coefficient - ³ viscosity - ⁶ kinematic viscosity - ⁷ particle relaxation time - ⁴ frequency of oscillation of the sphere - f ⁹ mass concentration of the dust particles     

Construction of the velocity potential of a semiinfinite liquid column excited by a spherical calotte oscillating inside a cylindrical cavity

A semiinfinite liquid column excited by a spherical calotte oscillating inside a rigid cylindrical cavity is considered. The solution of the Laplace equation is searched for under boundary conditions on spherical, cylindrical, and flat surfaces bounding the liquid. The possibility of decomposing a spherical harmonic function in terms of cylindrical harmonic functions and vice versa is considered. The potential constructed is used to evaluate the pressure and the velocity of the liquid. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 81–89, March, 2000.     

Waves induced by a submerged moving dipole in a two-layer fluid of finite depth

The waves induced by a moving dipole in a twofluid system are analytically and experimentally investigated.The velocity potential of a dipole moving horizontally in the lower layer of a two-layer fluid with finite depth is derived by superposing Green‘s functions of sources (or sinks). The far-field waves are studied by using the method of stationary phase. The effects of two resulting modes, i.e. the surfaceand internal-wave modes, on both the surface divergence field and the interfacial elevation are analyzed. A laboratory study on the internal waves generated by a moving sphere in a two-layer fluid is conducted in a towing tank under the same conditions as in the theoretical approach. The qualitative consistency between the present theory and the laboratory study is examined and confirmed.     

The unsteady motion of a sphere in an elastico-viscous liquid

Summary Consideration is given to the unsteady motion of a sphere moving under a constant force in elastico-viscous liquid, the sphere being initially at rest. The problem is solved by the familiarLaplace-transform method. It is shown that the presence of elasticity in the liquid increases the velocity of the sphere. This increase is very pronounced for small values of the time, but is not very significant for large values of the time. It is concluded that the time taken to reach the terminal velocity is unaffected by the presence of elasticity in the liquid.Formulae are given which may be of use to experimentalists who use the falling-ball method to determine the zero shear-rate viscosity.     

Mixed convection around a liquid sphere in an air stream

 A linearized finite-difference scheme has been used to investigate the mixed convection boundary-layer flow about a liquid sphere subjected to an air stream. For Prandtl number = 0.7, velocity and temperature profiles are obtained for a wide range of the other controlling parameters: Reynolds number, interior-to-exterior (liquid- to-air) viscosity ratio and Grashof number. Both aiding and opposing natural convections are considered in this study. The effect of the controlling parameters on engineering quantities such as the shear stress and the Nusselt number is also presented. Received on 27 September 2000 / Published online: 29 November 2001     

Self-consistent bunches of oscillating heavy particles in an accelerator

The possibility of the existence of self-consistent spheroidal bunches having a constant density which consists of heavy particles or bodies is demonstrated. In a projection onto the transverse plane the particles describe circles or ellipses, while along the spheroid axis the particles oscillate sinusoidally. It is possible for an infinite set of particle distributions to appear with respect to the half-axes of the transverse ellipses and with respect to the amplitudes of the longitudinal oscillations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 140–142, July–August, 1970.