Behavior of a semi-infinite ice cover under periodic dynamic impact

Oscillations of a semi-infinite ice cover in an ideal incompressible liquid of finite depth under local time-periodic axisymmetric load are considered. The ice cover is simulated by a thin elastic plate of constant thickness. An analytical solution of the problem is obtained using the Wiener–Hopf method. The asymptotic behavior of the amplitudes of oscillations of the plate and the liquid in the far field is studied. It is shown that the propagation of waves in the far field is uneven: in some directions, the waves propagate with a significantly greater amplitude.     

Surface wave diffraction at a crack in sheet ice

The time-periodic motions of a liquid layer of finite depth beneath an ice sheet with a straight infinite crack having a periodic dependence on the horizontal coordinate in the direction of the crack are considered. The ice sheet is simulated by a thin elastic plate. It is assumed that the thickness of the plate changes abruptly across the crack. The problems of plane-wave diffraction at a crack, plane-wave diffraction atN cracks in a uniform ice sheet, and plane-wave reflection from a rigid wall are solved. The effect of the pre-existing state of stress of the ice sheet on the properties of the reflected waves is investigated. The condition of nontransmission of fix-frequency waves beneath the edge of the ice is obtained.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 93–102, March–April, 1993.     

Instability of Waveguides in a Liquid with Surface Effects

Long surface capillary-gravity waves and waves beneath an elastic plate simulating an ice sheet are considered for a liquid of finite depth. These waves are described by a generalized Kadomtsev-Petviashvili equation containing higher (as compared with the ordinary Kadomtsev-Petviashvili equation) space derivatives. The generalized Kadomtsev-Petviashvili equation has waveguide solutions (waveguides) corresponding to traveling waves which are periodic in the direction of propagation and localized in the transverse direction. These waves result from the instability of uniform (carrier) periodic waves with respect to transverse perturbations. The stability of the waveguides with respect to longitudinal longwave perturbations is studied. The behavior of these perturbations depends on the wavenumber of the carrier periodic wave. Three intervals of wavenumbers corresponding to all the possible types of governing equations are considered.     

Dynamic problem for a two-layer medium with a vibrational source at the boundary interface

The present study is concerned with an analysis of gravitational and acoustic waves which are excited by a vibrational source deeply placed in a liquid covered by ice. An analysis of the rigidity characteristics of ice modeled by an elastic layer or by a Kirchhoff plate is done by factorization of the solution to the integral equation equivalent to an initially combined boundary value problem. The uncombined boundary condition is used to solve problems for unrestricted ice fields in [1–3], whereas combined conditions with vibrational sources positioned at the boundary of the medium are used in [4].Translated from Zhurnal Prikladnoi Mekhaniki, No. 3, pp. 125–129, May–June, 1986.     

Theory of two-dimensional nonlinear waves in liquid covered by ice

The aim is to develop a method of Hamiltonian formalism for the waves in the liquid beneath an ice sheet and on that basis to construct a systematic nonlinear theory. Attention is concentrated on the investigation of the essentially two-dimensional effects whose properties depend to a large extent on the stresses in the ice.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 125–133, July–August, 1991.     

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.     

Interaction of surface and flexural-gravity waves in ice cover with a vertical wall

The problem of the interaction of surface and flexural-gravity waves with a vertical barrier is solved in a two-dimensional formulation. It is assumed that the fluid is ideal and incompressible, has infinite depth, and is partially covered with ice. The ice cover is modeled by an elastic plate of constant thickness. The eigenfrequencies and eigenmodes of oscillation of the floating elastic ice plate, the deflection and deformation of ice, and the forces acting on the wall are determined.     

Weak Solutions to a Nonlinear Variational Wave Equation

 We establish the global existence of weak solutions to the Cauchy problem for a nonlinear variational wave equation, where the wave speed is a given monotone function of the wave amplitude. The equation arises in modeling wave motions of nematic liquid crystals, long waves on a dipole chain, and a few other fields. We use the Young-measure method in the setting of L ^p spaces. We overcome the difficulty that oscillations get amplified by the growth terms of the equation. (Accepted July 9, 2002) Published online December 3, 2002 Dedicated to Tony Zhang on his seventieth birthday Communicated by C. M. Dafermos     

Melting heat transfer along a horizontal heated tube immersed in a fluidized liquid ice bed

An experimental study was performed to determine the melting heat transfer characteristics along a horizontal heated circular tube immersed in a solid-air-liquid three-phase fluidized liquid ice bed. A mixture of fine ice particles and ethylene glycol acqueous solution was adopted as the liquid ice for the test. Measurements were carried out for a range of parameters such as airflow rate, heated tube diameter, and initial concentration of acqueous binary solution. It was found that the heat transfer coefficient for the fluidized liquid ice bed might be more than 20 times as large as that for the fixed liquid ice bed.     

Plane Problem of Vibrations of an Elastic Floating Plate under Periodic External Loading

The Wiener–Hopf technique is used to construct an analytical solution of the problem of vibrations of a semiinfinite elastic floating plate under periodic external loading. The solution is obtained in explicit form ignoring draft. The dependences of the amplitudes of surface waves and iceplate deflection on the loading distribution and frequency, ice thickness, and liquid depth are studied numerically. It is established that for some types of acting load, no waves propagate in the plate and liquid and the plate vibrations are standing waves localized near the loading region. An example of such vibrations is given and a condition for the occurrence of localized vibrations is found.     

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.     

海冰与波流耦合动力学的研究进展

随着全球气候变暖,北极活动频次的逐渐增加,海冰与波流的耦合作用成为了国内外的热点研究问题. 海冰的存在会改变波浪的传播特性和色散关系,也会改变海流运动的边界条件,使得海流在冰面下边界处可能产生漩涡脱落等现象;而海冰在波浪、海流等动力作用下,也会不断发生生消、断裂、重叠和堆积等动力学行为.海冰与波流耦合动力学中存在几大难点问题:一是海冰模型的构建,需要针对海冰类型和性质的不同,考虑不同区域的海冰分布情况建立合适的海冰模型.二是冰水之间的耦合问题,海冰边界影响着冰水之间的动量和能量交换,对于冰盖、浮冰等不同类型海冰,需分别处理边界问题;冰水耦合引起的海冰破坏,其破坏模式也是多样的.三是波流联合场的构建,目前尚无较好的方法构建波流联合场,导致海冰与波流联合场作用的相关研究仍极其匮乏.因此,本文针对海冰与波流相互作用问题,回顾和讨论国内外对海冰与波浪、海冰与海流及海冰与波流相互作用的研究现状和技术难点,展望了未来可以进一步深入研究的问题,提出了初步的思路以供参考.      

Acoustic emission from interaction of a vortex ring with a sphere

Acoustic waves emitted by a vortex ring interacting with a fixed solid sphere are studied experimentally and theoretically. The experiments are carried out for two kindsof vortex-sphere arrangement: (A) a vortex ring passes over the sphere, and (B) a vortex ring passes by the sphere. The vortex motion is examined optically by means of a photosensor system, and the pressure signals of the emitted wave are detected by 1/2-inch microphones in the far field. In case A, the measured diameter of the vortex ring after passing the sphere increases from its initial diameter. The observed acoustic wave is dominated mainly by a dipole emission, and some contribution from a quadrupole radiation is present. In case B, the emitted wave is characterized by a rotating dipole emission in which the dipole axis rotates as the vortex position changes relative to the sphere.     

Swell wave propagation in an inhomogeneous ice sheet

The propagation of surface waves beneath a periodically inhomogeneous ice sheet is considered. Areas of broken ice and hummock ridges are considered as irregularities. It is shown that waves with frequencies corresponding to wind and swell waves are strongly scattered by the irregularities and are damped exponentially as they propagate beneath the ice.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 162–169, September–October, 1996.     

Hydrodynamic loads acting on an oscillating cylinder submerged in a stratified fluid with ice cover

The two-dimensional problem of steady oscillations of a horizontal cylinder submerged in a linearly stratified fluid layer whose upper boundary is ice cover is considered in a linear treatment using the Boussinesq approximation. The method of mass sources distributed along the body contour is used for the internal wave generation regime, and the integral equation for the disturbed pressure in the fluid is used for the regime of no internal waves. The hydrodynamic load acting on the body was calculated as a function of the oscillation frequency for the case of a continuous ice cover and for special cases (broken ice, free surface, and rigid lid).     

Two-dimensional problem for internal waves generated by moving singular sources

When bodies move in a liquid with inhomogeneous density in a gravitational field waves are excited even at low velocities and in the absence of boundaries. They are the so-called internal waves (buoyancy waves), which play an important part in geophysical processes in the ocean and the atmosphere [1–4]. A method based on the replacement of the bodies by systems of point sources is now commonly used to calculate the fields of internal waves generated by moving bodies. However, even so the problems of the generation of waves by a point source and dipole are usually solved approximately or numerically [5–11]. In the present paper, we obtain exact results on the spectral distribution of the emitted waves and the total radiation energy per unit time for some of the simplest sources in the two-dimensional case for an incompressible fluid with exponential density stratification. The wave resistance is obtained simply by dividing the energy loss per unit time by the velocity of the source. In the final section, some results for the three-dimensional case are briefly formulated for comparison.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 77–83, March–April, 1981.     

Unsteady gravity-elastic and gravity-capillary ship waves

The development of three-dimensional waves generated by a region of pressures moving uniformly and rectilinearly over the surface of a thin elastic isotropic plate covering an ideal fluid layer of finite depth is investigated. The pressures act starting at a certain instant. A qualitative similarity between the waves occurring and gravity-capillary waves is noted. The calculations are made for an ice cover. This model problem permits examining a number of properties of the oscillations of the ice cover occurring when hauling freight over ice roads, landing and takeoff of aircraft from ice fields, etc. [1]. The development of ship waves in a fluid of finite depth in the absence of a floating plate was investigated in [2, 3] and gravity-capillary waves were studied in [4–6]. Certain properties of steady three-dimensional waves occurring during movement of a load over the surface of a floating elastic plate were established in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–32, September–October, 1978.     

Experiments on melting of a vertical ice layer immersed in immiscible liquid

Experiments on the melting of a vertical ice layer immersed in immiscible liquid yielded quantitative results both for the timewise evolution of the melting front and the heat transfer. Vegetable oil, which was contained in a rectangular vessel, was adopted as a testing liquid. A bubble-free ice block stuck on a cooled wall was installed vertically in the vessel. The experiments were carried out for the immiscible liquid temperatures from 7.6 to 30.0 ^°C, while for the cooled wall temperatures from 0 to ?11.5 ^°C. The flow structure of the liquid and the melting front were extensively observed and recorded photographically. It was found that the heat transfer and the rate of melting are significantly affected by a couple of fluid motions of both the water melt induced by melting of ice and the immiscible liquid based on free convection.     

Motion of an External Load over a Semi-Infinite Ice Sheet in the Subcritical Regime

The three-dimensional problem of steady-state forced vibrations of fluid and semiinfinite ice sheet under the action of a local external load traveling along the rectilinear sheet edge at a constant velocity is considered. Two cases are analyzed. In the first case the fluid surface outside the ice sheet is free and in the second the fluid is confined by a rigid vertical wall and the ice sheet edge adjacent to the wall can be both clamped and free. The ice sheet is simulated by a thin elastic isotropic plate floating on the surface of fluid of finite depth. The load traveling velocity is assumed to be not higher than the minimum phase velocity of the flexural-gravity waves (subcritical regime). The solution to the linear problem is obtained by means of the integral Fourier transform and matching the expansions of the velocity potential in the vertical eigenfunctions. Examples of the numerical investigation of the ice sheet and fluid displacements are given.     

Gravitational and acoustic waves due to the motion of an oscillating thin plate beneath the surface of a heavy weakly-compressible fluid

The three-dimensional problem of the motion of a thin plate in an inviscid, heavy, weakly-compressible fluid is solved. The surface tension is disregarded. The plate moves rectilinearly at a constant velocity under the surface of an infinite-depth fluid and oscillates at a given frequency. The fluctuating dipole potential is obtained from the Euler and continuity equations with account for the conditions on the free surface (linear theory of small waves) and the conditions at infinity. The density distribution function of the dipole layer is determined from the boundary conditions imposed on the plate surface. Formulas for calculating the far acoustic field are derived. The calculations for a square plate are carried out.