Wave-guide properties of an underwater ridge

Fluid Dynamics - In 1957, M. A. Lavrent'ev suggested that an elevation of the bottom, which we shall call an underwater ridge, could act as a wave guide for waves on the water surface. This...     

Influence of elastic material compressibility on parameters of an expanding spherical stress wave

We investigated the influence of elastic material compressibility on parameters of an expanding spherical stress wave. The material compressibility is represented by Poisson’s ratio, ν, in this paper. The stress wave is generated by a pressure produced inside a spherical cavity surrounded by the isotropic elastic material. The analytical closed form formulae determining the dynamic state of the mechanical parameters (displacement, particle velocity, strains, stresses, and material density) in the material have been derived. These formulae were obtained for surge pressure p(t) = p ₀ = const inside the cavity. From analysis of these formulae, it is shown that the Poisson’s ratio substantially influences the course of material parameters in space and time. All parameters intensively decrease in space together with an increase of the Lagrangian coordinate, r. On the contrary, these parameters oscillate versus time around their static values. These oscillations decay in the course of time. We can mark out two ranges of parameter ν values in which vibrations of the parameters are “damped” at a different rate. Thus, Poisson’s ratio in the range below about 0.4 causes intense decay of parameter oscillations. On the other hand in the range 0.4 < ν < 0.5, i.e. in quasi-incompressible materials, the “damping” of parameter vibrations is very low. In the limiting case when ν = 0.5, i.e. in the incompressible material, “damping” vanishes, and the parameters harmonically oscillate around their static values. The abnormal behaviour of the material occurs in the range 0.4 < ν < 0.5. In this case, an insignificant increase of Poisson’s ratio causes a considerable increase of the parameter vibration amplitude and decrease of vibration “damping”.      

Thermocapillary motion of a liquid with a free surface with nonlinear dependence of the surface tension on the temperature

The present note considers two problems concerning the thermocapillary motion, due to the existence of a temperature gradient, of a weightless liquid with a parabolic dependence of the surface tension on the temperature. These problems admit self-similar solutions (in the generalized sense) within the framework of the Navier-Stokes equations. It is noted that the solution may not be unique. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 132–137, September–October, 1988.     

Start-up of an elastico-viscous liquid draining from a vertical surface

The free drainage of thin films of non-Newtonian liquids from vertical surfaces occurs in a variety of industrial processes. Consideration is given in this paper to the effect of liquid elasticity on the much neglected “start-up” phase of the flow. The analysis utilizes the solution derived in 1970 by Waters and King for the generation of plane Poiseuille flow, to show that the presence of elasticity has a profound effect on the initial and the subsequent drainage profile.     

Reflection of a shock wave from the free surface of an elastoplastic body

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 148–157, July–August, 1991.     

Influence of porosity of the base on a plane standing wave of a heavy liquid

A study is made of the simple problem of the contact of two plane-parallel potential flows of incompressible fluid when one takes place in a layer of finite thickness and the other in a semiinfinite space of a porous medium. At the interface, which is taken to be a plane, the same conditions are used as earlier in problems of the contact of two wave flows of fluids with different densities and the contact of a wave motion in a layer of compressible fluid and wave motions in an elastic semi-infinite space. These conditions reduce to equalities of the pressures and projections of the velocity vectors onto the normal to the interface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 160–163, July–August, 1984.     

Behavior of the surface of a bubbly liquid after detonation wave impact

In safety engineering, one position of interest inside heterogeneous systems of the type liquid–gas is the contact surface between these two phases. Under certain conditions, e.g. shock wave impact, phenomena can take place at this position that can have a significant influence on the explosion behavior of the system. In this work an investigation is presented about the existence of such phenomena on the surface of liquid cyclohexane with or without the existence of oxygen containing bubbles. The observations have been performed during the time before, as well as after, a detonation wave reflection on that surface. High-speed pressure and optical measurements have been applied. Apart from the experimental observations, also a theoretical analysis and discussion is presented in this contribution, which contains the comparison between calculated and experimental values.     

Application of underwater shock wave and laser-induced liquid jet to neurosurgery

Paper deals with applications of underwater shock waves to medicine. A historical development of underwater shock wave generation by using pulsed Ho:YAG laser beam irradiation in water is briefly described and an overview is given regarding potential applications of shock waves to neuro-surgery. The laser beam irradiation in a liquid-filled catheter produces water vapor bubble and shock waves intermittently produces micro-liquid jets in a controlled fashion from the exit of the catheter. Correlations between shock dynamics and bubble dynamics are emphasized. To optimize the jet motion, results of basic parametric studies are briefly presented. The liquid jet discharged from the catheter exit has an impulse high enough to clearly exhibit effectiveness for various medical purposes. In liquid jets we observed reasonably strong shock waves and hence invented a compact shock generator aiming to apply to microsurgery. We applied it to a rat's bone window and developed an effective method of brain protection against shock loading. The insertion of Gore-Tex® sheet is found to attenuate shock waves drastically even for very short stand off distance and its physical mechanism is clarified. The laser-induced liquid jet (LILJ) is successfully applied to soft tissue dissection. Animal experiments were performed and results of histological observations are presented in details. Results of animal experiments revealed that LILJ can sharply dissect soft tissue with a minimum amount of liquid consumption, while blood vessels larger than 0.2 mm in diameter are preserved. Shock waves and LILJ have a potential to be indispensable tools in neuro-surgery.This paper was based on work that was presented at the 2nd International Symposium on Interdisciplinary Shock Wave Research, Sendai, Japan, March 1–3, 2005.Communicated by K. Takayama PACS 42.62.Be, 47.40.-x, 42.62.-b     

Experimental study of the stochastic nature of wave phenomena on the surface of a liquid film

An experimental study was made of wave phenomena on the surface of a liquid film freely flowing down the walls of a vertical channel in the range of Reynolds numbers for film flow (Re=Γ/η= 50–2500, where Γ is the mass spray density and η is the dynamic viscosity) at various distances from the entrance. The working fluid (water) was fed into the operating section at a temperature of 15–30 °C. The dependence of typical wave parameters on mode parameters was obtained.     

关于平动相对平衡问题的液面不动点

为了方便叙述,我们定义平动相对平衡问题变形前后两液面交线上的点为不动点． 一般《工程流体力学》教材均采用等加速度运动罐车或其它容器来作为典型例题,以说明平动相对平衡问题的求解方法．其中不少教材［１～６］既不说明容器的具体形状,也不说明是变形前还是变形后的液面中心,或者简单地给出‘腋面中心点不变化”［１］的结论后,将坐标原点取在液面中心点;另有一些教材则将坐标原点取在液面上的某一点,从而得出压强分布规律和等压面方程．这就引出了以下两个问题; （１）液面中心点是否一定是不动点？如果不是,则由该点的边界…     

Motion of a solitary wave over a submerged ridge

The two- and three-dimensional motion of a stationary wave in a layer of liquid with a variable depth was studied earlier by Grimshaw [1, 2], who showed that if the unperturbed state of the liquid were a state of rest, then a certain integrated quantity characterizing the energy of the wave (referred to one element on the leading edge of the wave) was conserved during the motion. In the present investigation (which is based on this property) we shall establish the shape of the wave front for the case of steady motion over an infinite submerged cylindrical ridge; we shall present a model describing a wave of limiting amplitude and shall consider the transient perturbation of the steady-state solution. We should note that one particular case (the motion of a straight front, orthogonal to the axis of the ridge, in a direction parallel to this axis) was considered by another method in [3].     

Influence of a longitudinally compressed elastic plate on the nonstationary wave motion of a homogeneous liquid

In a linear formulation, a study is made of the influence of a longitudinally compressed elastic isotropic plate on the nonstationary wave motion of a stream of homogeneous liquid of finite depth on which the plate floats. The waves are generated by periodic (in time) normal stresses applied to a restricted region of the plate surface and beginning at a certain initial time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–75, September–October, 1980.     

Thermal imaging study on the surface wave of heated falling liquid films

By using thermal imaging technique and film thickness metering system, the surface wave and film thickness of the heated falling liquid film were experimentally investigated. Temperature variations of the heated film induce surface tension gradient and so-caused Marangoni flow that attempts to avoid the temperature variations. There are three kinds of Marangoni flow appearing in the heated falling liquid film. It is found that the lateral Marangoni flow (MF I) and the streamwise Marangoni flow (MF II) make the heated film thick, while the Marangoni flow in the surface wave (MF III) reinforces the wave and makes the heated film thin. The intensity of Marangoni flow is determined by the flow rate and the heating conditions. MF I and MF II are both enhanced with the increasing liquid flow rate. Moreover, MF III is prominent under moderate flow rates and is gradually weakened at high flow rates. The distance over which MF III starts, increases with a rise in flow rate, but is independent of the heating condition.     

Dynamics of the cavitation zone during an underwater explosion near a free surface

The problem of the development of the cavitation zone and the rarefaction wave profile in the region of regular reflection of the spherical shock wave of an underwater explosion from a free surface is analyzed for the axisymmetric formulation within the framework of a model of the two-phase medium consisting of a liquid with cavitation nuclei of the free gas uniformly distributed in it. An example of the calculation of the rarefaction wave profile and the zone of visible cavitation at different times is given for the case of the explosion of 1-g charge at depths of 3 and 5.3 cm for an initial volumetric gas concentration of 10^?11 and an initial cavitation nucleus radius of 5 · 10^?5 cm. The results of the calculation are compared with experiment.     

Evolution of bubble spectrum in the process of cavitational fragmentation by a shock wave reflected from a free liquid surface

Equations which describe the evolution of the bubble spectrum in the process of cavitational fragmentation by a shock wave reflected from a free liquid surface are formulated. As an example, the effect of artificial saturation of the initial fluid with large bubbles on the dispersity of a liquid-drop gas suspension focused by dispersion is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 51–58, May–June, 1992.     

Natural vibrations of a hummock ridge in an elastic ice sheet floating on the surface of an infinitely deep fluid

The properties of the natural vibrations of a hummock ridge in an elastic ice sheet are investigated. Typical shapes of the dispersion curves for symmetric and antisymmetric boundary waves which propagate along the hummock and damp exponentially with distance from the latter are obtained. It is shown that natural vibrations can initiate failure of the ice sheet at a certain distance from the hummock. Under compression this process leads to the formation of a parallel hummock ridge.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 99–105, November–December, 1995.