Capillary waves in an inhomogeneous three-layer liquid with a free surface

In the domain of capillary waves, a bicubic dispersion relation is derived and analyzed for surface and internal capillary–gravitational waves in a three-layer liquid with a free surface. It is shown that the ratio of the internal wave amplitudes to the surface wave amplitudes is fairly large if the trivial condition of a “homogeneous liquid” is discarded. The amplitude ratio between the internal waves themselves (generated at different interfaces) may be both greater and smaller than unity depending on the physical parameters of the system. Specifically, it strongly depends on the densities of the layers and their thicknesses.     

On the theory of a boundary layer associated with wave motion on the free surface of a liquid

A modified theory of a boundary layer associated with a periodic capillary-gravitational motion on the free surface of an infinitely deep viscous liquid is proposed. The flow in the boundary layer is described in terms of a simplified (compared with the complete statement) model problem a solution to which correctly reflects the main features of an exact asymptotic solution: the rapid decay of the flow eddy part with depth of the liquid and insignificance of some terms appearing in the complete statement. The boundary layer thickness at which the discrepancy between the exact asymptotic solution and model solution is within a given margin is estimated.     

Stability of a velocity field tangential discontinuity in a three-layer density-stratified liquid with a moving middle layer

A dispersion relation is analytically derived for gravitational waves in an ideal incompressible threelayer liquid with a free surface in the presence of a velocity field tangential discontinuity between the layers. The discontinuity results from the motion of the middle layer. The instability of the tangential discontinuity is shown to depend on the relative velocity of contacting layers, which, in turn, depends on the ratio of their densities. The closer the density ratio to unity, the lower the moving layer velocity causing instability. In the given case, instability involves internal waves arising at the second and third interfaces in accordance with the Kelvin–Helmholtz concept of instability development. Internal waves with wavelengths far exceeding the thickness of the middle layer are found to interact with each other. Surface waves only change their frequencies.     

On capillary motion of a viscoelastic liquid with a charged free surface

The structure of the capillary-relaxation motion spectrum in a liquid with a charged free surface has been investigated taking into account the viscosity relaxation effect. On the basis of numerical analysis of the dispersion equation for the wave motion in a viscoelastic incompressible liquid, it is shown that for a given wave number the range of characteristic relaxation times in which relaxation-type wave motion exists is limited and expands with increasing wave number. The growth rate of instability of the charged liquid surface markedly depends on the characteristic relaxation time and increases with its growth; in liquids with elastic properties, the energy dissipation rate of capillary motion is enhanced. At a surface charge density that is supercritical for the onset of Tonks-Frenkel instability, both purely gravitational waves and waves of a relaxational nature exist.     

Thickness of a boundary layer attributed to the wave motion on the charged free surface of a viscous liquid

It is shown that the analytical estimator for the boundary layer thickness that contains the wave frequency in the denominator and is proposed for approximate calculation of the wave motion on the free surface of a viscous liquid cannot be formally applied to the wave motion on the uniformly charged liquid surface. The fact is that, when the surface charge density attains a value critical in terms for the Tonks-Frenkel instability, the wave frequency tends to zero. From the analysis of liquid motions near the electric charge critical density, a technique is proposed for calculating the thickness of a boundary layer attributed to flows of various kinds. It is found that the thickness of the boundary layer due to aperiodic flows with amplitudes exponentially growing with time (such flows take place at the stage of instability against the surface charge) does not exceed a few tenths of the wavelength, whereas the thickness of the boundary layer due to exponentially decaying liquid flows is roughly equal to the wavelength.     

轴向振动对圆柱形液体自由表面流的影响

通过光学实时观察法研究了轴向振动对恒温圆柱形容器内液体自由表面流动行为的影响。该地面实验是在一个频率为100赫兹的电磁振动台上进行的，水－甘油的混合溶液作为模型体系。结果发现，小于100mm的振动振幅能够使自由表面产生稳定的流动。这种流动主要是由沿自由表面传播的毛细波与斯托克斯边界层效应的共同作用驱动的。随着振动振幅的变化，稳态流会呈现不同的流动花样。高振幅作用下，稳态流动趋向于周期性流甚至成为湍流，这个过程可以通过临界无量纲雷诺数(Nre)c来表征，实验中得到的(Nre)c值在10-2 ～ 10-1范围内。此外，利用示踪粒子散射技术对自由表面的流动速度进行了测量，结果显示流速随粘度的增大而减小，并且随振幅的增加呈抛物线形增长。     

Exact solutions of the equations of motion of liquid helium with a charged free surface

The dynamics of the development of instability of the free surface of liquid helium, which is charged by electrons localized above it, is studied. It is shown that, if the charge completely screens the electric field above the surface and its magnitude is much larger than the instability threshold, the asymptotic behavior of the system can be described by the well-known 3D Laplacian growth equations. The integrability of these equations in 2D geometry makes it possible to describe the evolution of the surface up to the formation of singularities, viz., cuspidal point at which the electric field strength, the velocity of the liquid, and the curvature of its surface assume infinitely large values. The exact solutions obtained for the problem of the electrocapillary wave profile at the boundary of liquid helium indicate the tendency to a change in the surface topology as a result of formation of charged bubbles.     

法拉第对液体表面波的研究

介绍了法拉第由克拉尼图形进入液体表面波研究领域的过程,回顾了法拉第研究液体表面波的实验;分析了法拉第怀有强烈好奇心和能够正确对待权威学者观点的精神特质,以及法拉第思维开阔和实验技巧高超的研究特点.     

Effect of surface-tension relaxation on the spectrum of motions of a liquid with charged free surface

The spectrum of capillary-relaxational motions of a charged free liquid surface is analyzed. The analysis takes into account the effect of surface-tension relaxation and the existence of two relaxation times due to different physical mechanisms. Each relaxation mechanism is associated with certain liquid wave motions. Motions due to different relaxation processes interact with each other and with capillary-gravity waves through nonlinear mechanisms.     

Correlations for the circular Dyson brownian motion model with Poisson initial conditions

The circular Dyson brownian motion model refers to the stochastic dynamics of the log-gas on a circle. It also specifies the eigenvalues of certain parameter-dependent ensembles of unitary random matrices. This model is considered with the initial condition that the particles are non-interacting (Poisson statistics). Jack polynomial theory is used to derive a simple exact expression for the density-density correlation with the position of one particle specified in the initial state, and the position of one particle specified at time τ, valid for all β > 0. The same correlation with two particles specified in the initial state is also derived exactly, and some special cases of the theoretical correlations are illustrated by comparison with the empirical correlations calculated from the eigenvalues of certain parameter-dependent Gaussian random matrices. Application to fluctuation formulas for time-displaced linear statistics in made.     

液体表面波光栅的研究

在液体表面形成的一维正弦形表面波,作为一种理想的反射式光栅,称之液体表面波光栅.本文通过它对激光束的衍射,研究液体表面与界面的物理特性.     

Highly directional liquid surface wave source based on resonant cavity

By placing a point source inside a resonant cavity structure, we present a method to realize a highly directional liquid surface wave source. The resonant cavity is surrounded by two slabs of different thickness, with each slab consisting of a finite square array of rigid cylinders standing vertically in the liquid. It is shown that more than 68% of the total energy is emitted out along the normal directions of the cavity within a very narrow angular range. At the resonant frequency, narrow emission pattern with half-power angular width of only several degrees is obtained.     

Vibration of a liquid with a free surface in a spinning spherical tank

The problem of forced fluid vibrations in a partially filled spinning spherical tank is solved numerically by using the finite element method. The governing equations include Coriolis acceleration and spatially homogeneous vorticity. An exponential instability is detected in the present simulation for fill ratios below 0·5 and centrifugal acceleration to thrust ratios less than 1·7. This fictitious instability appears in the model as a result of the homogeneous vortex assumption since the free slosh equations are neutrally stable in the Liapunov sense.     

自由液态锡表面结构的流体模型

应用SolidWorks 和ANSYS 软件设计了自由液态锡表面流体结构模型,计算了初始流速和热通量不同时液态锡的速度变化和温度变化,得到了流动液态锡的速度分布和温度分布。结果表明,垂直流动方向液态锡流速较为均匀,沿流动方向液态锡流速逐渐增大、液态锡液面厚度逐渐变薄。初始温度为600K 的条件下,热通量为1MW·m⁻² 时,液态锡出口温度为623.38K;热通量为5MW·m⁻² 时,液态锡出口温度为720.18K。在相同条件下使用液态锂作为计算流体,结果表明出口处液态锂的温度低于液态锡的温度。     

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应用SolidWorks和ANSYS软件设计了自由液态锡表面流体结构模型,计算了初始流速和热通量不同时液态锡的速度变化和温度变化,得到了流动液态锡的速度分布和温度分布。结果表明,垂直流动方向液态锡流速较为均匀,沿流动方向液态锡流速逐渐增大、液态锡液面厚度逐渐变薄。初始温度为600K的条件下,热通量为1MW·m?2时,液态锡出口温度为623.38K;热通量为5MW·m?2时,液态锡出口温度为720.18K。在相同条件下使用液态锂作为计算流体,结果表明出口处液态锂的温度低于液态锡的温度。     

Effect of a longitudinal wave on the self-resonant motion of electrons

The effect of the longitudinal component of an electromagnetic wave on the self-resonant motion of electrons in waveguides is considered. The equation of motion for electrons in a plane, longitudinal-transverse, circularly polarized wave has been solved by the method of successive approximations with allowance for the longitudinal integral of motion present in such a wave. The expansion parameter is the ratio of the amplitudes of the longitudinal and transverse components of the wave. For the case n < 1 the longitudinal field of the wave does not change the nature of the electron motion, but only induces weak oscillations about a solution that does not include the longitudinal field. For n > 1 with spontaneous phasing of the electrons a criterion is obtained for neglecting the effect of the longitudinal field, and numerical estimates are given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 66–71, September, 1978.     

Instability development on the charged free surface of a horizontal liquid layer with thermal convection

The instability of the charged free surface of a horizontal liquid layer heated from the solid bottom against excess electric charge is studied theoretically for the case in which this type of instability is combined with thermal-convective instability. The structure of the total spectrum of unstable wave flows and physical parameters influencing the structure of the spectrum are determined.     

近自由面水下爆炸气泡的运动规律研究

基于边界积分法建立水下爆炸气泡与自由面耦合数值模型;并开发相应的计算程序,计算值与实验值符合较好.从气泡与自由面相互作用的基本现象入手,运用开发的程序系统地研究了近自由面水下爆炸气泡的动态特性,包括近自由面气泡的环状回弹及自由面的水冢现象;研究距离参数、浮力参数以及强度参数等特征参数与自由面Bjerknes效应之间的关系,总结相关规律,近自由面气泡的动态特性与这些特征参数有密切的关系.并在研究过程中,讨论了基于Kelvin-impulse理论的Blake准则的适用范围,并解释了Blake准则的失效的原因. 关键词： 气泡 自由面 环状 水冢     

近自由面水下爆炸气泡的运动规律研究

基于边界积分法建立水下爆炸气泡与自由面耦合数值模型；并开发相应的计算程序，计算值与实验值符合较好.从气泡与自由面相互作用的基本现象入手，运用开发的程序系统地研究了近自由面水下爆炸气泡的动态特性，包括近自由面气泡的环状回弹及自由面的水冢现象；研究距离参数、浮力参数以及强度参数等特征参数与自由面Bjerknes效应之间的关系，总结相关规律，近自由面气泡的动态特性与这些特征参数有密切的关系.并在研究过程中，讨论了基于Kelvin-impulse理论的Blake准则的适用范围，并解释了Blake准则的失效的原因.