液体横向射流在气膜作用下的破碎过程

为了研究液体横向射流在气膜作用下的破碎过程,采用背景光成像技术及VOF TO DPM方法进行了实验研究和仿真研究,模拟介质为水和空气.研究结果表明,液体射流在气膜作用下主要存在两种破碎过程:柱状破碎和表面破碎.Rayleigh-Taylor(R-T)不稳定性产生的表面波是液体射流发生柱状破碎的主要原因,气流穿透表面波的波谷导致射流柱破碎,破碎后的液丝沿流向逐渐发展呈带状分布.Kelvin-Helmholtz(K-H)不稳定性产生的表面波是液体射流发生表面破碎的主要原因,液丝和液滴从射流表面剥离.局部动量比对液体横向射流的破碎过程具有重要影响,当局部动量比较低时,液体射流的破碎由K-H不稳定性主导;随着局部动量比的增大液体射流的破碎逐渐由R-T不稳定性主导.液体射流的破碎长度及穿透深度均随局部动量比的增大而增大.     

A three-body scattering problem in the molecular mass limit

A three-body problem is studied that involves the scattering of a heavy particle from a bound state of a heavy and a light particle. For fairly large mass ratios we find many partial waves involved in the scattering with both elastic and inelastic resonances present. It is also found that virtually all of the breakup inelasticity is in the odd partial waves, if the heavy particles are identical bosons. The same problem is solved in the Born-Oppenheimer approximation and it is found that the effective potential between the heavy particles develops an imaginary part in the odd partial waves and thus gives a quantitative account of the three-body results including the inelasticity. The linear combination of nuclear orbitais method is applied to the same problem and is found to be inadequate.     

台风“彩虹”(2015)高分辨率数值模拟及涡旋Rossby波特征分析

采用中尺度数值预报模式对2015年22号台风"彩虹"进行高分辨率的数值模拟,成功地模拟出台风"彩虹"的移动路径、强度和降水分布,尤其是在台风登陆前后,模拟结果与实况比较接近.以此为基础,利用模式输出资料,分析台风的动力、热力精细结构和台风雨带的宏观特征.眼墙处具有低层径向入流、高层径向出流的动力配置.在眼墙附近,同时存在切向风速高值区、垂直上升区、正温度距平区,并随高度向外侧倾斜,雷达回波较强,对流系统比较深厚.次级雨带、主雨带和远距离雨带的雷达回波相对较弱,对流系统垂直厚度略小.再利用尺度分离方法,得到涡旋Rossby波的扰动场资料,进一步分析涡旋Rossby波的特征.1波、2波同时朝切向和径向传播,1波的振幅明显大于2波.研究结果表明,1波、2波正涡度扰动对应强雷达回波,存在强对流活动.降水区上空的垂直涡度扰动呈上正下负的配置,与水平散度扰动的垂直配置相似时,会加强低层辐合和高层辐散,有很强的垂直上升运动,有利于对流系统发展,降水增强.1波、2波扰动的动力配置影响了对流系统的发展,并对降水强度和分布有一定的诊断作用.     

Strong spatial resonance and travelling waves in benard convection

We study the normal form for the onset of convection in a fluid layer when conditions are such that two modes whose horizontal wavenumbers are in the ratio 1:2 bifurcate simultaneously. It is shown that when the boundary conditions on the convection layer are such that there is no symmetry between the top and bottom of the layer, then the normal form possesses additional quadratic terms, and these equations have been shown to admit solutions in the form of travelling waves, modulated waves and standing waves. We give a discussion of the stability properties of these waves and describe a further form of nonsteady motion, namely an attracting homoclinic trajectory. The generality of the circumstances leading to this resonant behaviour suggests that such complex time dependence may play a role in convective disorder just above threshold. The results may also explain phenomena observed in laboratory experiments on cylindrical convection by Azouni, and Azouni and Normand.     

On bending instability of a volumetrically charged capillary jet of dielectric liquids

It is shown that jets of volumetrically charged dielectric liquids in the vicinity of point k = 0 are characterized by a finite range of wavenumbers, in which a jet exhibits bending instability. The interval of wavenumbers corresponding to unstable waves with azimuth number m = 1, as well as the increment of the most unstable wave and its wavenumber, increase in proportional to the electric charge per unit length of the jet and the permittivity of the liquid.     

Steady vortices in plasmas and geophysical flows

A number of two-dimensional fluid models in geophysical fluid dynamics and plasma physics are examined to find out whether they have steady and localized monopole vortex solutions. A simple and general method that consists of two steps is used. First the dispersion relation is calculated, to find all possible values of the phase velocity of the linear waves. Then an integral relation that determines the center-of-mass velocity of localized structures must be found. The existence condition is that this velocity should be outside the region of linear phase velocities. After a presentation of the method, previous work on the plasma drift wave model and the shallow-water equations is reviewed. In both cases it is found that the center-of-mass velocity is larger than the maximum phase velocity of the linear waves if the amplitude is large enough, and steady localized vortices can therefore exist. New results are then obtained for a number of two-field models. For the coupled ion acoustic-drift modes in plasmas, it is found that the center-of-mass velocity depends on the ratio between the parallel ion velocity component and the electrostatic potential in the vortex. If this ratio is large enough, the vortex can be steady. For the drift-Alfven mode the "center-of-charge" velocity is proportional to the ratio between the parallel current and the total charge in the vortex. It can therefore be steady if this ratio satisfies the appropriate conditions. For the quasigeostrophic two-layer equations, describing stratified flow on a rotating planet, it is found that the center-of-mass velocity is determined by the ratio between the baroclinic and the barotropic components in the vortex. If a baroclinic component with an appropriate sign is added to a barotropic vortex, it propagates faster than the barotropic Rossby waves, and can be steady. Finally, the existence conditions for a vortex in an external zonal flow are examined. It is found that the center-of-mass velocity acquires an additional westward contribution in an anticyclonic shear zone in the framework of the shallow-water equations, and also that an easterly jet south of this shear zone partly shields a vortex situated in the shear zone from the dispersive influence of the fast Rossby waves on the equatorward side.     

聚能射流高速光学测试技术

本文介绍了用正文同步扫描测量技术对聚能射流的动态参数进行测试,拍摄到非常清晰的射流头部在空气中飞行所产生的空气冲击波。运用计算机图象处理技术对拍摄的底片进行处理以后,获得了较为理想的射流图象。对底片进行测量,获得了射流在X平面内和Y平面内的离轴偏差,以及射流在X、Y平面内的飞行姿态,射流的累积长度作为速度的函数,射流的速度分布,射流的质量分布和动能分布,射流的断裂时间和断裂位置。     

Liquid jet response to internal modulated ultrasonic radiation pressure and stimulated drop production

Experimental evidence shows that a liquid jet in air is an acoustic waveguide having a cutoff frequency inversely proportional to the jet diameter. Ultrasound applied to the jet supply liquid can propagate within the jet when the acoustic frequency is near to or above the cutoff frequency. Modulated radiation pressure is used to stimulate large amplitude deformations and the breakup of the jet into drops. The jet response to the modulated internal ultrasonic radiation pressure was monitored along the jet using (a) an optical extinction method and (b) images captured by a video camera. The jet profile oscillates at the frequency of the radiation pressure modulation and where the response is small, the amplitude was found to increase in proportion to the square of the acoustic pressure amplitude as previously demonstrated for oscillating drops [P.L. Marston and R.E. Apfel, J. Acoust. Soc. Am. 67, 27-37 (1980)]. Small amplitude deformations initially grow approximately exponentially with axial distance along the jet. Though aspects of the perturbation growth can be approximated from Rayleigh's analysis of the capillary instability, some detailed features of the observed jet response to modulated ultrasound are unexplained neglecting the effects of gravity.     

Antiferromagnetic material with the magnetoelectric effect as an example of a left-handed medium

The propagation of electromagnetic waves in an antiferromagnetic material with the magnetoelectric effect is theoretically studied. The frequency dependences of the wavenumbers, dynamical permeability and permittivity, and reflection coefficient of electromagnetic waves for various energy parameters of the antiferromagnetic material have been obtained. It has been shown that there is a frequency range where the dynamical permeability and permittivity, as well as one of the wavenumbers, are simultaneously negative in the antiferromagnetic material with the magnetoelectric effect. In this case, the antiferromagnetic material is an example of a so-called left-handed medium. The reflection coefficient of electromagnetic waves from the surface of the antiferromagnetic material decreases anomalously in this frequency range.     

On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid

The shallow water equations coupled to the set of reaction–advection–diffusion equations are discretized on a geodesic icosahedral mesh using the finite volume technique. The method of solution of this coupled system is based on the principle of semi-discretization. The algorithm is mass conserving and stable for advection with the Courant numbers up to 2.7. The important part of the methodology is the optimization of the node positions in the icosahedral grid. It is shown that a slight adjustment of the mesh is instrumental in improving the accuracy of the numerical approximation. The convergence of the approximation of the differential operators is evaluated and compared to the data published in the literature. Numerical tests performed with the shallow water solver include two advection experiments, steady and unsteady zonal balanced flow, mountain flow, and the Rossby wave. The mountain flow and the Rossby wave cases are used to test the transport properties of the method in the case of both passive and reactive scalar fields. The investigation of essential numerical characteristics of the method is concluded by the simulation of an unstable zonal jet. The numerical simulation is performed using the set of shallow water equations without dissipation as well as with the viscosity term added to the momentum equation. Results show that the behavior of the model is consistent with both the literature published on the subject and the general empirical evidence.     

层结流体中在热外源和β效应地形效应作用下的非线性Rossby孤立波和非齐次Schrödinger方程

在层结流体中, 从带有地形、热外源耗散的下边界条件以及带有热外源的准地转位涡方程开始, 使用小参数展开方法和多尺度时空伸长变换推导出了具有热外源、β效应和地形效应的强迫Rossby孤立波方程, 得到孤立Rossby振幅满足的带有地形与热外源的非齐次非线性的Schrödinger方程. 通过分析Rossby孤立波振幅的变化, 指出了热外源、β效应和地形效应都是诱导Rossby孤立波产生的重要因素, 给出了切变基本流下地形、热外源和层结流体中Rossby的相互作用.     

层结流体中具有β效应与地形效应的强迫Rossby孤立波

层结流体中,从绝热位涡的扰动方程出发采用摄动方法和时空伸长变换推导了具有β效应和地形效应的强迫Rossby孤立波方程,得到孤立Rossby波振幅的演变满足带有地形强迫的非齐次mKdV方程的结论. 通过分析孤立Rossby波振幅的演变,即使基本气流没有切变,仍可能激发出Rossby孤立波.指出了科氏力效应、地形效应以及Vaisala-Brunt频率都是诱导Rossby孤立波产生的重要因素,说明了在地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次的mKdV方程.讨论 关键词： 非齐次mKdV方程 β效应')" href="#">β效应 地形 Vaisala-Brunt 频率     

Internal nonlinear resonance on a charged jet

Nonlinear analytical asymptotic calculations of the second order of smallness show that the motion of a charged jet in a material medium generates periodic wave motions of the jet-medium interface (Kelvin-Helmholtz instabilities), which grow in time. In addition, the motion of the jet gives rise to nonlinear internal resonance interaction of waves. The parameters of this interaction (intensity and characteristic time) depend on the physical parameters of the system: electric charge density of the jet, its velocity in the medium, mass density, wavenumbers of interacting waves, and the interfacial tension coefficient.     

切变基本纬向流中β效应的赤道Rossby孤立波包

从描写赤道Rossby 波的正压大气位涡方程出发,采用多重尺度摄动方法推导出在切变基本纬向流中具有β效应的非线性赤道Rossby波包演变满足非线性Schrdinger方程,并得到单个包络孤立子波解,分析了基本切变流,β效应对非线性赤道Rossby波的影响. 关键词： 赤道Rossby波 β效应 非线性Schrö dinger方程 包络孤立子     

Nonlinear development of capillary waves in a viscous liquid jet

The one-dimensional approximate equations describing the dynamics of a Newtonian viscous fluid are used to analyze the nonlinear development of capillary waves in a jet. It is shown that the size of satellite droplets resulting from a nonuniform jet breakup decreases with the Reynolds number at a constant wavenumber. The satellite-droplet formation ceases at a certain value of the Reynolds number, which depends on the wavenumber and initial perturbation amplitude.     

Dissipative Nonlinear Schrödinger Equation with External Forcing in Rotational Stratified Fluids and Its Solution

The dissipative nonlinear Schrödinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency and β effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schrödinger equation and forced nonlinear Schrödinger equation are derived, respectively. With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves.     

Resonant excitation and nonlinear evolution of waves in the equatorial waveguide in the presence of the mean current

We study interactions of planetary waves propagating across the equator with trapped Rossby or Yanai modes, and the mean flow. The equatorial waveguide with a mean current acts as a resonator and responds to planetary waves with certain wave numbers by making the trapped modes grow. Thus excited waves reach amplitudes greatly exceeding the amplitude of the incoming wave. Nonlinear saturation of the excited waves is described by an amplitude equation with one or two attracting equilibrium solutions. In the latter case spatial modulation leads to formation of characteristic defects in the wave field. The evolution of the envelopes of long trapped Rossby waves is governed by the driven complex Ginzburg-Landau equation, and by the damped-driven nonlinear Schr?dinger equation for short waves. The envelopes of the Yanai waves obey a simple wave equation with cubic nonlinearity.     

(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect

In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.     

Experimental evidence of a Rayleigh-plateau instability in free falling granular jets

A granular jet falling out of a funnel shaped container, subjected to small vertical vibrations, develops an instability farther downstream as may happen for ordinary liquid jets. Our results show that this instability is reminiscent of the Rayleigh-Plateau capillary instability leading to breakup of the jet at large scales. The first stages of this instability are captured in detail allowing a determination of the dispersion relation. Surface tensions measured in this unstable regime (of the order of mN/m) are in agreement with previously reported measurements carried out at much smaller scales. This instability and the breakup of the jet can be inhibited when the effect of the surrounding medium (air) is reduced by enclosing the jet in an evacuated chamber, showing that the effective surface tension measured is the result of a strong interaction with the surrounding air.