Laboratory experiments on internal wave interactions with a pycnocline

Laboratory experiments have been performed to investigate the interaction of internal waves with a pycnocline. An oscillating cylinder generated internal wave beams, which were observed using the synthetic schlieren technique. Internal waves incident on the pycnocline layer excited higher-frequency modes. In the absence of shear, a discrete spectrum of harmonic modes was generated due to nonlinear effects. These harmonic modes might play a role in the formation of internal solitary waves which have been observed in ocean pycnoclines. With shear, a continuous spectrum of excited modes was found.     

Tomographic reconstruction of internal wave patterns in a paraboloid

Using tomographic synthetic schlieren, we are able to reconstruct the three-dimensional density field of internal waves. In this study, the waves are radiating from an oscillating sphere positioned eccentrically at the surface of a paraboloidal domain filled with a uniformly stratified fluid. We find that the prediction by ray tracing corresponds well with the observed intensities of the wave field. Remarkably, for a specific value of the forcing frequency, we observe convergence of internal wave energy to an internal wave attractor. The attractor is found to dominate fluid motion in the plane perpendicular to the plane spanned by the symmetry axis and the oscillator position.     

A THEORETICAL ANALYSIS OF THE FLOW DISTURBANCE INDUCED BY A SPHERE OSCILLATING IN INCOMPRESSIBLE FLUID

为了改进基于不可压缩流场的声类比法的气动声数值预测方法,首先要明确扰动在可压缩和不可压缩流体媒介中的传播特性. 推导了震荡小球在不可压缩流体中产生的小扰动的理论解,分析其速度场与压力场的特点,并与可压缩情况的解进行比较. 结果显示,速度场中包含传播速度为无穷大和有限值的分量;而压力场只有传播速度为无穷大的分量. 当流体黏性趋于零或小球震荡频率趋于无穷大时,其流场与经典声学中震荡小球声辐射问题的近场声一致,这表明震荡小球产生的近场扰动为不可压缩流场,即伪声.     

Internal Gravity Waves Generated by an Oscillating Source of Perturbations Moving with Subcritical Velocity

This paper considers the problem of constructing far-field asymptotics of internal gravity waves generated by an oscillating local source of perturbations moving in a stratified flow of finite depth. The velocity of the perturbation source does not exceed the maximum group velocity of an individual wave mode. The wave pattern consists of waves of two types: annular and wedge-shaped. Solutions expressed in terms of the Hankel function are obtained for the asymptotics of annular waves. The asymptotics of wedge-shaped waves are expressed in terms of the Airy function and its derivative.     

水表面波微振幅测量

采用一种非接触光学方法——Fourier变换光栅法，对受外激励的连续变化的水表面波进行实验测量，获得变形光栅图像，通过对变形光栅图像进行反演计算，获得连续变化的水表面波振幅，是定量测量变化快的非定常运动的微幅波的一种全场测量手段。     

Calculation and measurement of conical beams of three-dimensional periodic internal waves excited by a vertically oscillating piston

The structure of the wave field given by an exact solution of the linearized problem of radiation of three-dimensional periodic internal waves in a continuously stratified viscous fluid is analyzed numerically. The waves are generated by a piston, i.e., a disk lying on a fixed horizontal plane and oscillating in the vertical direction. The flow fields and the wave displacements are compared with the data of shadow visualization and measurements of the wave amplitudes made using a contact sensor. The calculated and observed wave patterns are in satisfactory agreement and the displacement distributions coincide correct to a fitting coefficient 0.7 < K < 1.1 characterizing the role of the nonlinear effects and other factors neglected in this model.     

Effect of Time Periodic Boundary Conditions on Convective Flows in a Porous Square Enclosure with Non-Uniform Internal Heating

The problem of unsteady natural convection in a square region filled with a fluid-saturated porous medium having non-uniform internal heating and heated laterally is considered. The heated wall surface temperature varies sinusoidally with the time about fixed mean temperature. The opposite cold wall is maintained at a constant temperature. The top and bottom horizontal walls are kept adiabatic. The flow field is modelled with the Darcy model and is solved numerically using a finite difference method. The transient solutions obtained are all periodic in time. The effect of Rayleigh number, internal heating parameters, heating amplitude and oscillating frequency on the flow and temperature field as well as the total heat generated within the convective region are presented. It was found that strong internal heating can generate significant maximum fluid temperatures above the heated wall. The location of the maximum fluid temperature moves with time according to the periodically changing heated wall temperature. The augmentation of the space-averaged temperature in the cavity strongly depends on the heating amplitude and rather insensitive to the oscillating frequency.     

Generation of impulsive pressure wave by spark discharge in water and its propagation

An experimental investigation was performed to find a new method for diagnosing three-dimensional flows in which obstacle bodies or cavities are included by means of a pressure wave. In rectangular closed tanks 200 × 337 × 250 mm (acrylic resin) and 300 × 450 × 400 mm (brass) filled with water, an impulsive pressure wave was generated by an instantaneous small spark discharge. The pressure waveforms were measured at a point on the wall with a high-frequency pressure transducer, and the data were recorded with an A/D converter. The measured wave fluctuations differed depending on wall conditions of the tank and on whether there was a submerged body in the water. The size of the submerged body also affected the pressure fluctuation. When acrylic resin and brass were used as wall materials, both the phase and amplitude of the reflecting wave differed. When a stainless steel sphere of diameters of 50.8, 30.2, or 19.1 mm was submerged in the tank, two kinds of pressure waves were observed, one passing through the sphere and the other diffracted around it. These results suggest the possibility of identifying bodies of simple shape by interpreting the precisely measured output pressure wave signals.     

分层流体中内孤立波在台阶上的反射和透射

基于匹配渐近展开和格林函数的方法,研究了两层流体系统中内孤立波在台阶地形上透射、 反射及其分裂的演化特征. 通过保角变换和求解奇异Fredholm积分方程,获得了反映地形 效应对Boussinesq方程影响的约化边界条件,藉此建立了KdV演化方程的``初值'问题, 根据散射反演理论获得了反射波和透射波的解析表达式. 分析结果表明：上下流体层的厚度 比、密度比以及台阶高度对于反射和透射波振幅及其分裂具有显著的影响. 尤其当上层流体 厚度小于下层厚度时,由于存在临界点,在其附近反射波的幅值随台阶高度的演化由单调增 变为单调减,透射波的幅值由单调减变为单调增;上台阶的反射波与入射波反相,其最大幅 值可达到入射波的数倍;此外,下台阶反射波也可发展为单支孤立波,它区别于单层流体中 反射波仅为衰减的振荡波列.     

Rotationally symmetric internal gravity waves

Many mathematical models formulated in terms of non-linear differential equations can successfully be treated and solved by Lie group methods. Lie group analysis is especially valuable in investigating non-linear differential equations, for its algorithms act here as reliably as for linear cases. The aim of this article is to provide the group theoretical modeling of internal waves in the ocean. The approach is based on a new concept of conservation laws that is utilized to systematically derive the conservation laws of non-linear equations describing propagation of internal waves in the ocean. It was shown in our previous publication that uni-directional internal wave beams can be obtained as invariant solutions of non-linear equations of motion. The main goal of the present publication is to thoroughly analyze another physically significant exact solution, namely the rotationally symmetric solution and the energy carried by this solution. It is shown that the rotationally symmetric solution and its energy are presented by means of a bounded oscillating function.     

Waves in a heavy two-layer liquid excited by an oscillating sphere

An approximate solution of an initial-boundary-value problem appropriate for the semiaxist>0 (t is time) is constructed for a system of integrodifferential equations which describes the waves excited in an initially stationary unbounded heavy two-layer fluid by a vertically oscillating sphere located at a distance from the interface that is significantly greater than its radius. The shape of the steady-state wave is found by passing to the limit as time increases indefinitely. The wave resistance experienced by the sphere during the transient process and in the steady-state regime is studied as a function of frequency. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–133, March–April, 1998.     

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.     

基于复数矢径的波叠加法解声辐射问题

利用波叠加法与结构动力分析中的相似性，提出了一种在波叠加法中克服解非唯一的通用方法，即在虚拟源强系统中加入一定的虚拟阻尼从而能获得全波数域内的唯一解，并以此为基础提出了一种新的加入虚拟阻尼的方法——复数矢径波叠加法。文中给出了脉动球和摆动球两个数值算例，计算结果表明：本文方法不仅能有效解决数值求解过程中解非唯一的问题，且计算时间只与标准波叠加法相当，计算精度却比同类方法高。     

Dipole Electromagnetic Radiation by a Charged Drop Oscillating in a Uniform Electrostatic Field

The intensity of electromagnetic radiation generated by a charged drop oscillating in a uniform electrostatic field is studied within the framework of analytical calculations retaining the terms of the second order of smallness with respect to the ratio of the droplet oscillation amplitude to the droplet radius. It is found that the charge induced in the drop surface oscillations generates a dipole radiation detected in the first-order calculations and a self-charge detected with allowance for the second-order terms only. It is shown that the order of the magnitude of the total intensity of radiation generated by a cloud can be determined from small-droplet radiation. Among two radiation sources, namely, the radiation generated by small droplets oscillating at low modes and the radiation generated by hydrometeors oscillating at high modes, the first plays a dominant role.     

Schlieren measurements of internal waves in non-Boussinesq fluids

Previous experiments that have examined the generation of internal gravity waves by a monochromatic source have been restricted to small amplitude forcing in Boussinesq stratified fluids. Here we present measurements of internal waves generated by a circular cylinder oscillating at large amplitude in a non-Boussinesq fluid. The ‘synthetic schlieren’ optical measurement technique (Sutherland et al. in J Fluid Mech 390:93–126, 1999) is extended to stratifications in which the index of refraction of the fluid may vary nonlinearly with density. The method is applied to examine disturbances in approximately uniformly stratified ambient fluids consisting either of sodium chloride (NaCl) or sodium iodide (NaI) solutions whose concentrations increase to near-saturation at the bottom of the tank. In particular, we report upon the first extensive measurements of the optical properties of NaI solutions as they depend upon concentration and density. Applying the results to experiments, we find that large amplitude forcing generates a patch of oscillatory turbulence surrounding the cylinder, thereby increasing the effective cylinder size and decreasing the amplitude of the waves in comparison with the predictions of linear theory. We parameterize the influence of the turbulent boundary layer in terms of an effective cylinder radius and forcing amplitude.     

Waves generated by an inclined-plate wave generator

This paper describes the characteristics of small-amplitude waves generated by a sinusoidally oscillating, inclined paddle-type wavemaker operating in a constant-depth channel. Two-dimensional, linearized potential flow is assumed. A semi-analytical method, the boundary collocation method, is used to establish the relationship between wave amplitude and paddle stroke. The numerical results are compared with the numerical results of the boundary integral equation method. It is found that the boundary collocation method is simpler and more flexible to implement and faster to compute. In addition, the numerical results are in reasonably good agreement with the laboratory experimental data. For the vertical wavemaker, which is a special case of the inclined wavemaker, an analytical series solution can be found. By using the boundary collocation method and the boundary integral equation method to solve the vertical wavemaker problem and comparing the results with the analytical series solution, it is found that the boundary collocation method yields a solution which is much more accurate than that from the boundary integral equation method. Finally, the relationships between wave amplitude and paddle stroke are established for different inclinations of the paddle-type wavemaker, based on the boundary collocation method.     

周期性非均匀介质中气相爆轰波演变模式研究

气相爆轰波在周期性非均匀介质中的起爆, 稳态传播和失效机制都极为复杂, 很多物理机制尚不明确, 是当前爆轰物理领域研究的热点和难点. 本文使用反应欧拉方程和两步化学反应模型对爆轰波在非均匀介质中的传播机理进行了数值模拟研究, 非均匀性由横向周期性分布的温度扰动体现, 重点分析不同波长、不同幅度的温度扰动对波阵面波系结构的影响. 计算结果表明, ZND爆轰波在温度扰动下向胞格爆轰波的转变主要受制于两种竞争性因素: 一是爆轰波内在的不稳定性; 二是温度扰动的波长和幅度, 前者是内因, 后者是外因. 温度扰动的存在抑制横波的发展, 延迟了ZND爆轰波向胞格爆轰波的演化, 并且内在不稳定性的增加可以减慢这种延迟现象. 这说明, 温度扰动可以在一定的范围内抑制胞格不稳定性的发展, 但是不能够终止这一过程. 温度的不连续性使得爆轰波阵面更为扭曲, 并在横波附近存在较弱的三波点结构, 即温度扰动可增加爆轰波固有的不稳定性, 改变爆轰波阵面的传播机理. 幅值较大的人工温度扰动可抑制爆轰波的传播和爆轰波自身的不稳定性. 爆轰波阵面胞格结构的形成取决于温度扰动与其自身的不稳定性.      

Gravity waves under nonuniform pressure over a free surface. Exact solutions

Plane periodic oscillations of an infinitely deep fluid are studied in the case of a nonuniform pressure distribution over its free surface. The fluid flow is governed by an exact solution of the Euler equations in the Lagrangian variables. The dynamics of an oscillating standing soliton are described, together with the scenario of the soliton evolution and the birth of a wave of an anomalously large amplitude against the background of the homogeneous Gerstner undulation (freak wave model). All the flows are nonuniformly vortical.     

Force and pressure distribution under vibratory tillage tool

Experiments were conducted to study the force requirement and pressure distribution under vibratory tillage tools in a soil bin with a sandy loam soil. The tool was oscillated sinusoidally in the direction of soil bin travel. An octagonal ring transducer and pressure sensors were used to measure the forces and soil pressure on the blade. The tool was operated at oscillating frequency of 4.5–15.6 Hz and amplitude of 11–26 mm. The soil bin travel speed was varied from 0.05 to 0.224 m/s. The test results obtained showed both the horizontal force and the vertical force decreased with increase in oscillating frequency. The normal pressure on the blade surface varied considerably. The peak normal pressure was found to increase with increase in oscillating frequency, oscillating amplitude and soil bin travel speed. The change in average normal pressure with change in oscillating frequency and amplitude was also investigated.