交通流相变过程的能量谱分析

为研究交通流相变过程问题,对一维交通流进行元胞自动机模拟,进行截面车流率数据提取,并将数据经过离散的傅里叶变换进行能量谱分析．研究结果发现：在阻塞相,系统周期即为因采用周期边界条件而形成的交通激波周期;在高密度区所对应的同步交通流状态中,系统中仍然存在着周期性波动,该周期明显异于交通激波周期,因而其形成原因不能简单归结为周期边界条件的影响;在低密度区对应的自由流状态下,没有此类波动存在．     

Local Bifurcation for Steady Periodic Capillary Water Waves with Constant Vorticity

We study periodic capillary waves at the free surface of water in a flow with constant vorticity over a flat bed. Using bifurcation theory the local existence of waves of small amplitude is proved even in the presence of stagnation points in the flow. We also derive the dispersion relation.     

An experimental study of oblique transition in a Blasius boundary layer flow

Transition initiated by a pair of oblique waves was investigated experimentally in a Blasius boundary layer flow by using hot-wire measurements and flow visualisation. The oblique waves were generated by periodic blowing and suction through an array of pipes connecting to the flow through a transverse slit in the flat plate model. The structure of the flow field is described and the amplitude of individual frequency-spanwise wave number modes was determined from Fourier transforms of the disturbance velocity. In contrast to results from investigations of oblique transition at subcritical flow conditions, the transition process at the present conditions suggests the combined effect of non-modal growth of streaks and a second stage with exponential growth of oblique waves to initiate the final breakdown stage.     

Existence and uniqueness of a solution to a problem of steady composite waves on the surface of a liquid flowing over a wavy bottom

Composite waves on the surface of the stationary flow of a heavy ideal incompressible liquid are steady forced waves of finite amplitude which do not disappear when the pressure on the free surface becomes constant but rather are transformed into free nonlinear waves [1]. It will be shown that such waves correspond to the case of nonlinear resonance, and mathematically to the bifurcation of the solution of the fundamental integral equation describing these waves. In [2], a study is made of the problem of composite waves in a flow of finite depth generated by a variable pressure with periodic distribution along the surface of the flow. In [3], such waves are considered for a flow with a wavy bottom. In this case, composite waves are defined as steady forced waves of finite amplitude that, when the pressure becomes constant and the bottom is straightened, do not disappear but are transformed into free nonlinear waves over a flat horizontal bottom. However, an existence and uniqueness theorem was not proved for this case. The aim of the present paper is to fill this gap and investigate the conditions under which such waves can arise.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–98, July–August, 1980.     

The effect of pipe diameter on the structure of gas/liquid flow in vertical pipes

Experimental work on two-phase vertical upward flow was carried out using a 19 mm internal diameter, 7 m long pipe and studying the time series of cross-sectional average void fractions and pressure gradient which were obtained simultaneously. With the aid of a bank of published data in which the pipe diameter is the range from 0.5 to 70 mm, the effect of pipe diameter on flow characteristics of two-phase flow is investigated from various aspects. Particularly, the work focuses on the periodic structures of two-phase flow. Average film thicknesses and the gas flow rate where slug/churn and churn/annular flow transitions occur all increase as the diameter of the pipe becomes larger. On the other hand, the pressure gradients, the frequencies of the periodic structures and the velocities of disturbance waves decrease. The velocity of disturbance waves has been used to test the model of Pearce (1979). It is found that the suggested value of Pearce coefficient 0.8 is reasonable for lower liquid flow rates but becomes insufficient for higher liquid flow rates.     

Selection of solitary waves in vertically falling liquid films

Two-dimensional solitary waves at the surface of a film flow down a vertical plane are considered. When the system is subjected to inlet white noise, solitary waves are formed after an inception region and interact with each other. Using open-domain simulations of reduced equation models, we investigate numerically their late time process dynamics. Close to the instability threshold, the waves synchronize themselves into bound states. For higher values of the Reynolds number, the separation distance between the waves increases and the synchronization process at work is weaker. Performing statistics, we show that the mean characteristics of the waves correspond to the minimal value of the mean film thickness along the traveling-wave branch of solutions. In this regime, synchronization occurs through the waves tails which is associated with a change of scaling of the waves features. A similar behavior is observed performing simulations in periodic domains: the selected waves maximize the mean flow rate.     

非线性周期波及破碎波对杆件的作用力

本文采用十五阶 Stokes 波的 Pade 逼近,获得了与实验较为一致的流场,并且利用已有的破碎波的速度、加速度场,计算了非线性波和破碎波对各种杆件作用力,比较了它们的主要特征,为海洋工程设计提供依据。     

Wave propagation in periodic and disordered layered composite elastic materials

A powerful complex transfer matrix approach to wave propagation perpendicular to the layering of a composite of periodic and disordered structure is worked out showing propagating and stopping bands of time-harmonic waves and the singular cases of standing waves. A state ratio of left- and right-going plane waves is defined and interpreted geometrically in the complex plane in terms of fixed points and flow lines. For numerical considerations and extension of the approach to higher dimensional problems a continued fraction expansion of the state ratio mapping is presented. Impurity modes of wave propagation in composites with widely spaced impurity cells of different elastic materials are discussed. Stopping bands in the frequency spectrum of global waves in fully disordered composites are found to exist in the range of frequencies corresponding to common gaps in the spectrum of cnstituent regular periodic composites which are constructed from the cells of the disordered system. For those frequencies, waves propagate only a (short) finite distance and are therefore strongly localized modes in a composite of fairly large extent.     

Nash-Moser Theory for Standing Water Waves

We consider a perfect fluid in periodic motion between parallel vertical walls, above a horizontal bottom and beneath a free boundary at constant atmospheric pressure. Gravity acts vertically downwards. Suppose the underlying flow is two-dimensional in a vertical plane orthogonal to the walls and satisfies the constant-pressure condition on the free boundary where surface tension is neglected. Suppose also that it is symmetric about a plane midway between the walls, and periodic in time. Such motion, which can be extended to give a two-dimensional flow of infinite horizontal extent that is periodic in space as well as in time, is referred to as a standing wave. Unlike progressive (or steady) Stokes waves, standing waves are not stationary relative to a moving reference frame. The purpose of this paper is to show how the Nash-Moser iteration method can be adapted to give a rigorous proof of the existence of small-amplitude standing waves for which the normal component of pressure gradient on the free surface satisfies additional constraints. These constraints are imposed in advance to facilitate the a priori bounds needed for the Nash-Moser method and only solutions satisfying them have been found.(They have no obvious analogue in the theory of Stokes waves.) The presentation is self-contained and includes a version of the Nash-Moser theorem tailored for the purpose. The imposed constraints are used to define a manifold upon which iteration is carried out and a detailed account from first principles of the a priori bounds required to implement the method is given. We use the Lagrangian form of the Euler equations throughout.     

An Estimate for the Morse Index of a Stokes Wave

Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two-dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler–Lagrange equation of a certain functional; this allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result.     

Dispersion Equation for Water Waves with Vorticity and Stokes Waves on Flows with Counter-Currents

The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how flows with small-amplitude Stokes waves on the free surface bifurcate from a horizontal parallel shear flow in which counter-currents may be present. Two bifurcation mechanisms are described: one for waves with fixed Bernoulli’s constant, and the other for waves with fixed wavelength. In both cases the corresponding dispersion equations serve for defining wavelengths from which Stokes waves bifurcate. Necessary and sufficient conditions for the existence of roots of these equations are obtained. Two particular vorticity distributions are considered in order to illustrate the general results.     

Nonstationary waves in the continuously stratified flow of a fluid of finite depth

A theoretical investigation is made of the development of linear two-dimensional waves in a continuously stratified flow of an ideal incompressible fluid. The waves are generated by pressures that are independent of time and that are applied at time t=0 to a bounded region on the free surface of an initially undisturbed flow. The stationary internal waves generated by such a disturbance have been investigated in [1–3]. The nonstationary waves in a continuously stratified fluid that are generated by initial disturbances or periodic surface pressures applied to the entire free surface have been studied in [4–7] in the absence of a slow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 87–93, November–December, 1976.     

Generation of Nonlinear Waves on a Viscoelastic Coating in a Turbulent Boundary Layer

Self–induced excitation of periodic nonlinear waves on a viscoelastic coating interacting with a turbulent boundary layer of an incompressible flow is studied. The response of the flow to multiwave excitation of the coating surface is determined in the approximation of small slopes. A system of equations is obtained for complex amplitudes of multiple harmonics of a slow (divergent) wave resulting from the development of hydroelastic instability on a coating with large losses. It is shown that three–wave resonant relations between the harmonics lead to the development of explosive instability, which is stabilized due to the deformation of the mean (Sover the wave period) shear flow in the boundary layer. Conditions of soft and hard excitation of divergent waves are determined. Based on the calculations performed, qualitative features of excitation of divergent waves in known experiments are explained.     

Solitary waves and conjugate flows in a three-layer fluid

Interfacial symmetric solitary waves propagating horizontally in a three-layer fluid with constant density of each layer are investigated. A fully nonlinear numerical scheme based on integral equations is presented. The method allows for steep and overhanging waves. Equations for three-layer conjugate flows and integral properties like mass, momentum and kinetic energy are derived in parallel. In three-layer fluids the wave amplitude becomes larger than in corresponding two-layer fluids where the thickness of a pycnocline is neglected, while the opposite is true for the propagation velocity. Waves of limiting form are particularly investigated. Extreme overhanging solitary waves of elevation are found in three-layer fluids with large density differences and a thick upper layer. Surprisingly we find that the limiting waves of depression are always broad and flat, satisfying the conjugate flow equations. Mode-two waves, obtained with a periodic version of the numerical method, are accompanied by a train of small mode-one waves. Large amplitude mode-two waves, obtained with the full method, are close to one of the conjugate flow solutions.     

New families of pure gravity waves in water of infinite depth

Nonlinear periodic gravity waves propagating at a constant velocity at the surface of a fluid of infinite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. It is known that there are both regular waves (for which all the crests are at the same height) and irregular waves (for which not all the crests are at the same height). We show numerically the existence of new branches of irregular waves which bifurcate from the branch of regular waves. Our results suggest there are an infinite number of such branches. In addition we found additional new branches of irregular waves which bifurcate from the previously calculated branches of irregular waves.     

On two-dimensional linear waves in Blasius boundary layer over viscoelastic layers

This work concerns the direct numerical simulation of small-amplitude two-dimensional ribbon-excited waves in Blasius boundary layer over viscoelastic compliant layers of finite length. A vorticity-streamfunction formulation is used, which assures divergence-free solutions for the evolving flow fields. Waves in the compliant panels are governed by the viscoelastic Navier's equations. The study shows that Tollmien–Schlichting (TS) waves and compliance-induced flow instability (CIFI) waves that are predicted by linear stability theory frequently coexist on viscoelastic layers of finite length. In general, the behaviour of the waves is consistent with the predictions of linear stability theory. The edges of the compliant panels, where abrupt changes in wall property occur, are an important source of waves when they are subjected to periodic excitation by the flow. The numerical results indicate that the non-parallel effect of boundary-layer growth is destabilizing on the TS instability. It is further demonstrated that viscoelastic layers with suitable properties are able to reduce the amplification of the TS waves, and that high levels of material damping are effective in controlling the propagating CIFI.     

Generation of Periodic Motions by a Disk Performing Torsional Oscillations in a Viscous, Continuously Stratified Fluid

The solution of the problem of nonlinear generation of periodic internal waves by a boundary flow on a vertical cylinder or a horizontal disk performing torsional oscillations in an exponentially stratified fluid is constructed. The calculations are in satisfactory agreement with the results of experiments in which both horizontal and inclined disks of various diameters and a model propeller performing periodic torsional oscillations, including oscillations against a background of uniform rotation, are used as perturbation sources. The experiments were carried out over a wide range of parameters including the laminar, transition, and turbulent flow regimes. The limits of applicability of the proposed analytic theory of wave radiation are determined.     

Do huge waves exist in horizontal gas-liquid pipe flow?

Huge waves are periodic interfacial structures which are observed in vertical co-current gas-liquid two-phase flow under churn and the transition between churn and annular flows. Published data examining vertical gas-liquid flow indicate that a huge wave has either a continuous gas core surrounded by a large-scale interfacial wave or a core with a highly-agitated mixture of gas and liquid.Employing a Wire-Mesh Sensor (WMS), the spatio/temporal investigation of high flow rate horizontal air-water flow divulged some recurrent liquid structures (one may call pseudo-slugs) analogous to huge waves of (vertical) churn flow. In both cases, the blow-through (penetration of gas into the liquid structure) was the most manifest feature.Different qualitative and quantitative methods were employed to compare the behavior of pseudo-slug to churn flow. The quantitative measures included Probability Density Function analysis (PDF), distribution coefficient in drift flux model, structural velocity, core average velocity, interfacial friction factor, and slippage number. Both flow regimes demonstrated similar behavior.     

Nonlinear travelling waves in a hyperelastic rod composed of a compressible Mooney-Rivlin material

In this paper, we study strongly nonlinear axisymmetric waves in a circular cylindrical rod composed of a compressible Mooney-Rivlin material. To consider the travelling wave solutions for the governing partial differential system, we first reduce it to a nonlinear ordinary differential equation. By using the bifurcation theory of planar dynamical systems, we show that the reduced system has seven periodic annuluses with different boundaries which depend on four parameters. We further consider the bifurcation behavior of the phase portraits for the reduced one-parameter vector fields when other three parameters are fixed. Corresponding to seven different periodic annuluses, we obtain seven types of travelling wave solutions, including solitary waves of radial contraction, solitary waves of radial expansion, solitary shock waves of radial contraction, solitary shock waves of radial expansion, periodic waves and two types of periodic shock waves. These are physically acceptable solutions by the governing partial differential system. The rigorous parameter conditions for the existence of these waves are given.