Strong interference of sound pressure generated by vortex soliton with axial flow

Sound pressure generated by a thin vortex filament with axial flow is investigated on the base of soliton theory. The pressure is estimated by using the experimental results of Maxworthy et al. [J. Fluid Mech. 151, 141] where one-soliton propagation and head-on collision of two solitons are observed. Collision of two solitons gives rise to very enhanced interference of the sound pressure.     

Poisson geometry of the filament equation

Summary The Hasimoto transformation (relating vortex filament flow to the nonlinear Schrödinger equation) is interpreted in the context of Poisson geometry with the aid of a compact formula for its differential. A useful relationship is derived between Killing fields for soliton solutions of the filament flow and the sequence of commuting Hamiltonian flows.     

A note on the modified simple equation method applied to Sharma-Tasso-Olver equation

Jawad et al. have applied the modified simple equation method to find the exact solutions of the nonlinear Fitzhugh-Naguma equation and the nonlinear Sharma-Tasso-Olver equation. The analysis of the Sharma-Tasso-Olver equation obtained by Jawad et al. is based on variant of the modified simple equation method. In this paper, we provide its direct application and obtain new 1- soliton solutions.     

耗散双曲Yamabe流的精确解

本文介绍了一种新的几何流, 得到了这种流的一些精确解. 首先得到了初始度量为Einstein的解. 其次得到了具有轴对称的解. 最后, 作为这种流的特殊解, 定义了稳定耗散双曲Yamabe孤子, 而且给出了这种孤子解所满足的方程.     

A new type of soliton behavior of the Davey-Stewartson equations in a plasma system

The Davey-Stewartson equations are derived in a plasma system by the reductive perturbation method. Modulational instability of a plane wave is discussed including a finite ion temperature effect. Certain particular solutions of the equations are also obtained by means of a linearization technique. One of them shows the reconnection of solitons. We show that this reconnection solution corresponds to the resonant type of usual soliton solutions.Department of Aeronautics, Faculty of Engineering, The University of Tokyo, Hongon 7-3-1, Bunkyo-ku, Tokyo 113, Japan. College of Arts and Sciences, The University of Tokyo, Komaba 3-8-1, Meguroku, Tokyo 153, Japan. Department of Mathematical Sciences, The University of Tokyo, Komaba 3-8-1, Meguroku, Tokyo 153, Japan. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 487–498, June, 1994.     

Asymptotic Analysis of Pulse Dynamics in Mode-Locked Lasers

Solitons of the power-energy saturation (PES) equation are studied using adiabatic perturbation theory. In the anomalous regime individual soliton pulses are found to be well approximated by solutions of the classical nonlinear Schrödinger (NLS) equation with the key parameters of the soliton changing slowly as they evolve. Evolution equations are found for the pulse amplitude(s), velocity(ies), position(s), and phase(s) using integral relations derived from the PES equation. The results from the integral relations are shown to agree with multi-scale perturbation theory. It is shown that the single soliton case exhibits mode-locking behavior for a wide range of parameters, while the higher states form effective bound states. Using the fact that there is weak overlap between tails of interacting solitons, evolution equations are derived for the relative amplitudes, velocities, positions, and phase differences. Comparisons of interacting soliton behavior between the PES equation and the classical NLS equation are also exhibited.     

On the bidirectional vortex and other similarity solutions in spherical coordinates

The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid, rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex. This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach to other complex fluid motions that are easier to capture using spherical coordinates.     

Point vortices and classical orthogonal polynomials

Stationary equilibria of point vortices in the plane and on the cylinder in the presence of a background flow are studied. Vortex systems with an arbitrary choice of circulations are considered. Differential equations satisfied by generating polynomials of vortex configurations are derived. It is shown that these equations can be reduced to a single one. It is found that polynomials that are Wronskians of classical orthogonal polynomials solve the latter equation. As a consequence vortex equilibria at a certain choice of background flows can be described with the help of Wronskians of classical orthogonal polynomials.     

Computational study of decaying annular vortex flow using the Rε/k − ε turbulence model

In this article, we present three dimensional CFD study of turbulent vortex flow in an annular passage using OpenFOAM 1.6. The vortex flow is generated by introducing the flow through a tangential entry to the passage. For the analysis presented in this article, turbulence was modeled using the R_ε/k − ε model, in addition, a comparison between such model with the standard k − ε model was conducted and discussed. The main characteristics of the flow such as vortex structure and recirculation zone were investigated. It was found that flow is subjected to Rankine vortex structure with three forced vortex regimes and a free vortex region near to the outer wall. The phenomenon of vortex decay was investigated by depicting the swirl number trend along the axial direction of the flow domain. It was found that the vortex decay is subjected to an exponential decay behavior. New coefficients for the exponential decay correlation were derived based on local values of velocity components in different radial planes.     

Dark soliton dynamics under the complex Ginzburg–Landau equation

The dynamical properties of the complex Ginzburg–Landau equation are considered in the defocusing (normal dispersion) regime. It is found that under appropriate conditions stable evolution of dark solitons can occur. These conditions are derived using a newly developed perturbation theory that also reveals an important aspect of the dynamics: the formation of a shelf that accompanies the soliton and is an intricate part of its evolution. Further conditions to suppress this effect are also derived. These analytical predictions are found to be in excellent agreement with direct numerical simulations.     

Analytical solutions of laminar swirl decay in a straight pipe

In this work, the laminar swirl flow in a straight pipe is revisited and solved analytically by using prescribed axial flow velocity profiles. Based on two axial velocity profiles, namely a slug flow and a developed parabolic velocity profiles, the swirl velocity equation is solved by the separation of variable technique for a rather general inlet swirl velocity distribution, which includes a forced vortex in the core and a free vortex near the wall. The solutions are expressed by the Bessel function for the slug flow and by the generalized Laguerre function for the developed parabolic velocity. Numerical examples are calculated and plotted for different combinations of influential parameters. The effects of the Reynolds number, the pipe axial distance, and the inlet swirl profiles on the swirl velocity distribution and the swirl decay are analyzed. The current results offer analytical equations to estimate the decay rate and the outlet swirl intensity and velocity distribution for the design of swirl flow devices.     

气流排除倾斜管道积水的理论分析

运用作者推导的动量积分关系式,分析了向有积水的斜置管道中分别吹入轴向气流和螺旋气流时积水的运动情况。结果表明:在大多数情况下,螺旋气流能除去斜置管道中积水;而轴向气流不能除去积水,一段时间后会出现逆流。这一结果与Horii和赵耀华等人在这个问题上所做的实验结果一致。此外,还讨论了不同的初始条件对排水情况的影响。     

Existence and numerical modelling of vortex rings with elliptic boundaries

We revisit in this paper the theory of axisymmetric vortex rings in an ideal fluid. The boundary separating the vortex ring from the external (potential) flow is assumed of elliptic shape. For a given distribution of vorticity in the vortex core, we theoretically put into evidence the critical parameter for the existence of non-trivial solutions, thus confirming the numerical observation of Durst et al. [ZAMP 32 (1981) 156]. A sharp estimation of the critical threshold is analytically derived. Theoretical predictions are confirmed by numerical simulations using finite elements. A new numerical algorithm is presented and shown to display better performances compared to previous published algorithms using finite differences. The convergence of the iterative algorithm is proved using the theory of elliptic partial differential equations with discontinuous nonlinearities.     

Numerical simulation of the interaction between vortex ring and bubble plume

In present paper a three-dimensional Vortex-In-Cell method with two-way coupling effect was developed to study the bubble plume entrainment by a vortex ring. In this method the continuous flow was calculated by the three-dimensional Vortex-In-Cell method and the bubbles are tracked through bubble motion equation. Two-way coupling effect between continuous flow and dispersed bubbles is considered by introducing a vorticity source term, which is induced by the change of void fraction gradient in each computational cell. After validated by the comparison between experimental measurements and simulation results for the motion of vortex rings and the rising velocity of bubble plume, present method is implemented to simulate the interaction between an evolving vortex ring and a rising bubble plume. It was found that there is little effect of the bubble entrainment to the total circulation of vortex ring while the effect of bubble entrainment to the vortex ring structure is quite obvious. The bubble entrainment by the vortex ring not only changed the vorticity distribution in the vortex structure, but also displaced the positions of the vortex cores. The vorticity in the lower vortex core of the vortex ring decreases more than that in the upper vortex core of the vortex ring while the vortex core in the upper part of the vortex ring is displaced to the center of vortex ring by the entrained bubbles. Smaller bubbles are easier to be entrained by the large scale vortex structure and the transportation distance is in inverse proportion to bubble diameter.     

Numerical simulation of vortex induced vibrations and its control by suction and blowing

The vortex formation and shedding behind bluff structures is influenced by fluid flow parameters such as, Reynolds number, surface roughness, turbulence level, etc. and structural parameters such as, mass ratio, frequency ratio, damping ratio, etc. When a structure is flexibly mounted, the Kármán vortex street formed behind the structure gives rise to vortex induced oscillations. The control of these flow induced vibrations is of paramount practical importance for a wide range of designs. An analysis of flow patterns behind these structures would enable better understanding of wake properties and their control. In the present study, flow past a smooth circular cylinder is numerically simulated by coupling the mass, momentum conservation equations along with a dynamical evolution equation for the structure. An active flow control strategy based on zero net mass injection is designed and implemented to assess its efficacy. A three actuator system in the form of suction and blowing slots are positioned on the cylinder surface. A single blowing slot is located on the leeward side of the cylinder, while two suction slots are positioned at an angle α = 100°. This system is found to effectively annihilate the vortex induced oscillations, when the quantum of actuations is about three times the free stream velocity. The dynamic adaptability of the proposed control strategy and its ability to suppress vortex induced oscillations is verified. The exact quantum of actuation involved in wake control is achieved by integrating a control equation to decide the actuator response in the form of a closed loop feed back system. Simulations are extended to high Reynolds number flows by employing eddy viscosity based turbulence models. The three actuator system is found to effectively suppress vortex induced oscillations.     

Maxwell流体在有限长管道中作不稳定的蠕动传输:食道吞咽进程分析

解析地研究了有限长管道中Maxwell流体的不稳定蠕动传输.管壁受到不超过静止边界的收缩波作用.对无量纲形式的方程,应用长波长近似进行分析.导出了轴向速度和径向速度的表达式,评估了沿波长和管道长度方向的压力.讨论了回流现象,确定了回流极限区域.对食道中咀嚼食物(如面包、蛋白等)传输的数学公式给出了物理上的解释.可以看出,与Newton流体相比,Maxwell流体有利于在食道中的流动.与Takahashi等[Rheology,1999,27:169-172]的实验结果相符合.进一步揭示了松弛时间既不影响剪应力,也不影响回流极限.发现了压力的峰值,对整数值波列是相同的,而对非整数值波列是不同的.     

Soliton solutions and Bäcklund transformation for the complex Ginzburg-Landau equation

Symbolically investigated in this paper is the complex Ginzburg-Landau (CGL) equation. With the Hirota method, both bright and dark soliton solutions for the CGL equation are obtained simultaneously. New Bäcklund transformation in the bilinear form is derived. Relevant properties and features are discussed. Solitons can be compressed (amplified) when the nonlinear (linear) dispersion effect is enhanced. Meanwhile, central frequency of the soliton can be affected by the nonlinear and linear dispersion effects. Besides, directions of the movement for the soliton central frequency can be adjusted. Results of this paper would be of certain value to the studies on the soliton compression and amplification.     

Solitary waves in dusty plasmas with variable dust charge and two temperature ions

Propagation of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions is analyzed. The Kadomtsev–Petviashivili (KP) equation is derived by using the reductive perturbation theory. A Sagdeev potential for this system has been proposed. This potential is used to study the stability conditions and existence of solitonic solutions. Also, it is shown that a rarefactive soliton can be propagates in most of the cases. The soliton energy has been calculated and a linear dispersion relation has been obtained using the standard normal-modes analysis. The effects of variable dust charge on the amplitude, width and energy of the soliton and its effects on the angular frequency of linear wave are discussed too. It is shown that the amplitude of solitary waves of KP equation diverges at critical values of plasma parameters. Solitonic solutions of modified KP equation with finite amplitude in this situation are derived.     

热源强迫的边界层低涡解及其应用

考虑边界层低涡为受非绝热加热和摩擦强迫并满足热成风平衡的轴对称涡旋系统,采用Boussinesq近似,通过求解柱坐标系中涡旋模式的初值问题,分析了热源强迫对低涡流场结构的影响．结果表明:热源强迫对低涡的流场结构有重要影响,并且这种影响的具体表现形式与加热的径向分布有密切关系．对边界层涡旋解讨论的结果可以解释青藏高原低涡系统的某些重要结构特征．