Self-Similar Unsteady Viscous Flow

Four examples of self-similar flows of a viscous fluid are considered: separated flow over an expanding plate immersed in an unbounded unsteady viscous flow, the evolution of the velocity field induced by a vortex-source, the flow near an unsteadily moving permeable flat plate, and the flow near an unsteadily rotating disc. For the first example, a numerical solution is constructed. For the next two examples, an analytical solution is found, while the solution of the last problem is reduced to a system of ordinary differential equations.     

Mass-conserving self-similar solutions to coagulation–fragmentation equations

Existence of mass-conserving self-similar solutions with a sufficiently small total mass is proved for a specific class of homogeneous coagulation and fragmentation coefficients. The proof combines a dynamical approach to construct such solutions for a regularized coagulation–fragmentation equation in scaling variables and a compactness method.     

不稳定性对爆轰波楔面马赫反射的影响规律研究

采用一种两步化学反应模型对胞格爆轰波的楔面马赫反射过程进行了数值研究,从而澄清和解释胞格不稳定性对马赫反射发展模式和自相似性的影响。考虑到反应欧拉方程源项的刚性问题,本文采用附加RungeKutta方法耦合非刚性对流项和刚性反应源项,对流项的离散采用五阶精度的WENO格式。计算结果表明,对于稳定胞格爆轰波而言,其马赫反射过程本质上与ZND爆轰波的马赫反射是一致的,整体上不存在自相似性,胞格不稳定性只是造成了三波点轨迹线局部小振幅的波动。在楔面顶点附近,由于马赫杆是强过驱的,爆轰波的马赫反射过程是自相似的。在远场,爆轰波马赫反射的三波点轨迹线渐近的趋向于一条直线,说明重新获得了自相似性。对于不稳定的爆轰波,由于自身的不稳定性可以与马赫反射的强度相匹配,定义其三波点的轨迹是困难的,进行自相似性分析没有意义。     

The Plane Wedge Problem Loaded at Its Apex – the Self-similarity Property and the Characteristic Vector

In the present paper the elastostatic problem of a generally anisotropic and angularly inhomogeneous plane wedge loaded at its apex by a concentrated force, is studied in linear elasticity. At first the self-similarity property is formulated and the stress field of the inhomogeneous anisotropic self-similar wedge problem, is deduced. The wedge is radially separated and the plane wedge problem is reformulated by the introduction of a characteristic vector. Furthermore, the angular distribution of the load is determined. The multi-material wedge problem in terms of a formulation based on the isotropic angularly inhomogeneous wedge, is confronted, and necessary conditions that ensure the self-similarity property, are found. Finally, the similar elastostatic wedge problems and the involution between stresses, are studied. Mathematics Subject Classifications (2000) 74B05, 74K30, 34B05, 51N15.     

Effect of boundary conditions on turbulence characteristics in two-phase jet flows with phase transitions

It is shown that there are no self-similarity and similarity of transverse fields of correlation moments of fluctuating parameters of phases in two-phase jets, in contrast to one-phase jets. The influence of the initial values of a number of parameters of a two-phase jet (gas temperature, volume concentration of droplets in the initial cross section, and radius of the initial cross section of the jet) on turbulence characteristics is analyzed on the basis of numerical simulations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 29–40, May–June, 2005.     

Self-similar solutions of the second-order model of the far turbulent wake

A second-order semi-empirical two-dimensional model of turbulence in the approximation of the far turbulent wake is considered. The sought quantities are the velocity defect, kinetic turbulent energy, energy dissipation, and Reynolds stress. The full group of transformations admitted by this model is found. Self-similar solutions satisfying natural boundary conditions are constructed. The solutions obtained agree with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 74–78, March–April, 2008.     

Dynamics Behaviors and Scaling in Intermittent Turbulence of a Shell Model

In this paper, the dynamics behaviors on fo-δ parameter surface is investigated for Gledzer-Ohkitani- Yamada model We indicate the type of intermittency chaos transitions is saddle node bifurcation. We plot phase diagram on fo-δ parameter surface, which is divided into periodic, quasi-periodic, and intermittent chaos areas. By means of varying Taylor-microscale Reynolds number, we calculate the extended self-similarity of velocity structure function.     

Fractal growth kinematics abstracted from snowflakes: topological evolution

Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.     

xistence condition of one-dimensional self-similar motion of ideal gas

流体力学自相似运动的外延判据不太完备,对微分方程组做无量纲化处理后,得到以空间相 对坐标\xi和距离$r$为自变量的理想气体一维自相似运动微分方程的基本物理特 征量解函数,它们具有Y(\xi ,r ) = y ( \xi )r^{C_Y }的形式,即对于确定 的\xi, 特征量函数Y ( \xi ,r )具有空间标度不变性. 这种标度不变性是理 想气体一维不定常流自相似运动的存在条件.     

Towards a Characterization of Self-Similar Tilings in Terms of Derived Voronoï Tessellations

In this paper, a technique for analyzing levels of hierarchy in a tiling of Euclidean space is presented. Fixing a central configuration P of tiles in , a `derived Voronoï' tessellation _P is constructed based on the locations of copies of P in . A family of derived Voronoï tilings is formed by allowing the central configurations to vary through an infinite number of possibilities. The family will normally be an infinite one, but we show that for a self-similar tiling it is finite up to similarity. In addition, we show that if the family is finite up to similarity, then is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided.