Free-surface Boundary-layer Flow on a Curved Bed

We consider high-Reynolds-number flow on a curved bed with afree surface at constant pressure. If the dimensionless filmthickness and the Reynolds number R based on film thicknessare related by R = = O(1) for large values of R, then the boundary-layerequations with appropriate boundary conditions hold. An elementaryapproximation, related to lubrication theory, is obtained. Wealso consider approximations in transition regions which appearnecessary if a circular bed is joined directly to a straightbed, with continuous slope.     

涡旋流动的空间不稳定性分析

本文研究无粘、不可压缩流体的涡旋流动的空间不稳定性,假定扰动波的波数k=k_r+ik_i是一复数,而它的频率ω为一给定的实数。这一假定意味着扰动沿涡旋流动的轴向随距离的增长而增长,但不随时间而增长。这种扰动的产生称之为空间不稳定性;与之相对应的是时间不稳定性,扰动波的波数k为一实数,而频率ω=ω_r+iω_i是一复数。本文的结果表明空间不稳定性分析是全面认识涡旋流动不稳定性的一种有用的工具。     

Long-Wave Instability in a Three-Layer Stratified Shear Flow

In inviscid fluid flows, instability can occur because of a resonance between two wave modes. For the case when the modes remain distinct at the critical point where the wave phase speeds coincide, then in the weakly nonlinear, long-wave limit, there is an expectation that the generic outcome is a model consisting of two coupled Korteweg–deVries equations. This situation is examined for a certain three-layer stratified shear flow.     

弯曲血管中的血液流动和大分子传质

采用数值模拟的方法,研究主动脉弯曲血管中的定常/脉动流动及低密度脂肪蛋白(LDL)和血清白蛋白(Albumin)传质．计算结果表明,对于主动脉弓模型,二次流漩涡的位置随时间变化．在弯曲变化比较剧烈的区域大分子浓度较高,壁面浓度外壁高于内壁．这些流动变化比较剧烈的区域可能是动脉硬化或血栓形成的危险区域．     

非轴对称模型Hagen-Poiseuille流的不稳定性

本文讨论流体通过圆管的运动不稳定性问题.作为流体运动所受的扰动波,我们考虑一个三维非线性模型.它的相关振幅函数满足扩散方程,当流体的雷诺数增大时,由于复杂的分子扩散和流体粘性的相互作用.该方程的扩散系数会出现负值.在"负扩散"现象出现时.在流体运动中出现的"湍流段"内部会引起能量的集中和使流体的阻尼减少.文中所得结果对说明圆管流中出现湍流段的实验现象是有价值的.     

轴对称模型的Hagen-Poiseuille流的运动不稳定性

本文讨论流体通过圆管的运动不稳定性问题。作为流体运动所受的干扰波,我们考虑了一个非线性轴对称模型。它对应的相关振幅函数满足扩散方程,且由于复杂的分子运动和流体粘性的相互作用,当流体的雷诺数增大时其扩散系数会出现负值。如负扩散现象出现,在流体运动中出现的湍流段内会引起流体的能量集中,并扮演减少阻尼的角色。     

圆截面弯管流动的数值研究

本文利用有限差分方法研究稍微有点弯曲的圆截面管道中粘性流体的稳定流动,数值结果表明我们所取的算法是合理的和有效的。     

Long-Time Instability of the Couette Flow in Low Gevrey Spaces

We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2. A big novelty is that this critical space is due to an instability mechanism which is completely nonlinear and is due to some energy cascade. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

Asymptotic Behavior of Micropolar Fluid Flow Through a Curved Pipe

We study the stationary motion of a micropolar fluid in a thin (or long) curved pipe via rigorous asymptotic analysis. An asymptotic solution is found, showing explicitly the effects of pipe’s distortion and microstructure on the effective behavior of the flow. We justify the obtained model by proving the corresponding error estimate.     

Global Existence of Supersonic Flow Past a Curved Convex Wedge

In this paper we discuss the supersonic flow past a curved convex wedge. Our conclusion is that if the vertex angle of the wedge is less than a critical angle, the shock attached the head of the wedge is weak, and if the wedge is formed by a smooth convex curve, monotonically increasing, then the global solution of such a boundary value problem exists.     

Local Change of Coordinates for Grid-Functions on Regions with Curved Boundary

Local change of coordinates, providing an appropriate transformation of functions on a domain Ω ∩ R ⁿ into functions on R ⁿ and R ⁺_n, is a well-known and frequently used technical tool in the theory of Sobolev-spaces W^m,p (Ω) and partial differential equations. In this paper we propose a corresponding transformation mapping grid-functions on regular grids Ω_h into functions on R ⁿ_h and R ⁿ_h,+ which as in the continuous case can be used to remedy various difficulties arising the curved boundary of Ω.     

Factors Influencing the Disturbed Flow Patterns Downstream of Curved Atherosclerotic Arteries

Pulsatile blood flows in curved atherosclerotic arteries are studied by com- puter simulations.Computations are carried out with various values of physiological parameters to examine the effects of flow parameters on the disturbed flow patterns downstream of a curved artery with a stenosis at the inner wall.The numerical re- suits indicate a strong dependence of flow pattern on the blood viscosity and inlet flow rate,while the influence of the inlet flow profile to the flow pattem in downstream is negligible.     

弯曲圆管内漩涡结构分叉现象的理论研究

利用拓扑结构分析方法,分析了弯曲圆管内定常流在横截面上流线的奇点个数及分布规律,给出了二次流的漩涡数目由2个变为4个,流态结构发生分叉现象的理论判据。进而,利用Galerkin方法,得到了弯曲圆管内定常流的流函数和轴向速度的半解析表达式,给出了流态结构发生分叉现象的临界Dean数,所得结果与理论判则一致。     

重力场中Navier-Stokes方程的线性不稳定性

研究了三维不可压粘性Navier-Stokes方程的线性不稳定性.即当流体处在重力场时,若稳态密度有一定的连续性并随着高度的增加而增加时(即Rayleigh-Taylor密度),重力场中的Navier-Stokes流体是线性不稳定的.利用变分法解出线性方程的线性不稳定解.     

A Necessary and Sufficient Instability Condition for Inviscid Shear Flow

We derive a condition that is necessary and sufficient for the instability of inviscid, two-dimensional, plane-parallel, shear flow with equilibrium velocity profiles that are monotonic, real analytic, functions of the cross-stream coordinate. The analysis, which is based upon the Nyquist method, includes a means for delineating the possible kinds of bifurcations that involve the presence of the continuous spectrum, including those that occur at nonzero wave number. Several examples are given.     

Asymptotic Approach to the Problem of Boundary Layer Instability in Transonic Flow

Tollmien–Schlichting waves can be analyzed using the Prandtl equations involving selfinduced pressure. This circumstance was used as a starting point to examine the properties of the dispersion relation and the eigenmode spectrum, which includes modes with amplitudes increasing with time. The fact that the asymptotic equations for a nonclassical boundary layer (near the lower branch of the neutral curve) have unstable fluctuation solutions is well known in the case of subsonic and transonic flows. At the same time, similar solutions for supersonic external flows do not contain unstable modes. The bifurcation pattern of the behavior of dispersion curves in complex domains gives a mathematical explanation of the sharp change in the stability properties occurring in the transonic range.     

Local Entropy Conditions in Transonic Potential Flow Problems

The transonic potential flow problem is handled as a variational problem over a closed convex set which is given by a bound for the gas velocity and by a local entropy condition. It can be shown that the minimum problem has a solution though the functional need not be convex and the given set is not compact. Furthermore, the convergence of an approximation method (KATCHANOV'S method) for the solution to the corresponding variational inequality is proved.     

Buckling Instability of a Thick Rectangular Plate of a Composite Material with a Spatially Periodically Curved Structure

Within the framework of the continuum approach for composite materials with a spatially curved structure developed by Akbarov and Guz', with the use of the three-dimensional linearized theory of stability, the buckling instability of a rectangular plate made of a composite material is investigated. Various edge conditions are considered, and, for obtaining a numerical result, a three-dimensional FEM modelling is developed. Uniaxial and biaxial precritical compression of the plate is analyzed. The numerical results presented illustrate the influence of problem parameters on the critical relative shortening of the plate.