Localization of Analytic Regularity Criteria on the Vorticity and Balance Between the Vorticity Magnitude and Coherence of the Vorticity Direction in the 3D NSE

The first part of the paper provides spatio-temporal localization of a family of analytic regularity classes for the 3D NSE obtained by Beirao Da Veiga (space-time integrability of the gradient of the velocity on \mathbbR³ ×(0,T){\mathbb{R}^3 \times (0,T)} which is out of the range of the Sobolev embedding theorem reduction to the classical Foias-Ladyzhenskaya-Prodi-Serrin space-time integrability conditions on the velocity) as well as the localization of the Beale-Kato-Majda regularity criterion (time integrability of the L ^∞-norm of the vorticity). The second part introduces a family of local, scaling invariant, hybrid geometric-analytic classes in which coherence of the vorticity direction serves as a weight in the local spatio-temporal integrability of the vorticity magnitude.     

Investigation of Turbulent Transition in Plane Couette Flows Using Energy Gradient Method

The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this method, it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance, for given imposed disturbance. For a given flow geometry and fluid properties, when the maximum of the function $K$ (a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction) in the flow field is larger than a certain critical value, it is expected that instability would occur for some initial disturbances. In this paper, using the energy gradient analysis, the equation for calculating the energy gradient function $K$ for plane Couette flow is derived. The result indicates that $K$ reaches the maximum at the moving walls. Thus, the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high $\operatorname{Re}$ for given same level of normalized perturbation in the domain. The critical value of $K$ at turbulent transition, which is observed from experiments, is about 370 for plane Couette flow when two walls move in opposite directions (anti-symmetry). This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow (385-389). Therefore, it is concluded that the critical value of $K$ at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure (symmetrical case) and shear driven flows (anti-symmetrical case).     

Determining the Spatial Properties of a Turbulent Transverse Flow via Multi-Frequency Acoustic Probing

The results are presented from an experimental study of solving the inverse problem of recovering a turbulent flow’s velocity and its position in space by analyzing the spectrum of fluctuations in an acoustic signal of different frequencies intersecting the flow. The conditions for and accuracy of recovering turbulent flow characteristics are discussed in terms of a multifrequency signal propagating along one acoustic path. The study is performed using a muffled acoustic chamber with a jet of air serving as a turbulent flow. Despite the physical character of the experiments, their results can be applied to problems of atmospheric, aero-, and oceanic acoustics.     

湍流大气对量子密钥分布系统性能的影响

自由空间量子密钥分布系统是全球性量子保密通信的关键组成部分之一。因此研究湍流大气信道对量子密钥分布系统性能的影响就非常重要。使用光束近场传播和统计分析的方法定量分析了湍流大气信道对基于BB84协议的自由空间量子密钥分布系统的误码率的影响。数值计算结果表明,大气衰减系数超过-3dB/km时,大气衰减对量子密钥分布系统的误码率影响很大;在大气传输因子小于0.5的区域,系统误码率比无湍流影响时的系统误码率高出一个数量级。     

Jet-medium interactions: Wakes in the QCD medium

We calculate the wake induced in a hot, dense QCD medium by a fast parton in the framework of linear response theory. We discuss two different scenarios: i) a weakly coupled quark gluon plasma (pQGP) described by hardthermal loop (HTL) perturbation theory and ii) a scenario where the plasma has the properties of a quantum liquid. We show that a Mach cone can appear in the second scenario, but not in the first one.     

测定微束微区X射线探针分析仪焦平面的实验研究

微束微区X射线探针分析仪借助会聚X光透镜把X射线聚焦.针对仪器调试过程中需确定出口焦平面位置的难题.采用拟合曲线荧光分析方法方便快速地确定出口焦平面的位置.方法是用直径小于X焦斑直径的金属丝在不同测量平面上进行微动测量,因X光强度沿径向呈高斯分布,所以金属丝中元素荧光强度随位移也呈高斯分布.通过计算得出不同测量平面上同...     

光束在尾流气泡中传输的复散射效应

为了了解光束在尾流气泡中的传输特性,为前向光尾流的探测提供理论依据,研究了光束在尾流中传输时传播方向上和横截面方向上的辐射强度分布特性.基于辐射传输方程的小角度近似解,得到了探测截面上的约化强度和漫射强度的表达式,其中漫射强度表征了复散射的强弱|针对典型的尾流气泡分布,通过数值计算分析了光束传输方向上的约化强度和漫射强度与接收视场角、光学厚度和光束大小的关系,也计算分析了光束横截面方向上的辐射强度随光束大小和横向距离的变化关系.结果表明,光束在尾流气泡中传输时复散射效应明显,且复散射的强弱与接收视场角、光束直径、光学厚度和横向距离密切相关.     

气泡数密度对尾流光束衰减测量的影响

为准确地测量出尾流气泡群的衰减,提高前向光尾流探测的可靠性,研究了气泡数密度对尾流光束衰减测量的影响.基于辐射传输方程的小角度近似解,得到了探测截面上的约化功率和漫射功率的表达式.根据测量条件,引入了有尾流气泡和无尾流气泡时探测截面上接收到的辐射功率之比作为透射函数,并进一步引进了复散射校正因子,它表征了复散射效应的强弱.针对典型的尾流气泡分布,通过数值计算得到了不同测量条件下气泡数密度与复散射校正因子、透射函数的关系.数值计算结果表明：复散射校正因子都随气泡数密度的增大单调的增大,透射函数都随气泡数密度的增大单调的减小;测量条件不同,气泡数密度对光束衰减的影响也不同.研究结果表明,给定测量条件和透射比时,利用小角度辐射方程可以得到气泡群数密度的量化信息.     

光束在尾流气泡中传输的复散射效应

为了了解光束在尾流气泡中的传输特性,为前向光尾流的探测提供理论依据,研究了光束在尾流中传输时传播方向上和横截面方向上的辐射强度分布特性.基于辐射传输方程的小角度近似解,得到了探测截面上的约化强度和漫射强度的表达式,其中漫射强度表征了复散射的强弱;针对典型的尾流气泡分布,通过数值计算分析了光束传输方向上的约化强度和漫射强度与接收视场角、光学厚度和光束大小的关系,也计算分析了光束横截面方向上的辐射强度随光束大小和横向距离的变化关系.结果表明,光束在尾流气泡中传输时复散射效应明显,且复散射的强弱与接收视场角、光束直径、光学厚度和横向距离密切相关.     

Vorticity affects the stability of neutron stars

The spin rate Omega of neutron stars at a given temperature T is constrained by the interplay between gravitational-radiation instabilities and viscous damping. Navier-Stokes theory has been used to calculate the viscous damping time scales and produce a stability curve for r modes in the (Omega,T) plane. In Navier-Stokes theory, viscosity is independent of vorticity, but kinetic theory predicts a coupling of vorticity to the shear viscosity. We calculate this coupling and show that it can in principle significantly modify the stability diagram at lower temperatures. As a result, colder stars can remain stable at higher spin rates.     

Boltzmann's Formulation of the Helmholtz Vorticity Theorem

A dual form of the general relativistic and covariant generalization of the first vorticity theorem of Helmholtz is proven. This dual form is the generalization of Boltzmann's formulation of the Helmholtz theorem.     

Vorticity conditioning in the computation of two-dimensional viscous flows

The problem of evaluating the boundary values of the vorticity in the calculation of two-dimensional viscous flows is considered. It is shown that the splitting of the fourth-order equation for the stream function into two second-order problems implies specific integral conditions which fix the abstract projection of the vorticity field with respect, to the linear manifold of the harmonic functions. These conditions are a direct consequence of the boundary conditions on the velocity, and ensure satisfaction of physically essential conservation laws for the vorticity. The discrete analogue of, the projection conditions produces as many algebraic equations as the number of boundary points and requires the solution of an equal number of Dirichlet problems. In the particular case of stationary linearized equations (Stokes equations) a direct, i.e., noniterative method of solution is obtained. Steady and unsteady computational schemes relying on the projection conditions on the vorticity are introduced and extensive numerical results of finite difference calculations of the driven-cavity model problem are reported and discussed.     

Vorticity waves in problems of hydrodynamic stability

The known problem of flow transition near a circular cylinder at Re = 40 from a symmetrical form to the Karman vortex street can be considered as the problem of vortex wave development and intensification. Development of three bundles of vortex waves of low intensity is observed in a wake of a cylinder; these bundles are easily visualized as the structures of relative vorticity $ \bar \Omega $ \bar \Omega = Ω(t ₁) − Ω(t ₀): difference of vorticity Ω at two time moments, t ₀ being fixed. In the field of $ \bar \Omega $ \bar \Omega the alternating structure of quadrupoles is characterized by linear parameter l = h/d: the ratio of the width of the central bundle of vortex waves to the distance between the centers of quadrupoles of a “single sign”. When l = 0.281 is achieved, which coincides with the value of the same parameter of a stable Karman street, the transition from symmetrical streamlining by viscous incompressible liquid to the vortex street occurs.     

用传感器探究影响向心力大小因素的实验装置研究

实验探究向心力F的大小与质量m、角速度ω和半径r之间的关系是高中物理的一个重要实验。针对传统实验装置存在的不足,新设计的实验装置利用PASCO力传感器测向心力的大小,用调速电机来改变金属小球作圆周运动的角速度,并用霍尔传感器测量电机的转速,金属小球的质量和小球的旋转半径则定量改变。新的实验装置能定量地探究向心力的大小F与质量m、角速度ω和半径r之间的关系,实验结果精确度高,演示效果明显,方便师生使用和操作,值得推广。     

舰船远场尾流气泡分布特性的数值模拟

为了了解舰船尾流中气泡的分布特征,为激光探测舰船尾流提供依据,建立了计算热分层环境中舰船远场尾流中气泡数密度分布的数学模型,该模型由抛物化的RaNS方程及气泡输运方程组成,采用k－ε两方程湍流模式.利用该模型数值模拟了舰船尾流中的气泡数密度分布特征、气泡尾流宽度扩展规律,气泡数密度衰减规律,并与实测结果进行了比较,二者定性符合得较好.数值模拟表明舰船尾流中半径为10~30 μm的气泡存活时间最长, 为了确保能在距船尾5 km处还能探测到舰船气泡尾流,其探测的对象应以半径10~30 μm的气泡为主,并且探测准确度至少应能达到识别出初始截面上气泡数密度的3%.     

Magnitude of Regge cut contributions in the triple-Regge region

Starting from the reggeon calculus, the various possibilities of absorptive pomeron cut corrections in the triple-Regge region are considered. For the case of pp → pX, we estimate their importance at present day energies. We conclude that at highest ISR energies, pomeron cuts of the eikonal type are not enough, and enhanced diagrams with at least one additional triple-pomeron coupling need be included.     

影响玻璃微珠回向反射性能的主要因素分析

从理论和实验两方面分析了玻璃微珠的回向反射特性,主要讨论了玻璃微珠的折射率和其反射层面积这两个因素对回向反射性能的影响. 研究结果表明,折射率增大, 折射率小于2时,回向反射性能逐渐增强, 相反, 在折射率大于2时, 回向反射性能减弱; 反射层面积的大小会影响入射光线的完整回向反射过程; 最后定义了有效回向反射角度, 并给出了玻璃微珠在激光照射下的二维回向反射光照度分布.     

影响光谱辐亮度标定因素的分析

在利用漫反射板标定光谱辐亮度的实验装置中,标准灯完全可以近似为点光源。通过对进入光谱仪的辐射通量的数值积分,可以对应求出仪器的实测光谱辐亮度的计算公式。计算表明,实测光谱辐亮度并不等于漫反射板表面的光谱辐亮度,而有一个随标定条件变化的微小差值。通过计算,对光谱仪与漫反射板的距离、光谱仪入射挟缝的光轴与漫反射板法线的夹角以及标准灯与漫反射板的距离等影响光谱仪标定的因素进行分析,得到了最佳的标定条件。讨论了理想标定情况、光谱仪视场趋于一点的极限情况和采用实际的双向反射分布函数已知的漫反射板标定时,实测光谱辐亮度的计算情况。