Homogeneous Isotropic Turbulence: Geometric and Isometry Properties of the 2-point Velocity Correlation Tensor

The emphasis of this review is both the geometric realization of the 2-point velocity correlation tensor field B_ij (x,x′,t) and isometries of the correlation space K³ equipped with a (pseudo-) Riemannian metrics ds²(t) generated by the tensor field. The special form of this tensor field for homogeneous isotropic turbulence specifies ds²(t) as the semi-reducible pseudo-Riemannian metric. This construction presents the template for the application of methods of Riemannian geometry in turbulence to observe, in particular, the deformation of length scales of turbulent motion localized within a singled out fluid volume of the flow in time. This also allows to use common concepts and technics of Lagrangian mechanics for a Lagrangian system (M^t, ds²(t)), M^t ? K³. Here the metric ds²(t), whose components are the correlation functions, evolves due to the von Kármán-Howarth equation. We review the explicit geometric realization of ds²(t) in K³ and present symmetries (or isometric motions in K³) of the metric ds²(t) which coincide with the sliding deformation of a surface arising under the geometric realization of ds²(t). We expose the fine structure of a Lie algebra associated with this symmetry transformation and construct the basis of differential invariants. Minimal generating set of differential invariants is derived. We demonstrate that the well-known Taylor microscale λ_g is a second-order differential invariant and show how λ_g can be obtained by the minimal generating set of differential invariants and the operators of invariant differentiation. Finally, we establish that there exists a nontrivial central extension of the infinite-dimensional Lie algebra constructed wherein the central charge is defined by the same bilinear skew-symmetric form c as for the Witt algebra which measures the number of internal degrees of freedom of the system. For turbulence, we give the asymptotic expansion of the transversal correlation function for the geometry generated by a quadratic form.     

复合材料模量细观分析的一般性模型

基于细观力学理论,提出了横观各向异性复合材料弹性常数的分析模型,并给出了纵向(纤维长度方向) 与横向弹性模量、横截面内剪切模量和泊松比等材料性能参数的理论推导和计算公式. 此方法简洁准确地反映了材料横观各向异性性能,改进了常规细观力学模型,也为工程分析提供了理论依据;同时在复合材料力学课程教学中,有助于深化学生对复合材料细观分析的理解,具有一定的启发性.     

Switching the direction of spin accumulation in the spin Hall effect of light by adjusting the optical axis of an uniaxial crystal

We theoretically and experimentally investigate a switchable spin Hall effect (SHE) of light in reflection near the Brewster angle at an air-uniaxial crystal interface. We find a large transverse spin splitting near the Brewster angle, whose sign can be altered by rotating the optical axis. As an analogy of the SHE in an electronic system, a switchable spin accumulation in the SHE of light is detected. We are able to switch the direction of the spin accumulation by adjusting the optical axis angle of the uniaxial crystal. These findings may give opportunities for photon spin manipulating and developing a new generation of nano-photonic devices.     

Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin’s model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.     

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infinite circular cylinder subjected to certain boundary conditions.An analytical procedure for evaluation of thermal stresses,displacements,and temperature in rotating cylinder subjected to thermal load along the radius is presented.The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed.Such situation can arise due to melting of insulating material deposited on the surface cylinder.A solution and numerical results are obtained for the stress components,displacement components,and temperature.The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.     

爆轰波与激波对撞爆轰状态演化机理研究

对当量比氢氧混合气体中爆轰波与激波的正面对撞过程进行了二维数值研究. 采用了二阶精度NND差分格式与改进的两阶段化学反应模型,并以数值x-t纹影图以及烟迹图记录了对撞过程. 数值研究表明,透射爆轰波受到膨胀影响首先会衰减,甚至产生局部解耦现象;然后由于三波点的碰撞又能再次重新耦合. 在爆轰波对撞过程中,由于燃烧不均匀性而产生的弱横波对爆轰胞格的形成起着重要作用.      

）IRECT NUMERICAL SIMULATION OF DECAYING COMPRESSIBLE ISOTROPIC TURBULENCE

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等.研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量（压缩）耗散率所占比率也显著增长.标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高（p≥5）时,纵向速度结构函数的扩展自相似性则不再成立.对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的间歇性要强于横向湍流脉动.     

可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.     

各向同性钢材的断裂模型和屈服模型

基于钢材断裂前必先屈服的基本事实, 以钢材断裂面为屈服面后继扩大直至材料完整性(连续性）发生破坏为假设, 以已有的屈服模型的共同特征为切入点, 建议了各向同性钢材在主应力空间的二次函数型断裂模型和屈服模型. 根据不同钢材的特征应力值, 量化了各向同性钢材的二次函数型断裂模型和屈服模型. 依据不同钢材的特征应力值的相互关系, 建议的各向同性钢材的二次函数型断裂模型和屈服模型相应地描述为主应力空间的圆柱面、椭球面、抛物面和双曲面. 建议的各向同性钢材的二次函数型断裂模型和屈服模型较已有的强度模型更具一般性.