Inviscid Dynamical Structures Near Couette Flow

Consider inviscid fluids in a channel {-1\leqq y\leqq1}{\{-1\leqq y\leqq1\}} . For the Couette flow u ₀ = (y, 0), the vertical velocity of solutions to the linearized Euler equation at u ₀ decays in time. Whether the same happens at the non-linear level is an open question. Here we study issues related to this problem. First, we show that in any (vorticity) H^s(s < \frac32){H^{s}\left(s<\frac{3}{2}\right)} neighborhood of Couette flow, there exist non-parallel steady flows with arbitrary minimal horizontal periods. This implies that nonlinear inviscid damping is not true in any (vorticity) H^s(s < \frac32){H^{s}\left(s<\frac{3}{2}\right)} neighborhood of Couette flow for any horizontal period. Indeed, the long time behaviors in such neighborhoods are very rich, including nontrivial steady flows and stable and unstable manifolds of nearby unstable shears. Second, in the (vorticity) ${H^{s}\left(s>\frac{3}{2}\right)}${H^{s}\left(s>\frac{3}{2}\right)} neighborhoods of Couette flow, we show that there exist no non-parallel steadily travelling flows \varvecv(x-ct,y){\varvec{v}\left(x-ct,y\right)} , and no unstable shears. This suggests that the long time dynamics in ${H^{s}\left(s>\frac{3}{2}\right)}${H^{s}\left(s>\frac{3}{2}\right)} neighborhoods of Couette flow might be much simpler. Such contrasting dynamics in H ^s spaces with the critical power s=\frac32{s=\frac{3}{2}} is a truly nonlinear phenomena, since the linear inviscid damping near Couette flow is true for any initial vorticity in L ².     

求解刚性振荡问题的两类带显式级的三级对角隐式Runge-Kutta方法

针对刚性振荡问题,讨论了两类带显式级的三级对角隐式Runge-Kutta方法的阶、级阶、A-稳定性、相误差和耗散误差,所构造的方法成功应用于一类大气化学反应问题的求解.     

粗糙接触界面超声非线性效应的概率模型

提出描述粗糙接触界面超声非线性效应的概率模型,利用分段均匀概率函数描述粗糙接触界面劲度系数变化,结合表面粗糙峰的几何分布特征,得到界面粗糙度和两侧表面相对运动对声波的非线性调制作用。实验观测了铝合金材料的粗糙接触界面的高次谐波现象和阈值现象,进一步分析了归一化非线性参数与界面加载压力、粗糙度之间的关系。实验测量结果与概率模型的理论预测一致,证明了该模型的正确性,为利用超声非线性效应评价粗糙接触界面提供了理论依据。      

表面裂纹对掠入射垂直偏振横波散射的动态光弹实验分析

利用动态光弹法研究掠入射垂直偏振横波(SV波)在表面裂纹处的散射声场,给出不同倾斜角度的表面裂纹引起的散射声场分布和简化波前示意图。以垂直表面裂纹为例,有限元仿真和电法测量分别直接地和间接地证明了光弹实验结果的可靠性。表面裂纹引起的各类散射波与裂纹参量密切相关且容易区分,可使用一阶散射声波到达时间反演表面裂纹的长度和倾角,实验测量值与真实值的相对误差在6%以下。      

Barotropic instability of shear flows

We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details and obtain the sharp stability boundary in the whole parameter space, which corrects previous results in the fluid literature. Our new results are confirmed by more accurate numerical computation. The addition of the Coriolis force is found to bring fundamental changes to the stability of shear flows. Moreover, we study dynamical behaviors near the shear flows, including the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping. The first ingredient of our proof is a careful classification of the neutral modes. The second one is to write the linearized fluid equation in a Hamiltonian form and then use an instability index theory for general Hamiltonian partial differential equations. The last one is to study the singular and nonresonant neutral modes using Sturm-Liouville theory and hypergeometric functions.     

时间触发总线验证技术研究

TTP协议定义了一种高确定性,无冲突,高安全的通信总线,能够满足包括飞行控制等的安全关键实时控制系统的应用要求。时间触发总线验证技术根据TTP协议规范要求,针对研制的节点进行测试,包括基本通信测试、时钟同步、故障注入等不同的测试场景,充分验证被测节点的各项功能、性能。通过这些测试,表明被测节点各项指标都满足研制需求,可用于安全关键实时控制系统。     

2018年度全国检测声学会议成功召开

2018年度全国检测声学会议成功召开     

小圆孔的正负焦距与小孔眼镜

提出了证明小圆孔具有正,负焦距的一种方法,简要地介绍子关于小孔眼镜的实验研究。