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1.
Long wave propagation in a two‐layer fluid with variable depth is studied for specific bottom configurations, which allow waves to propagate over large distances. Such configurations are found within the linear shallow‐water theory and determined by a family of solutions of the second‐order ordinary differential equation (ODE) with three arbitrary constants. These solutions can be used to approximate the true bottom bathymetry. All such solutions represent smooth bottom profiles between two different singular points. The first singular point corresponds to the point where the two‐layer flow transforms into a uniform one. In the vicinity of this point nonlinear shallow‐water theory is used and the wave breaking criterion, which corresponds to the gradient catastrophe is found. The second bifurcation point corresponds to an infinite increase in water depth, which contradicts the shallow‐water assumption. This point is eliminated by matching the “nonreflecting” bottom profile with a flat bottom. The wave transformation at the matching point is described by the second‐order Fredholm equation and its approximated solution is then obtained. The results extend the theory of internal waves in inhomogeneous stratified fluids actively developed by Prof. Roger Grimshaw, to the new solutions types.  相似文献   
2.
Let $G$ be a stratified Lie group and let $\{X_1, \cdots, X_{n_1}\}$ be a basis of the first layer of the Lie algebra of $G$. The sub-Laplacian $\Delta_G$ is defined by $$\Delta_G= -\sum^{n_1}_{j=1} X^2_j. $$ The operator defined by $$\Delta_G-\sum^{n_1}_{j=1}\frac{X_jp}{p}X_j$$ is called the Ornstein-Uhlenbeck operator on $G$, where $p$ is a heat kernel at time 1 on $G$. In this paper, we investigate Gaussian BV functions and Gaussian BV capacities associated with the Ornstein-Uhlenbeck operator on the stratified Lie group.  相似文献   
3.
采用室内混合箱研究稳定分层流(上层淡水、下层盐水) 无剪切密度界面处的湍流混合与分形结构. 湍流通过浸没在盐水层中的振动格栅产生, 密度界面结构通过在盐水层中添加荧光剂或染料可视化, 共进行12 组实验. 实验观测并记录了:(1) 淡、盐水密度界面距混合箱底部的平均高程(h);(2) 淡、盐水层的密度(ρ0,ρ), (3) 淡、盐水密度界面. 其中, 淡、盐水密度界面通过照片、录像进行记录. 观测结果用于计算:(1) 盐水层密度;(2) 卷挟速度, (3) 整体理查孙数(Rio), (4) 二维、三维密度界面, (5) 二维、三维密度界面的分形维度. 结果分析发现:(1) 湍流卷挟率随Rio 增大而减小, 并且满足Rio的-3=2 或-7=4 幂律;表明随着湍流强度的减弱, 混合的速度也越来越缓慢;(2) 二维密度界面分形维度大于1, 三维密度界面分形维度大于2;表明二维、三维密度界面存在分形结构;(3) 分形维度随Rio的增大而减小;表明随着湍流强度的减弱, 密度界面也越来越趋于光滑.  相似文献   
4.
Case-cohort sampling is a commonly used and efficient method for studying large cohorts. In many situations, some covariates are easily measured on all cohort subjects, and surrogate measurements of the expensive covariates also may be observed. In this paper, to make full use of the covariate data collected outside the case-cohort sample, we propose'a class of weighted estimators with general time-varying weights for the additive hazards model, and the estimators are shown to be consistent and asymptotically normal. We also identify the estimator within this class that maximizes efficiency, and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations. A real example is provided.  相似文献   
5.
In this paper, we prove that every standard Koszul (not necessarily graded) standardly stratified algebra is also Koszul. This generalizes a similar result of [3 Ágoston, I., Dlab, V., Lukács, E. (2003). Quasi-hereditary extension algebras. Algebras Represent. Theory 6:97117.[Crossref], [Web of Science ®] [Google Scholar]] on quasi-hereditary algebras.  相似文献   
6.
《Mendeleev Communications》2021,31(5):715-717
Nanoporous silicon carbide with a specific surface area of up to 186.45 m2 g−1 has been efficiently synthesized from waste rice husk using a magnesiothermic reduction at 950 °C as a key step. Throughout the entire process, the recovery rates of silicon, potassium and phosphorus from rice husk can reach 88.46, 91.5 and 65.5%, respectively. Turning rice husk waste into a real treasure, this promising method for producing porous SiC protects the environment and brings economic benefits.  相似文献   
7.
陈科  尤云祥  胡天群  朱敏慧  王小青 《物理学报》2011,60(2):24702-024702
采用水平移动射流方法模拟移动动量源,实验研究了该移动动量源在密度分层流体中生成准二维偶极子涡街的机理,分析了偶极子涡街的演化特性. 在系列实验基础上,获得了移动动量源在密度分层流体中能够演化为偶极子涡街的(Re,Fr)组合条件. 对不同的Re取值,获得了偶极子涡街无因次形成时间及其无因次涡街平均波长倒数与Fr之间的相关关系,表明它们不依赖于Re数,而与Fr近似为幂指数关系. 关键词: 分层流体 移动动量源 偶极子涡街 涡街形成时间  相似文献   
8.
In this paper, we study the properties of generalized power series modules and the filtration dimensions of generalized power series algebras. We obtain that [[△S,≤]]- gfd([[AS,≤]]) =△-gfd(A) if A is an R-module where R is a perfect and coherent commutative algebra, and(R, ≤) is standardly stratified.  相似文献   
9.
Large eddy simulations are used to examine the evolution of a shear layer in a thermocline with non-uniform density stratification. Unlike previous studies, the density in the present study is continuously stratified and has stratification in the upper half different from the lower half of the shear layer. The stratification in the upper half is fixed at Ju = 0.05, while the stratification in the lower half is increased to Jd = 0.05, 0.15, 0.25 and 0.35, leading to a progressively stronger asymmetry of the Rig profile in the four cases. Here, J is the bulk Richardson number and Rig is the gradient Richardson number. The type of shear instability and the properties of the ensuing turbulence are found to depend strongly on the degree of asymmetry in stratification. The shear instability changes from a Kelvin–Helmholtz (KH) mode at Jd = 0.05 to a Holmboe (H) mode at Jd = 0.35 and exhibits characteristics of both KH and H modes at intermediate values of Jd. Differences in the evolution among the cases are quantified using density visualisations and statistics such as mean shear, mean stratification and turbulent kinetic energy.  相似文献   
10.
We examine the applicability of the Prandtl mixing length model to transverse momentum and mass flux in strongly confined, stably stratified turbulent shear flows. These fluxes were measured in the vertical diametral plane of lock-exchange flows in an inclined pipe by the simultaneous use of planar laser-induced fluorescence and particle image velocimetry at local Reynolds numbers ranging from Re = 580 to 1770 and Richardson numbers ranging from Ri = 0.26 and 1.6. Measurements indicate that the eddy diffusivities of mass and momentum are symmetric about the pipe axis, with their maximum at the axis. The corresponding Prandtl mixing lengths decrease with increasing distance from the pipe axis within the central 60% of the pipe cross-section. Within the range of experimental conditions, the mixing lengths at the axis increase linearly with Ri so that the corresponding turbulent Prandtl number Prt decreases with Ri. In contrast, Prt and the mixing lengths do not display a systematic dependence on Re. Comparison with unbounded and semi-bound shear flows suggests that the strong confinement imposed by the pipe wall may be constraining the integral length scale and Prandtl mixing lengths.  相似文献   
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