The rule of affine similitude for the force coefficients of a body oscillating in a uniformly stratified fluid

 This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients is based on Fourier analysis of the time-history of damped oscillation tests. Received: 25 September 2000 / Accepted: 6 July 2001 Published online: 29 November 2001     

The elliptical dimension of space-time atmospheric stratification of passive admixtures using lidar data

State-of-the-art airborne lidar data of passive scalars have shown that the spatial stratification of the atmosphere is scaling: the vertical extent (Δz) of structures is typically ≈Δx^H_z where Δx is the horizontal extent and H_z is a stratification exponent. Assuming horizontal isotropy, the volumes of the structures therefore vary as ΔxΔxΔx^H_z=Δx^D_s where the “elliptical dimension” D_s characterizes the rate at which the volumes of typical non-intermittent structures vary with scale. Work on vertical cross-sections has shown that 2+H_z=2.55±0.02 (close to the theoretical prediction 23/9).In this paper we extend these (x, z) analyses to (z, t). In the absence of overall advection, the lifetime Δt of a structure of size Δx varies as Δx^H_t with H_t=2/3 so that the overall space-time dimension is D_st=29/9=3.22…. However, horizontal and vertical advection lead to new exponents: we argue that the temporal stratification exponent H_t≈1 or ≈0.7 depending on the relative importance of horizontal versus vertical advection velocities. We empirically test these space-time predictions using vertical-time (z, t) cross-sections using passive scalar surrogates (aerosol backscatter ratios from lidar) at ∼3 m resolution in the vertical, 0.5-30 s in time and spanning 3-4 orders of magnitude in scale as well as new analyses of vertical (x, z) cross-sections (spanning over 3 orders of magnitude in both x, z directions). In order to test the theory for density fluctuations at arbitrary displacements in (Δz, Δt) and (Δx, Δz) spaces, we developed and applied a new Anisotropic Scaling Analysis Technique (ASAT) based on nonlinear coordinate transformations. Applying this and other analyses to data spanning more than 3 orders of magnitude of space-time scales we determined the anisotropic scaling of space-time finding the empirical value D_st=3.13±0.16. The analyses also show that both cirrus clouds and aerosols had very similar space-time scaling properties. We point out that this model is compatible with (nonlinear) “turbulence” waves, hence potentially explaining the observed atmospheric structures.     

Analytical Treatment of a Push–Pull “Echo” Test

A semi-analytical streamline-based model, employing stratification and macro physics only, is developed and utilized to simulate injection/production phases of single-well push–pull tests. Modeling results are compared with experimental field data, giving an excellent match, without resorting to parameter fitting, simply by putting in known test-site properties, such as stratification data, hydraulic head gradients, and test parameters.     

赋层拓扑分子格及其紧性

拓扑分子格本身没有层次结构，为其构造某种层次成为很重要的问题。本文的构思是赋于分子格上的拓扑一种层次，从而使拓扑分子格具有丰富的层次性，其次讨论了保层次序同态与赋层积拓扑分子格，在此基础上建立了较理想的拓扑分子格的紧性。     

双峰聚合物分子刷的层化机理

建立了用于模拟双峰聚合物分子刷相结构的自洽场理论. 模拟结果表明, 良溶剂条件能够促使双峰聚合物分子刷裂分为内外两个亚分子层, 其中短链居于内分子层, 而长链伸展到外分子层. 体系溶解性的加强不仅使聚合物的密度分布逐渐趋近强分凝理论的解析结果, 而且加大了分子链的伸展和链段的局部取向程度. 分子链接枝密度的增加能够促使分子刷的层化, 并且在良溶剂区域, 不同接枝密度的分子链密度分布可以回归到同一条主线. 在良溶剂条件下, 长链的聚合度对短链的密度分布影响不大, 但能够导致长链向外分子层扩展.     

一类用于优化设计的T_(B-D)构造

本文以复杂系统的逻辑分析、多状态模糊控制为直观背景,建立了一类用于优化设计的 T_(B-D)构造,进而可以构筑其相应的、综合的语义模型。     

On incidence between strata of the Hilbert scheme of points on $$\mathbb{P}^{2}$$

The Hilbert scheme of n points in the projective plane has a natural stratification obtained from the associated Hilbert series. In general, the precise inclusion relation between the closures of the strata is still unknown. Guerimand, Ph.D Thesis, Universite’de Nice, 2002 studied this problem for strata whose Hilbert series are as close as possible. Preimposing a certain technical condition he obtained necessary and sufficient conditions for the incidence of such strata. In this paper we present a new approach, based on deformation theory, to Guerimand’s result. This allows us to show that the technical condition is not necessary. Michel Van den Bergh is a director of research at the FWO.     

Kinematic simulation for stably stratified and rotating turbulence

The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the rapid distortion theory (RDT) to a kinematic simulation (KS) of the Boussinesq equation with a Coriolis term.Scalings for one- and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction.     

Effect of vertical stratification on characteristics and energy of nonlinear internal solitary waves from a numerical model

A numerical model is set up to study the impact of changes in vertical stratification on the properties of internal solitary waves (ISWs) generated by tidal flow over a ridge. Based on modifications of the observed stratification with a secondary thermocline over a main one in the South China Sea, the effects of five kinds of stratification on the characteristics and energy conversion of ISWs are investigated. In general, the isopycnal undergoing maximum displacement in ISWs is from slightly below the main thermocline. When the stratification below the ridge crest is reduced, the wave amplitude and the number of ISWs in a wave packet increase, while the phase speed, the wave half-width, the sum of ISW kinetic energy (KE) and available potential energy (APE) and the ratio of KE to APE decrease. When the stratification in the upper layer is reduced, the ISW amplitude, the number of ISWs, the phase speed and the sum of KE and APE decrease, while the wave half-width and the ratio of KE to APE increase. If the main thermocline is over the secondary one, the ISW amplitude, the wave half-width, the sum of KE and APE and the ratio of KE to APE increase, while the phase speed reduces. For stratification with two thermoclines, the ISW phase speed increases but the half-width decreases. In addition, the ratio of baroclinic to barotropic energy is found to be between 10% and 40%, and the ratio of ISW KE to APE is between 1.30 and 1.65. It is also shown that the ratio of KE to APE for the stratification with two thermoclines is about 2–6% larger than that for the stratification with only one thermocline. If the thermocline is lowered by about 30 m (0.064 of the total water depth), the ratio of KE to APE reduces by about 10%.