Nonlinear Convection in a Rotating Annulus with a Finite Gap

Thermal convection in a fluid-filled gap between the two corotating, concentric cylindrical sidewalls with sloping curved ends driven by radial buoyancy was first studied by Busse (Busse, F.H., "Thermal instabilities in rapidly rotating systems", J. Fluid Mech . 44 , 441-460 (1970)). The annulus model captures the key features of rotating convection in full spherical geometry and has been widely employed to study convection, magnetoconvection and dynamos in planetary systems, usually in connection with the small-gap approximation neglecting the effect of azimuthal curvature of the annulus. This article investigates nonlinear thermal convection in a rotating annulus with a finite gap through numerical simulations of the full set of nonlinear convection equations. Three representative cases are investigated in detail: a large-gap annulus with the ratio of the radii ( s i and s o ) of the sidewalls ξ = s i / o s = 0.1, a medium-gap annulus with ξ = 0.35 and a small-gap annulus with ξ = 0.8. Near the onset of convection, the effect of rapid rotation through the sloping ends forces the first (Hopf) bifurcation in the form of small-scale, steadily drifting rolls (thermal Rossby waves). At moderately large Rayleigh numbers, a variety of different convection patterns are found, including mixed-mode steadily drifting, quasi-periodic (vacillating) and temporally chaotic convection in association with various temporal and spatial symmetry-breaking bifurcations. Our extensive simulations suggest that competition between nonlinear and rotational effects with increasing Rayleigh number leads to an unusual sequence of bifurcation characterized by enlarging the spatial scale of convection.     

Effects of boundary conditions on the onset of convection with tilted magnetic field and rotation vectors

The problem of the onset of thermal convection is considered, firstly when a uniform tilted magnetic field is present, and secondly in a frame rotating about an oblique axis. If up–down symmetry is broken we expect to find only bifurcations that lead to travelling waves. Numerical studies show, however, that in a Boussinesq fluid the spectrum of eigenvalues can be symmetrical about the real axis, even when the boundary conditions are asymmetrical. Here we show analytically that this symmetry property indeed holds for a wide range of boundary conditions and hence that both steady solutions and standing waves are allowed.     

近年来黄河下游断流的干旱背景分析

近年来黄河下游连年断流 ,引起社会的极大关注。文中根据全国 1 60个基本气象测站近47a的月降水量资料 ,应用旋转主分量分析等统计分析方法 ,分析了黄河流域平均降水量的年际变化 ,比较了全国各区域降水量异常及其累积程度 ,还与历史上著名的大旱灾荒和黄河下游断流事件作了对比分析。结果表明 ,近 2 0 a来 ,黄河流域尤其黄河下游山东省及其附近地区 ,遭遇到数百年一遇的气候上连续干旱阶段 ,近 1 0 a来累计少降的雨水总量 ,相当于黄河 4 a的径流量。黄河下游近 2 0 a里集中发生了 1 5 a明显的干旱年份 ,其中 5 a大旱 ,1 0 a干旱。其干旱的累积程度不仅是全国最严重的地区 ,而且超过了历史上著名的“崇贞大旱”(1 640年 )和 1 372年的大旱及黄河下游断流事件     

Laboratory studies of the effects of interrupted, sloping topography on intermediate depth boundary currents in linearly stratified fluids

Laboratory experiments are described which provide insight into the interaction of intermediate depth boundary currents (IDBCs) with interrupted sloping topography. Specifically, they contribute to the debate over meddy formation on the Iberian continental slope. The experiments were performed in a rectilinear rotating tank filled initially with a linearly-stratified fluid. A false bottom sloped away from the side-wall along which the current flowed, and was interrupted by a gap of variable length. The effects of varying gap length and rotation rate on the boundary current were observed.In the first of two sets of experiments, the current flowed above the slope, along the vertical sidewall. In the second, the current flowed along the sloping bottom. In the former, current nose speed was consistent with geostrophic predictions, but decreased in the presence of a gap in the topography. Kelvin wave radiation is postulated as a reason for this. The IDBCs exhibited vortical lateral intrusions at values of the Burger number Bu=(N₀/Ω)² at which counterpart flat-bottom studies had been stable, implying that the sloping topography had a de-stabilising effect. Energy measurements and qualitative observations suggest the intrusions were due to mixed barotropic/baroclinic instabilities, the latter dominating at higher rotation rates.In the second configuration, four distinct flows were observed, distinguished by the deformation radius:gap width ratio R_D/G^*. For a range of values of R_D/G^*, attached eddies formed at the upstream end of the gap. They remained at this position, unlike those in similar studies of surface boundary currents (Klinger, 1993). Their persistence and ability to move downstream – salient factors for meddy – formation were greater for a finite gap size than a permanent change from sloping to flat bottom.     

原子吸收分光光度法测定矿石中高含量的银和锌

本文介绍了用转角和降低喷雾量,在强盐酸介质中,火焰原子吸收直接测定矿石中高含量的银和锌。本法测得的结果稳定,未发现干扰,灵敏度、精密度、准确度及工作曲线均满足于许多矿石中高含量银和锌的测定。     

基于1.2m望远镜自适应光学系统激光信标转盘式机械快门的研究

基于激光信标发射和接收共光路系统中探测器受杂散光影响的关键问题,设计了一种新型转盘式机械快门装置,对光信号进行高频率开关控制,从而对自适应光学系统的波前探测器起到彻底保护作用.设计时,分析了瑞利信标的采样厚度以及快门开关与脉冲激光器的发射、探测器探测时间的时序控制.     

Motion on two-dimensional manifolds in rotating coordinates

The two degree-of-freedom system in rotating coordinates: \.u – 2nv = V _x, \.v + 2nu = V _y, \.x = u, \.y = v and its Jacobi integral define a time-dependent velocity field on a differentiable, two-dimensional manifold of integral curves. Explicit time dependence is determined by the dynamical system, coordinate frame, and initial conditions. In the autonomous cases, orbits are level curves of an autonomous function satisfying a second-order, quasi-linear, partial differential equation of parabolic type. Important aspects of the theory are illustrated for the two-body problem in rotating coordinates.     

顺斜向坡变形破坏特征研究

本文通过对黄河上游某水电站坝前坝后顺斜向坡变形破坏特征的分析,提出了顺斜向坡的变形破坏类型分类,并对边坡产生旋转滑移破坏的临界条件作了分析。     

Some questions arising from the application of hydraulic theory to the Faroe Bank Channel deep-water flow

The results from a recent oceanographic field experiment in the Faroe Bank Channel are discussed from the standpoint of determining how well the classical hydraulic assumptions of stationarity and a quiescent upper layers were fulfilled. Evidence from these as well as previous measurements indicated that both prerequisites for the application of simplified hydraulic theory are not always fulfilled in the Channel. The implications of these results for the theoretical treatment of the hydraulic problem are discussed.     

A heuristic framework for next-generation models of geostrophic convective turbulence

Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical systems, such models still inhabit modest ranges of the governing parameters that are difficult to extrapolate to planetary settings. The canonical problem of rotating Rayleigh-Bénard convection provides an alternate approach - isolating the fundamental physics in a reduced setting. Theoretical studies and asymptotically-reduced simulations in rotating convection have unveiled a variety of flow behaviors likely relevant to natural systems, but still inaccessible to direct simulation. In lieu of this, several new large-scale rotating convection devices have been designed to characterize such behaviors. It is essential to predict how this potential influx of new data will mesh with existing results. Surprisingly, a coherent framework of predictions for extreme rotating convection has not yet been elucidated. In this study, we combine asymptotic predictions, laboratory and numerical results, and experimental constraints to build a heuristic framework for cross-comparison between a broad range of rotating convection studies. We categorize the diverse field of existing predictions in the context of asymptotic flow regimes. We then consider the physical constraints that determine the points of intersection between flow behavior predictions and experimental accessibility. Applying this framework to several upcoming devices demonstrates that laboratory studies may soon be able to characterize geophysically-relevant flow regimes. These new data may transform our understanding of geophysical and astrophysical turbulence, and the conceptual framework developed herein should provide the theoretical infrastructure needed for meaningful discussion of these results.