Statistical equilibrium distributions of baroclinic vortices in a rotating two-layer model at low Froude numbers

The point-vortex equilibrium statistical model of two-layer baroclinic quasigeostrophic vortices in an unbounded f-plane is examined. A key conserved quantity, angular momentum, serves to confine the vortices to a compact domain, thereby justifying the statistical mechanics model, and also eliminating the need for boundary conditions in a practical method for its resolution. The Metropolis method provides a fast and efficient algorithm for solving the mean field non-linear elliptic PDEs of the equilibrium statistical theory. A verification of the method is done by comparison with the exact Gaussian solution at the no interaction limit of zero inverse temperature. The numerical results include a geophysically and computationally relevant power law for the radii at which the most probable vortex distribution is non-vanishing: For fixed total circulation, and fixed average angular momentum, the radii of both layers are proportional to the square root of the inverse temperature β. By changing the chemical potentials μ of the runs, one is able to model the most probable vorticity distributions for a wide range of total circulation and energy. The most probable vorticity distribution obtained at low positive temperatures are consistently close to a radially symmetric flat-top profiles. At high temperatures, the radially symmetric vorticity profiles are close to the Gaussian distribution.     

On the transition from the laminar to disordered flow in a precessing spherical-like cylinder

We investigate, through both asymptotic analysis and direct numerical simulation, precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. A particular emphasis is placed on a spherical-like cylinder whose diameter is nearly the same as its length. At this special aspect ratio, the strongest direct resonance occurs between the spatially simplest inertial mode and the precessional Poincaré forcing. An asymptotic analytical solution in closed form describing weakly precessing flow is derived in the mantle frame of reference for asymptotically small Ekman numbers. We also construct a nonlinear three-dimensional finite element model – which is validated against both the asymptotic solution and a constructed exact solution – for elucidating the nonlinear transition leading to disordered flow in the precessing spherical-like cylinder. Properties of both weakly and strongly precessing flows are investigated with the aid of a complete inertial-mode decomposition of the fully nonlinear solution. Despite a large effort being made, the well-known triadic resonance is not found in the precessing spherical-like cylinder. The energy contained in the precessionally forced inertial mode is primarily transferred, through nonlinear effects in the viscous boundary layers, to the geostrophic flow that becomes predominant when the precessional Poincaré force is sufficiently large. It is found that the nonlinear flow evolutes gradually and progressively from the laminar to disordered as the precessional force increases.     

副热带高压外围西北侧一次强对流天气的雷达回波特征

2005年7月15日14时到16日08时,宜昌市出现了一次强对流天气过程。根据宜昌多普勒天气雷达每6min一次体扫监测信息,分析了副热带高压外围西北侧强对流天气雷达回波的演变趋势。结果表明,在山地向平原过渡的地带,当对流云发展到最旺盛阶段并出现地面强降水时,在其基本反射率最低仰角产品中存在出流边界;弓形回波、带状回波的走向与环境风场几乎成正交时,给所经之地造成异常剧烈的天气,且灾害性大风均出现在径向速度场中具有旋转性环流的强单体移动的下风方。     

Interaction between an eddy and a zonal jet : Part II. Two-and-a-half-layer model

In a two-and-a-half-layer quasi-geostrophic model, a process study is conducted on the interaction between a vortex and a zonal jet, both with constant potential vorticity. The vortex is a stable anticyclone, initially located north of the eastward jet. The potential vorticity of the jet is allowed to have various vertical structures, while the vortex is concentrated in only one layer. The flow parameters are set to values characteristic of the Azores region.First, the jet is stable. Weak vortices steadily drift north of the jet without crossing it while strong vortices can cross the jet and tear off a cyclone with which they pair as a heton (baroclinic dipole). This heton often breaks later in the shear exerted by the jet; the two vortices finally drift apart. When crossed by deep anticyclones, the jet develops meanders with 375 km wavelength. These results exhibit a noticeable similarity with the one-and-a-half-layer case studied in Part I.Secondly, the jet is allowed to be linearly unstable. In the absence of the vortex, it develops meanders with 175 km wavelength and 25-day e-folding time on the β-plane. For various vertical structures of the jet, baroclinic instability is shown to barely affect jet–vortex interaction if the linear growth rate of unstable waves is smaller than 1/(14 days). Further simulations with a linearly unstable, nonlinearly equilibrated jet evidence its strong temporal variability when crossed by a deep vortex on the β-plane. In particular, long waves can dominate the spectrum for a few months after jet crossing by the vortex. Again in this process, the deep vortex couples with a surface cyclone and both drift southwestward.     

一类R~n空间上旋转椭球面簇的广义Radon变换

本文基于二维雷达成像的原理研究了其数学问题,对R~n 空间中的图像函数f(x),已知其旋转椭球面簇上的积分值,应用广义Radon 变换来重建图像函数f(x)。利用球谐函数展开和Funk-Heck 定理证明了这种重建图像问题的存在、唯一性,并在一定的函数类中给出了它的反演解的数学表达式和推广了V.G.Romanov的工作。     

Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory

The barotropic instability is traditionally viewed as an initial-value problem wherein wave perturbations of a laterally sheared flow in a homogeneous uniformly rotating fluid that temporally grows into vortices. The vortices are capable of mixing fluid on the continental shelf with fluid above the continental slope and adjacent deep-sea region. However, the instability can also be viewed as a boundary-value problem. For example, a laterally sheared coastal flow is perturbed at some location, creating perturbations that grow spatially downstream. This process leads to a time periodic flow that exhibits instability in space. This article first examines the linear barotropic instability problem with real frequency and complex wavenumber. It is shown that there exists a frequency band within which a spatially growing wave is present. It is then postulated that far downstream the spatially unstable flow emerges into a chain of identically axisymmetric vortices. Conservation of mass, momentum and energy fluxes are applied to determine the diameter, spacing and the speed of translation of the vortices.     

Effect of Coriolis force on the shapes of rotating stars and stars in binary systems

In this paper an attempt has been made to determine the effect of Coriolis force on the shapes of Roche equipotential surfaces of rotating stars and stars in binary systems. Equations of Roche equipotential surfaces have been obtained for rotating and binary stars which take into account the effects of Coriolis force besides the centrifugal and gravitational forces. Shapes of Roche equipotentials and values of Roche limits are obtained for different values of angular velocity of rotation for rotating stars and for different values of mass ratios for the binary stars. The obtained results have been compared with the corresponding results in which the effect of Coriolis force has not been considered.     

On the validity of series expansion being used for the position of a point on a Roche equipotential

The concept of Roche equipotentials has been frequently used in literature to study the problems of rotating stars and stars in binary systems. However in spite of using this simplifying concept, it is still not possible to express the position of a point in the potential field of such a system in a closed analytic form. In order to carry out further analytic studies, Kopal (Adv. Astron. Astrophys. 9:1–65, 1972), therefore, developed a series expansion for it. The series expansion of Kopal has often been used in the analysis of the problem of equilibrium structure and the periods of oscillations of rotating stars and stars in binary systems, but its validity and convergence has not been analytically established. It is important that this aspect of the problem is checked so that one is sure of the correctness of subsequent analysis and results based on this series expansion. In the present brief note, we have addressed ourselves to this problem and validated the correctness of the numerical results obtained through the use of this series expansion.     

Biologische Behandlung von synthetischen Abwässern mit Azofarbstoffen

Purification of Wastewaters Containing Azo Dyes This study describes the degradability of the azo dye C.I. Reactive Violet 5 by a continuous flow biological treatment system consisting of three rotating disc reactors. The azo dye was first decolorized in an anaerobic reactor. Decolorization was improved by adding an auxiliary substrate (yeast extract and acetic acid). Although severe operating conditions were experienced due to failures in the temperature and pH-controllers, the reactor recovered quickly and continued to decolorize reliably. The removal of the auxiliary substrate in the anaerobic reactor was not satisfactory, probably due to the copper in the azo dye. Batch experiments showed that copper was removed from the dye molecule and precipitated during the decolorization. In the continuous flow reactor, the copper precipitate on the disc can redissolve due to a pH-gradient in the fixed biomass becoming toxic again for the bacteria. In the following two aerobic reactors, the auxiliary substrate was degraded, but mineralization of the dye metabolites was insufficient. The aromatic amines produced by the anaerobic decolorization are more toxic in the bacterial luminescence test than the azo dye. Therefore, decolorization alone cannot be used to treat colored wastewater. Since the amines can also be produced in anaerobic parts of rivers, the dyes have to be removed in a more efficient way. That is the reason why in further experiments ozonation is being tested to increase the biological degradability of the azo dye for a following aerobic stage. Either ozonation can be used after the two stage treatment of the dye in anaerobic/aerobic reactors or the dye can be oxidized directly, making the addition of auxiliary substrate unnecessary. These configurations are being tested with the goal to degrade the dye with the least ozone consumption.