Influence of interactive stratospheric chemistry on large-scale air mass exchange in a global circulation model

A new globally uniform Lagrangian transport scheme for large ensembles of passive tracer particles is presented and applied to wind data from a coupled atmosphere-ocean climate model that includes interactive dynamical feedback with stratospheric chemistry. This feedback from the chemistry is found to enhance large-scale meridional air mass exchange in the northern winter stratosphere as well as intrusion of stratospheric air into the troposphere, where both effects are due to a weakened polar vortex.     

A variational theory of hyperbolic Lagrangian Coherent Structures

We develop a mathematical theory that clarifies the relationship between observable Lagrangian Coherent Structures (LCSs) and invariants of the Cauchy-Green strain tensor field. Motivated by physical observations of trajectory patterns, we define hyperbolic LCSs as material surfaces (i.e., codimension-one invariant manifolds in the extended phase space) that extremize an appropriate finite-time normal repulsion or attraction measure over all nearby material surfaces. We also define weak LCSs (WLCSs) as stationary solutions of the above variational problem. Solving these variational problems, we obtain computable sufficient and necessary criteria for WLCSs and LCSs that link them rigorously to the Cauchy-Green strain tensor field. We also prove a condition for the robustness of an LCS under perturbations such as numerical errors or data imperfection. On several examples, we show how these results resolve earlier inconsistencies in the theory of LCS. Finally, we introduce the notion of a Constrained LCS (CLCS) that extremizes normal repulsion or attraction under constraints. This construct allows for the extraction of a unique observed LCS from linear systems, and for the identification of the most influential weak unstable manifold of an unstable node.     

Computation of the vortex free energy in SU(2) gauge theory

We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the vacuum tends to unity. This is rigorously known to provide a necessary and sufficient condition for maintaining confinement at weak coupling in SU(N) gauge theories.     

Relative equilibria in systems with configuration space isotropy

We present a framework for studying Lagrangian and Hamiltonian systems with symmetries, near points with configuration space isotropy. We use twisted parametrisations corresponding to phase space slices based at zero points of (co-)tangent fibres. Given a hyperregular Lagrangian, we find a Legendre transform in the twisted coordinates. For simple mechanical systems, we state necessary and sufficient conditions for the existence of relative equilibria in terms of an augmented-amended potential.     

Chaotic scattering,transport, and fractals in a simple hydrodynamic flow

Advection of passive tracers in an unsteady hydrodynamic flow consisting of a background stream and a vortex is analyzed as an example of chaotic particle scattering and transport. A numerical analysis reveals a nonattracting chaotic invariant set Λ that determines the scattering and trapping of particles from the incoming flow. The set has a hyperbolic component consisting of unstable periodic and aperiodic orbits and a nonhyperbolic component represented by marginally unstable orbits in the particle-trapping regions in the neighborhoods of the boundaries of outer invariant tori. The geometry and topology of chaotic scattering are examined. It is shown that both the trapping time for particles in the mixing region and the number of times their trajectories wind around the vortex have hierarchical fractal structure as functions of the initial particle coordinates. The hierarchy is found to have certain properties due to an infinite number of intersections of the stable manifold in Λ with a material line consisting of particles from the incoming flow. Scattering functions are singular on a Cantor set of initial conditions, and this property must manifest itself by strong fluctuations of quantities measured in experiments.     

Computing Lagrangian coherent structures from their variational theory

Using the recently developed variational theory of hyperbolic Lagrangian coherent structures (LCSs), we introduce a computational approach that renders attracting and repelling LCSs as smooth, parametrized curves in two-dimensional flows. The curves are obtained as trajectories of an autonomous ordinary differential equation for the tensor lines of the Cauchy-Green strain tensor. This approach eliminates false positives and negatives in LCS detection by separating true exponential stretching from shear in a frame-independent fashion. Having an explicitly parametrized form for hyperbolic LCSs also allows for their further in-depth analysis and accurate advection as material lines. We illustrate these results on a kinematic model flow and on a direct numerical simulation of two-dimensional turbulence.     

热带低层弱涡旋中扰动的快速发展及其向中心传播的特征

台风发生的必要条件是热带低层具有气旋式扰动, 从卫星云图和诊断分析看,许多低层涡旋中存在分立的云团或中尺度系统. 这些涡旋能否发展成为台风,取决于其中的中尺度波动是否发展集合组成密闭云带. 本文利用柱坐标下的两层动力模式,研究了低层弱涡旋中第二类条件不稳定 机 制驱动下的波动的发展和移动问题. 结果表明:热带弱涡旋中的低层基本流垂直切变 可以很大地加强波动的不稳定性; 波动的相速度和群速度都指向涡旋中心, 波动向中心传播,能量向中心频散. 实例和数值研究也都表明,低层涡旋中的中尺度扰动会迅速发展并且向 中心靠近,促使台风形成.     

Study of ozone concentration variations in the upper stratosphere using millimeter wave spectroscopy methods

New results of the study of ozone concentration variations in the upper stratosphere over Moscow in the layer at a height of 40 km, which is most sensitive to anthropogenic impacts, are presented. Changes in the ozone concentration and its relation to other atmospheric parameters in cold periods of 2008–2009 and 2009–2010 are analyzed. It was shown that there exist regions with decreased ozone content in the polar vortex and outside of it in air with higher temperature in the upper stratosphere. These phenomena cause deformations of vertical ozone distribution profiles and an appreciable shift of the maximum of the relative content of ozone to lower stratosphere layers.     

Lie Symmetry and Conserved Quantity of Three-Order Lagrangian Equations for Non-conserved Mechanical System

Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.     

Finding finite-time invariant manifolds in two-dimensional velocity fields

For two-dimensional velocity fields defined on finite time intervals, we derive an analytic condition that can be used to determine numerically the location of uniformly hyperbolic trajectories. The conditions of our main theorem will be satisfied for typical velocity fields in fluid dynamics where the deformation rate of coherent structures is slower than individual particle speeds. We also propose and test a simple numerical algorithm that isolates uniformly finite-time hyperbolic sets in such velocity fields. Uniformly hyperbolic sets serve as the key building blocks of Lagrangian mixing geometry in applications. (c) 2000 American Institute of Physics.     

Hyperbolic Bending of Vortex Lines with Finite Number and Length in Rotating Trapped Bose-Einstein Condensates

The minimal energy configurations of hyperbolic bending vortex lines in the rotating trapped Bose-Einstein condensates are investigated by using a variational ansatz and numerical simulation. The theoretical calculation of the energy of the vortex lines as a function of the rotation frequency gives self-consistently vortex number, curvature and configuration. The numerical results show that bending is more stable than straight vortex line along the z-axis, and the vortex configuration in the xy-plane has a little expansion by increasing z.     

Finite time analyticity for the two and three dimensional Kelvin-Helmholtz instability

The well-posed property for the finite time vortex sheet problem with analytic initial data was first conjectured by Birkhoff in two dimensions and is shown here to hold both in two and three dimensions. Incompressible, inviscid and irrotational flow with a velocity jump across an interface is assumed. In two dimensions, global existence of a weak solution to the Euler equation with such initial conditions is established. In three dimensions, a Lagrangian representation of the vortex sheet analogous to the Birkhoff equation in two dimensions is presented.This work was performed while C.B. was visiting the Dept. de Mathématiques, Nice     

The use of conservative coordinates for reconstruction techniques and for the development of a two-dimensional transport model

Summary Conservation properties of Potential Temperature (PT) and Potential Vorticity (PV) in the middle atmosphere allow a Lagrangian approach to the study of tracer transport. A reference frame transformation, from the three-dimensional space to the PT-PV space, is used to analyse experimental measurements allowing reconstruction of data, and to develop a Lagrangian two-dimensional model. Some preliminary results of the application of this technique, that are particulary useful near the polar stratospheric vortex, are shown in this paper.     

Mechanics of plastic flow past a narrow-angle wedge indenter

ABSTRACT

The indentation of a metal specimen by a narrow-angle wedge produces extreme plastic deformation, with an effect akin to cutting into the metal. Simulation of such processes is challenging, and complicated by the need to model material separation along the indentation symmetry axis. Here we use an Arbitrary Lagrangian Eulerian (ALE) framework to enforce the symmetry boundary conditions (bcs) in their original, `strong’ form, as well as conventional Lagrangian FE to impose the bcs in a complementary, `weak’ form. Taken together these two cases, representing perfectly strong and perfectly weak interfaces, produce accurate bounds on the mechanical response for indentation by wedges with semi-apical angles as small as 15 degrees, and encompass intermediate cases that would require complicated models of ductile failure. The method accurately predicts the transition from the cutting pattern to the non-cutting (radially compressive) pattern as the apical angle is increased. In combination with Lagrangian particle tracking, the simulations reveal the deformation pattern as well as strain, strain-rate, and velocity fields in narrow angle indentation at high resolution. Interestingly, the strong form predicts a thin (tens of microns), near-wall layer of intense plastic strain, which has been observed recently in indentation experiments. With the exception of this feature, the strong and weak bc solutions are quite similar. The present approach reveals insights about plastic flow past narrow obstacles in a range of related problems including cone penetration and machining, and suggests using narrow-angle indentation as a way to probe material failure.     

Microwave Observations of Ozone Variability in the High-Latitude Stratosphere in the 2002/2003 Winter

Based on the results of long-term microwave observations, we analyze atmospheric-ozone variability at the polar latitudes in the altitude range from 20 to 60 km in the 2002/2003 winter and point out the ozone-layer vertical structure, observed during winter anomalous stratospheric warmings of various nature. Correlation between the ozone-content and temperature variations in the polar stratosphere is studied. These quantities are found to be correlated at up to 30 km (pressure range 30–10 hPa) and anticorrelated above 50 km (approximately 0.5–0.1 hPa).__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 2, pp. 134–141, February 2005     

Nonautonomous submersive second-order differential equations and lie symmetries

We give necessary and sufficient conditions for a nonautonomous second-order differential equation to be submersive. An application to nonautonomous Lagrangian systems is given: the existence of symmetries of the Lagrangian permits us to prove that the Euler-Lagrange vector field is submersive and hence that the motion equations may be simplified. Our results extend to the nonautonomous case the previous ones obtained by Kossowski and Thompson.     

Dynamical theory of topological defects

A method is presented to obtain stochastic equations of motion for topological defects from the underlying TDGL-like stochastic dissipative field equations. The method makes use of virtual displacements of the Goldstone coordinates of topological defects. Effects of kinematical constraints among Goldstone coordinates are studied. The method is applied to modulated systems and we obtain stochastic equations of motion for interfaces (domain walls) and vortex lines (dislocation or defect lines). The driving force for a vortex line is found to include besides the usual surface tension force a new force due to misfit, which is an analogue of the Magnus force on a quantized vortex line and the Peach-Kochler force on a dislocation. A general expression for interactions between parts of interfaces is obtained in terms of asymptotic forms of field variables far from interfaces.     

Features of interannual variations of ozone in the middle stratosphere over Moscow according to observations at millimeter waves

The features of interannual variations of ozone in the middle stratosphere over Moscow in cold half-years since 1995 to 2015 are considered. These features are most pronounced in two separated groups of winters (six winters in each group) in December–January. It appeared that the seasonal variation of ozone averaged within each group is characterized by a higher ozone concentration \({C_{{O_3}}}\) in group I (in comparison with group II) in December and lower values in January. The differences in the seasonal variation of ozone between these groups at the level of 10 mbar in December and January exceed 2 ppm. A feature of the stratosphere circulation for half-year group I is the existence of a stable polar vortex and the absence of strong midwinter perturbations and sudden stratospheric warmings. On the contrary, for cold half-years of group II, the appearance of strong stratospheric warmings in January–February is in common. The results presented provide a quantitative estimate of the effect of these stratospheric warmings on ozone of the middle stratosphere overMoscow.