The geodynamo as a bistable oscillator

Abstract

Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating α reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ∝(1 ? a ²)², subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2?3) × 10⁵ year, is shown to imply a secular variation of the axial dipole moment of ～ 15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data.     

螺旋度在分析一次三峡大暴雨中的应用

用螺旋度分析了1982年7月16日三峡区间出现的近27年来最大一次暴雨。结果表明，①在垂直剖面图上，在雨区上空300 hPa附近，螺旋度有一个负的极小值中心；在600 hPa附近，有一个正的极大值中心。②300 hPa螺旋度分布图上的极小值中心位置，与主要雨区中心位置非常靠近，相距约60 km。     

北京一次强降水过程的数值模拟

利用新一代中尺度数值预报模式WRF3.3和1°×1°的NCEP气象再分析资料,对2011年7月24日北京强降水天气过程进行数值模拟,并利用模式输出的高分辨率资料进行诊断分析。结果表明：WRF模式能较好地模拟出这次强降水过程。该过程不仅受到对流层中低层长波低槽和地面辐合区系统性的动力抬升作用,还受到对流层高层辐散的强迫作用。在这种配置下,中低层大尺度动力抬升与高层强辐散呈现出垂直耦合状态,有利于强降水区垂直环流和对流的发展。同时北京地区上空500 hPa以下相对湿度大于70 %,在降水区形成了深厚的高湿环境,为降水的产生、加强和维系提供了充沛的水汽条件。从大气稳定度方面看,北京市全境均处于K指数高值区,高峰值为42.5 ℃,反映了大气层结非常不稳定。从动力作用分析发现,高空辐散、低空辐合的流场特征促进了降水的产生,螺旋度低层正值、高层负值的耦合结构是触发并维持降水的动力机制。     

New energy and helicity bounds for knotted and braided magnetic fields

In this article we present a review of some of the author's most recent results in topological magnetohydrodynamics (MHD), with an eye to possible applications to astrophysical flows and solar coronal structures. First, we briefly review basic work on magnetic helicity and linking numbers, and fundamental relations with magnetic energy and average crossing numbers of magnetic systems in ideal conditions. In the case of magnetic knots, we focus on the relation between their groundstate energy and topology, discussing the energy spectrum of tight knots in terms of ropelength. We compare this spectrum with the one given by considering the bending energy of such idealized knots, showing that curvature information provides a rather good indicator of magnetic energy contents. For loose knots far from equilibrium we show that inflexional states determine the transition to braid form. New lower bounds for tight knots and braids are then established. We conclude with results on energy-complexity relations for systems in presence of dissipation.     

“05．8”十堰大暴雨的数值模拟与诊断分析

使用NCEP 1°×1°6h再分析格点资料和气象台站实测降水资料,采用WRF中尺度数值模式,对2005年8月14日20时至15日08时发生在十堰市的一次大暴雨过程进行了数值模拟与诊断分析,并着重分析了大暴雨的成因。结果表明：此次大暴雨是在西太平洋副热带高压、中高纬西风槽合理配置以及稳定有利的环流形势下发生的,同时与台风低压活动关系密切;东南风急流将低纬度地区暖湿气流输送到高纬度地区,使台风低压长时间维持,为强降水发生发展提供了水汽来源;低层辐合、高层辐散的配置有利于对流发展和低层水汽向高空输送;螺旋度正值中心的出现对未来3h强降水出现有一定的预示作用,螺旋度正值对暴雨落区有较好的指示性,主要暴雨区出现在螺旋度正值中心前方。     

Helicity as a Method for Forecasting Severe Weather Events

This paper introduces a method for forecasting severe weather which is yieded by integrating helicity as a dynamical parameter with K and TOT indexes as thermal parameters.The results of operational tests for two years ure detailed.And the seasonal suitability of the method applications is discussed as well.