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A 3D Self-consistent Propagation Model of the Lightning Leader
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摘要: 为研究上行先导发生发展的特征及其与地面构筑物间的相互作用，该文建立了闪电先导三维自持发展模式。该模式能够在给定雷暴云下空间电场初始分布情况、下行梯级先导始发位置及地面构筑物几何形状等参量时，进行自持发展模拟，计算出上行正先导随时间在三维空间内的头部位置、速度、电流强度、线电荷密度等物理特征量的变化。模拟发现上行正先导始发及发展过程中，其速度呈逐渐增加趋势，临近最后一跳发生前，上行正先导速度增加明显，整个过程中先导速度的变化范围为104~106 m·s-1量级，电流强度随时间也具有逐渐增加趋势，该变化趋势与光学观测得到的先导头部亮度的变化趋势相一致。该闪电先导三维自持模拟模型能够为进一步研究雷击地面构筑物特点提供参考。Abstract: The research on simulation of lightning discharge and propagation is one of key issues nowadays in the knowledge of lightning physics. To study propagation characteristics of the lightning leader and the interaction between the lightning leader and structures, a 3D self-consistent propagation model of lightning leader is proposed considering the limitation of the 2D random model that cannot describe physical features of lightning discharge three-dimension well. This model proposed can properly simulate the downward stepped leader in 3D space based on the initial conditions, such as the background electric field and the geometry of ground installations. Also, the upward continuous progression of positive connecting leaders from its inception to the final jump as the downward negative stepped leader approaches the ground can be simulated. Meanwhile, this model can self-consistently calculate physical parameters of the leader while it develops in three dimensional space based on the transient electric field under the influence of the downward stepped leader and the geometry of ground structures, such as tip location every step, leader velocity, current density, charge per unit length and the length every step moved. Compared with the optical and electrical data of the natural and artificially triggered lightning detected in Guangzhou experiment base, as well as research results available in literature, simulation results of the self-consistent propagation model show that the initiation of the positive upward leader mainly depends on the electric field intensity and the geometry of the structure in the simulated domain. As the upward leader initiates and propagates towards the downward stepped leader, its velocity increases from 104 m·s-1 to 105 m·s-1 order of magnitude gradually along with time during the first 0-600 μs, and then its velocity obviously increases to 106 m·s-1 order of magnitude when the upward positive leader connects to the downward stepped leader, during which the average velocity reaches about 5×105 m·s-1. Furthermore, the current intensity in the channel also increases with the upward positive leader moving forward, and the trend has a good coherence with the variation of the relative brightness of the leader, which is consistent with the optical data and existing research. Through simulation results of lightning flashes striking on high structure, it is also derived that the charge per unit length in the propagation channel of upward positive leader initiated from high structure reaches about 50.0-108.0 μC·m-1, with an average value of 64.3 μC·m-1. In addition, the average length of upward positive leader is approximately 417 m. The research of 3D self-consistent propagation model of lightning leader can provide reference for further study of characteristics of lightning flashes striking on structures.
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图 1 闪电先导三维自持发展数值模拟模型
Fig. 1 A 3D self-consistent propagation model of lightning leader
图 2 空间离散化示意图
(a) 对模拟区域格点化，(b) 七点差分模型
Fig. 2 The spatial discretization model
(a) gridding of the simulation field, (b)7-point finite difference scheme
图 3 上行先导始发判断数值模拟计算流程图
Fig. 3 The numerical simulation flowchart of calculating the upward leader inception condition
图 5 高建筑上方闪击事件模拟个例
(H为模型中建筑物理想高度，R为上行先导初始位置相对于建筑物中心的水平偏移距离，α为背景电场强度线性增加系数)
Fig. 5 Simulation cases of lightning flashes striking on tall structures
(H is the height of the structure, R is the horizontal distance between the upward leader and the center of the roof, α is the linear increation coefficient of the electric field intensity)
图 6 先导速度随时间变化图
Fig. 6 Variations of the upward leader speed under different conditions
图 7 电流强度变化
Fig. 7 Variations of currents of the upward leader under different conditions
表 1 不同情况下模拟得到的先导长度和线电荷密度
Table 1 Lengths and charge per-unit length of the upward leader under different conditions
序号 先导发展总长度/m 平均线电荷密度/(μC·m-1) 个例1 412 50.0 个例2 431 64.8 个例3 373 59.6 个例4 421 67.8 个例5 407 35.6 个例6 458 108.0 
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