Please wait a minute...
浙江大学学报(工学版)
水利工程、土木工程     
基于随机-动力学模型的非均匀推移质扩散
范念念1, 吴保生2
1. 四川大学水力学与山区河流开发保护国家重点实验室,水利水电学院,四川 成都 610065;2. 清华大学 水沙科学与水利水电工程国家重点实验室,北京 10084
Anomalous diffusion of non-uniform bed load particles based on a stochastic-mechanic model
FAN Nian-nian1, WU Bao-sheng2
1. State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, China; 2.State Key Laboratory of Hydroscience and Hydraulic Engineering, Tsinghua University, Beijing 100084, China
 全文: PDF(551 KB)   HTML
摘要:

为了研究非均匀颗粒与均匀颗粒扩散特性的差异,基于随机-动力学模型建立非均匀推移质泥沙运动的间歇朗之万方程,该方程不仅能够模拟推移质颗粒的间歇运动(运动-静止交替)过程,而且能够较好地反映颗粒速度统计分布特征与颗粒受力之间的联系.采用建立的模型对非均匀颗粒长尾分布停时进行模拟,分析均匀颗粒与非均匀颗粒扩散特征的差异.结果表明,颗粒的非均匀性可以导致某些随机量(如停时)满足长尾分布,但因为不满足中心极限定理,这种长尾分布与均匀颗粒的长尾分布将导致完全不同的扩散类型.说明非均匀颗粒在大的时间尺度上表现为弹道运动,这种弹道运动反映出的并不是反常扩散,而是确定性的沿程分选过程.

Abstract:

Aiming to study the different diffusion regimes between uniform and non-uniform particles, Episodic Langevin Equation (ELE) based on stochastic-mechanics model was developed, which could reproduce the episodic movement (start and stop) of bed load particles, moreover, the model could link the probability distribution of velocities to the forces exerted on one single particle. We incorporated heterogeneity of particle sizes and simulated power-law distributed waiting times. For the violation of independent and identical distribution assumption, non-uniform particles resulted in completely different diffusion regimes with uniform particles. Our results demonstrate that heterogeneity in particles results in ballistic in large scales, which illustrates that the transport process is deterministic sorting, rather than anomalous diffusion.

出版日期: 2015-02-01
:  TV 14  
基金资助:

国家自然科学基金资助项目(51039004);国家“十二五”科技支撑计划资助项目(2012BAB05B01,2012BAB05B02)

作者简介: 范念念(1988—),男,博士.主要从事河流泥沙和水文水资源方面的研究.E-mail: fannian7172@126.com
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章  

引用本文:

范念念, 吴保生. 基于随机-动力学模型的非均匀推移质扩散[J]. 浙江大学学报(工学版), 10.3785/j.issn.1008-973X.2015.02.008.

FAN Nian-nian, WU Bao-sheng. Anomalous diffusion of non-uniform bed load particles based on a stochastic-mechanic model. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 10.3785/j.issn.1008-973X.2015.02.008.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2015.02.008        http://www.zjujournals.com/eng/CN/Y2015/V49/I2/246

[1] 韩其为, 何明民. 推移质扩散的随机模型及统计规律[J]. 中国科学:A辑, 1980(4): 396-408.
HAN Qi-wei, HE Ming-min. Stochastic models for bed load particle diffusion and the statistical properties [J], Science China: Series A, 1980(4): 396-401.
[2] NIKORA V, HABERSACK H, HUBER T, et al. On bed particle diffusion in gravel bed flows under weak bed load transport [J]. Water Resources Research, 2002, 38(10816): 117.
[3] SCHUMER R, MEERSCHAERT M M, BAEUMER B. Fractional advection-dispersion equations for modeling transport at the earth surface [J]. Journal of Geophysical Research-Earth Surface, 2009, 114(F00A07): 115.
[4] MARTIN R L, JEROLMACK D J, Schumer R. The physical basis for anomalous diffusion in bed load transport [J]. Journal of Geophysical Research-Earth Surface, 2012, 117(F01018): 118.
[5] HASCHENBURGER J K. Tracing river gravels: insights into dispersion from a long-term field experiment [J]. Geomorphology, 2013, 200: 121-131.
[6] HASSAN M A, VOEPEL H, SCHUMER R, et al. Displacement characteristics of coarse fluvial bed sediment [J]. Journal of Geophysical Research-Earth Surface, 2013, 118(1): 155-165.
[7] GANTI V, MEERSCHAERT M M, FOUFOULA-GEORGIOU E, et al. Normal and anomalous diffusion of gravel tracer particles in rivers [J]. Journal of Geophysical Research-Earth Surface, 2010, 115(F00A12): 112.
[8] FAN N, ZHONG D, WU B, et al. A mechanistic-stochastic formulation of bed load particle motions: from individual particle forces to the Fokker-Planck equation under low transport rates [J]. Journal of Geophysical Research-Earth Surface, 2014, 119: 464-482.
[9] ROSEBERRY J C, SCHMEECKLE M W, FURBISH D J. A probabilistic description of the bed load sediment flux: 2. Particle activity and motions [J]. Journal of Geophysical Research-Earth Surface, 2012, 117(F03032): 121.
[10] YANG C T, SAYRE W W. Stochastic model for sand dispersion \[J\]. Journal of the Hydraulics Division,1971(97): 265-288.
[11] SUN Z L, DONAHUE J. Statistically derived bedload formula for any fraction of nonuniform sediment [J]. Journal of Hydraulic Engineering-ASCE, 2000, 126(2): 105-111.
[12] WU B S, MOLINAS A, JULIEN P Y. Bed-material load computations for nonuniform sediments [J]. Journal of Hydraulic Engineering-ASCE, 2004, 130(10): 1002-1012.
[13] PARKER G, SUTHERLAND A J. FLUVIAL ARMOR [J]. Journal of Hydraulic Research, 1990, 28(5): 529-544.
[14] 何文社. 非均匀沙运动特性研究 [D]. 成都:四川大学, 2002.
HE Wen-she. Study on laws of transport for non-uniform Sediment [D]. Chengdu: Sichuan University, 2002.
[15] DRAKE T G, SHREVE R L, DIETRICH W E, et al. Bedload transport of fine gravel observed by motion-picture photography [J]. Journal of Fluid Mechanics, 1988, 192: 193-217.
[16] ZHANG Y, MEERSCHAERT M M, PACKMAN A I. Linking fluvial bed sediment transport across scales [J]. Geophysical Research Letters, 2012, 39(L20404): 16.
[1] 匡翠萍, 宋竑霖, 顾杰, 马震. 黄骅港风生流及紊动的三维特性[J]. 浙江大学学报(工学版), 2017, 51(1): 38-45.
[2] 郭聪,孙志林,郑浩磊,潘桂娥. 河口冲淤对围垦的响应[J]. 浙江大学学报(工学版), 2016, 50(9): 1791-1797.
[3] 张晓雷, 夏军强, 邓珊珊, 王增辉. 断面间距对黄河下游高含沙洪水模拟结果影响[J]. 浙江大学学报(工学版), 2016, 50(4): 735-743.
[4] 张文君,孙红月,潘攀,魏振磊. 泥石流虹吸排水分流池自清淤能力分析[J]. 浙江大学学报(工学版), 2015, 49(11): 2159-2164.
[5] 胡德超, 池龙哲, 杨琼, 王敏. 水库坝区冲刷漏斗的形成机理[J]. 浙江大学学报(工学版), 2015, 49(2): 257-264.
[6] 夏军强, 宗全利, 邓珊珊, 许全喜, 张翼. 三峡工程运用后荆江河段平滩河槽形态调整特点[J]. 浙江大学学报(工学版), 2015, 49(2): 238-245.
[7] 孙志林, 倪晓静, 许丹, 聂会. 河口泥沙数学模型的若干问题[J]. 浙江大学学报(工学版), 2015, 49(2): 232-237.
[8] 周建银, 邵学军, 江磊, 假冬冬. 水库细颗粒淤积物的重力驱动流动[J]. 浙江大学学报(工学版), 2014, 48(12): 2254-2258.
[9] 孙志林, 杨仲韬, 高运, 许丹, 胡世祥. 长江分汊河口水力几何形态[J]. 浙江大学学报(工学版), 2014, 48(12): 2266-2270.
[10] 陈一帆, 程伟平, 蒋建群. 一种稳健的河流糙率反演方法[J]. J4, 2013, 47(8): 1361-1365.
[11] 张世瑕,王紫雯,吴赛男. 沿海围垦对防灾功能影响的景观生态机理研究
——以钱塘江河口海湾为例
[J]. J4, 2012, 46(7): 1281-1288.
[12] 李佳,姚炎明,孙志林,黄赛花,杨晓东. 大型海洋倾倒区悬浮物迁移扩散的数值模拟[J]. J4, 2011, 45(7): 1319-1328.
[13] 许丹, 孙志林. 钱塘江河口突发污染物扩散数值模拟分析[J]. J4, 2010, 44(9): 1767-1772.