分形理论在紊流与泥沙研究中的应用现状
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摘要
紊流与泥沙问题是河流动力学的基本问题,也是水科学中的公认难题,传统的线性数学方法在解决这类强非线性问题时存在较大局限性。分形理论作为非线性科学的一个重要分支,为紊流和泥沙问题的研究提供了新的途径。基于国内外大量研究资料,系统论述了分形理论在紊流和泥沙问题中的应用现状,探讨了其应用前景。
Turbulence and sediment problems are the basic topics of river dynamics,as well as the well-known hard-solved problems in hydroscience,for conventional linear mathematic methods have relatively more limitations in solving these non-linear problems.Fractal theory as one of the most important nonlinear science branches provides a new approach to study turbulence and sediment.Based on a large number of research materials at home and abroad,the application actuality of factal theory in turbulence and sediment studies is illustrated systematically and its application prospect is explored.
Turbulence and sediment problems are the basic topics of river dynamics,as well as the well-known hard-solved problems in hydroscience,for conventional linear mathematic methods have relatively more limitations in solving these non-linear problems.Fractal theory as one of the most important nonlinear science branches provides a new approach to study turbulence and sediment.Based on a large number of research materials at home and abroad,the application actuality of factal theory in turbulence and sediment studies is illustrated systematically and its application prospect is explored.
引文
[1]谢和平,薛秀谦.分形应用中的数学基础与方法[M].北京:科学出版社,1997.
[2][日]高安秀树.分数维[M].沈步明,常子文,译.北京:地震出版社,1989.
[3]杨培才.紊流运动与非线性科学理论[J].力学进展,1994,24(2):205-219.
[4]黄真理.紊流的分形特征[J].力学进展,2000,30(4):581-596.
[5]Fujisaka H,Mori H.A maximum principle for determiningthe intermittency exponent of fully developed steady tur-bulence[J].Prog Theorphys,1979,62(8):54-60.
[6]Tabelling P.Sudden increase of the fractal dimension in ahydrodynamic system[J].Phys Rev,1985,31(5):3460-3462.
[7]Sreenivasan K R,Meneveau C.The fractal facets of turbu-lence[J].Fluid Mech,1986,173(3):357-386.
[8]Prasad T,Murayama M,Tanida Y.Fractal analysis of tur-bulent premixed flame surface[J].Experiment in Fluids,1997,245(10):61-71.
[9]Ali Naghi Ziaei,Ali Reza Keshavarzi,Emdad Homayoun.Fractal scaling and simulation of velocity components andturbulent shear stress in open channel flow[J].Chaos,Solitons and Fractals,2005(24):1031-1045.
[10]汤一波,金忠青.分形理论在紊流力学中的应用[J].河海科技进展,1992,12(3):55-64.
[11]汤一波,金忠青.脉动压力的紊流分形特征[J].水科学进展,1998,9(4):361-365.
[12]王玲玲,金忠青.分形理论及其在紊流研究中的应用[J].河海大学学报,1997,25(1):1-5.
[13]肖勇,金忠青.紊流涡旋自相似性及标度不变性研究的进展[J].水利水电科技进展,2001,21(6):11-13.
[14]李玉梁,田晓东,梁东方.二维半岛紊动尾流的分维量测与分析[J].水力发电学报,2004,23(4):60-64.
[15]沈学会,陈举华.分形与混沌理论在紊流研究中的应用[J].河南科技大学学报(自然科学版),2005,26(19):27-30.
[16]Paladin G,Vulpiani A.Anomalous scaling law in multi-fractal objects[J].Physics Reports,1987,156(4):147-225.
[17][美]陈景仁,胡晓强.湍流模化的现状及发展趋势[J].力学进展,1992,22(3):381-384.
[18]She Z S,Leveque E.Universal scaling law in fully devel-oped turbulence[J].Phys Rey Lett,1994,72(3):336-339.
[19]佘振苏,苏卫东.紊流中的层次结构和标度律[J].力学进展,1999,29(3):289-303.
[20]Cao N,Chen S.An intermittency model for passive-scalarturbulence[J].Phys Fluids,1997,9(5):1203-1205.
[21]Leveque E.Scaling laws for the turbulent mixing of a pas-sive scalar in the wake of a cylinder[J].Phys Fluids,2001,11(7):1869-1879.
[22]刘代俊,钟本和,张允湘,等.颗粒与液相间的紊流涡旋裂变传质模型[J].化工学报,2004,55(1):25-31.
[23]Hentschel H,Procaccia I.Fractal nature of turbulence asmanifested in burbulent diffusion[J].Physical ReviewA,1983,27(2):1266-1269.
[24]Hentschel H,Procaccia I.Relative diffusion in burbulentmedia:the fractal dimension of clouds[J].Physical Re-view A,1984,29(3):1461-1470.
[25]杨宏?,顾?,刘勇,等.紊流预混火焰传播速度的分形模型研究[J].工程热物理学报,2001,22(4):507-510.
[26]Asher Yahalom.A DLA model for Turbulence[J].arXiv:math-ph/0611065 2006(24):1-3.
[27]武智生,魏春玲,马崇武,等.沙粒粗糙度和粒径分布的分形特性[J].兰州大学学报(自然科学版),1999,35(1):53-56.
[28]王协康,方铎,姚令侃.非均匀沙床面粗糙度的分形特征[J].水利学报,1999(7):70-74.
[29]王协康,方铎,曹叔尤.天然河道床面糙度特征的试验研究[J].水力发电学报,2000(2):49-55.
[30]Muaary AB.Acellular model of braided rivers[J].1994,371(1):54-57.
[31]姚令侃,方铎.非均匀沙自组织临界性及其应用研究[J].水利学报,1997(3):26-32.
[32]王协康,方铎,曹叔尤.宽级配卵石泥沙颗粒特性的分维值及其应用[J].长江科学院院报,1999,16(5):9-12.
[33]张之湘,惠仕兵,沈焕荣,等.宽级配卵石推移质输移随机过程的分维研究[J].泥沙研究,2000(4):60-64.
[34]汪富泉,李后强,艾南山,等.水流、泥沙运动及河床演变中的分形与自组织[J].大自然探索,1999,18(69):55-61.
[35]汪富泉,曹叔尤,丁晶.紊流猝发作用下悬移颗粒运动轨迹的分形与自组织特征[J].茂名学院学报,2001,11(3):13-18.
[36]杨清书,傅家谟,罗章仁.西北江三角洲来水来沙的非线性分形特征[J].泥沙研究,2002(6):15-18.
[37]孙厚才,李青云.应用分形原理建立小流域泥沙输移比模型[J].人民长江,2004,35(3):12-21.
[38]Nikora V.Fractal structures of river plan forms[J].WaterResour Res,1991,27(6):1327-1333.
[39]Nikora V I,Sapozhnikov V B.River network fractal geom-etry and its computer simulation[J].Water Resour Res,1993,29(10):3569-3575.
[40]Nikora V I,Sapozhnikov V B,Noever D A1.Fractal geom-etry of individual river channels and its computer simula-tion[J].Water Resour Res,1993,29(10):3561-3568.
[41]Sapozhnikov V B,Foufpula-Georgou E.Self-affinity inbraided rivers[J].Water Resour Res,1996,32(5):1429-1439.
[42]Foufpula-Georgou E,Sapozhnikov VB.Anisotropic scalingin braided rivers:an integrated theoretical framework andresults from application to an experimental river[J].Wa-ter Resour Res,1998,34(4):863-867.
[43]Nykane D K,Foufpula-Georgou E,Sapozhnikov VB.Stud-y of spatial scaling in braided river patterns using synthet-ic aperture radar images[J].Water Resour Res,1998,34(7):1795-1807.
[44]金德生,陈浩,郭庆伍.河道纵剖面分形-非线性形态特征[J].地理学报,1997,52(2):154-162.
[2][日]高安秀树.分数维[M].沈步明,常子文,译.北京:地震出版社,1989.
[3]杨培才.紊流运动与非线性科学理论[J].力学进展,1994,24(2):205-219.
[4]黄真理.紊流的分形特征[J].力学进展,2000,30(4):581-596.
[5]Fujisaka H,Mori H.A maximum principle for determiningthe intermittency exponent of fully developed steady tur-bulence[J].Prog Theorphys,1979,62(8):54-60.
[6]Tabelling P.Sudden increase of the fractal dimension in ahydrodynamic system[J].Phys Rev,1985,31(5):3460-3462.
[7]Sreenivasan K R,Meneveau C.The fractal facets of turbu-lence[J].Fluid Mech,1986,173(3):357-386.
[8]Prasad T,Murayama M,Tanida Y.Fractal analysis of tur-bulent premixed flame surface[J].Experiment in Fluids,1997,245(10):61-71.
[9]Ali Naghi Ziaei,Ali Reza Keshavarzi,Emdad Homayoun.Fractal scaling and simulation of velocity components andturbulent shear stress in open channel flow[J].Chaos,Solitons and Fractals,2005(24):1031-1045.
[10]汤一波,金忠青.分形理论在紊流力学中的应用[J].河海科技进展,1992,12(3):55-64.
[11]汤一波,金忠青.脉动压力的紊流分形特征[J].水科学进展,1998,9(4):361-365.
[12]王玲玲,金忠青.分形理论及其在紊流研究中的应用[J].河海大学学报,1997,25(1):1-5.
[13]肖勇,金忠青.紊流涡旋自相似性及标度不变性研究的进展[J].水利水电科技进展,2001,21(6):11-13.
[14]李玉梁,田晓东,梁东方.二维半岛紊动尾流的分维量测与分析[J].水力发电学报,2004,23(4):60-64.
[15]沈学会,陈举华.分形与混沌理论在紊流研究中的应用[J].河南科技大学学报(自然科学版),2005,26(19):27-30.
[16]Paladin G,Vulpiani A.Anomalous scaling law in multi-fractal objects[J].Physics Reports,1987,156(4):147-225.
[17][美]陈景仁,胡晓强.湍流模化的现状及发展趋势[J].力学进展,1992,22(3):381-384.
[18]She Z S,Leveque E.Universal scaling law in fully devel-oped turbulence[J].Phys Rey Lett,1994,72(3):336-339.
[19]佘振苏,苏卫东.紊流中的层次结构和标度律[J].力学进展,1999,29(3):289-303.
[20]Cao N,Chen S.An intermittency model for passive-scalarturbulence[J].Phys Fluids,1997,9(5):1203-1205.
[21]Leveque E.Scaling laws for the turbulent mixing of a pas-sive scalar in the wake of a cylinder[J].Phys Fluids,2001,11(7):1869-1879.
[22]刘代俊,钟本和,张允湘,等.颗粒与液相间的紊流涡旋裂变传质模型[J].化工学报,2004,55(1):25-31.
[23]Hentschel H,Procaccia I.Fractal nature of turbulence asmanifested in burbulent diffusion[J].Physical ReviewA,1983,27(2):1266-1269.
[24]Hentschel H,Procaccia I.Relative diffusion in burbulentmedia:the fractal dimension of clouds[J].Physical Re-view A,1984,29(3):1461-1470.
[25]杨宏?,顾?,刘勇,等.紊流预混火焰传播速度的分形模型研究[J].工程热物理学报,2001,22(4):507-510.
[26]Asher Yahalom.A DLA model for Turbulence[J].arXiv:math-ph/0611065 2006(24):1-3.
[27]武智生,魏春玲,马崇武,等.沙粒粗糙度和粒径分布的分形特性[J].兰州大学学报(自然科学版),1999,35(1):53-56.
[28]王协康,方铎,姚令侃.非均匀沙床面粗糙度的分形特征[J].水利学报,1999(7):70-74.
[29]王协康,方铎,曹叔尤.天然河道床面糙度特征的试验研究[J].水力发电学报,2000(2):49-55.
[30]Muaary AB.Acellular model of braided rivers[J].1994,371(1):54-57.
[31]姚令侃,方铎.非均匀沙自组织临界性及其应用研究[J].水利学报,1997(3):26-32.
[32]王协康,方铎,曹叔尤.宽级配卵石泥沙颗粒特性的分维值及其应用[J].长江科学院院报,1999,16(5):9-12.
[33]张之湘,惠仕兵,沈焕荣,等.宽级配卵石推移质输移随机过程的分维研究[J].泥沙研究,2000(4):60-64.
[34]汪富泉,李后强,艾南山,等.水流、泥沙运动及河床演变中的分形与自组织[J].大自然探索,1999,18(69):55-61.
[35]汪富泉,曹叔尤,丁晶.紊流猝发作用下悬移颗粒运动轨迹的分形与自组织特征[J].茂名学院学报,2001,11(3):13-18.
[36]杨清书,傅家谟,罗章仁.西北江三角洲来水来沙的非线性分形特征[J].泥沙研究,2002(6):15-18.
[37]孙厚才,李青云.应用分形原理建立小流域泥沙输移比模型[J].人民长江,2004,35(3):12-21.
[38]Nikora V.Fractal structures of river plan forms[J].WaterResour Res,1991,27(6):1327-1333.
[39]Nikora V I,Sapozhnikov V B.River network fractal geom-etry and its computer simulation[J].Water Resour Res,1993,29(10):3569-3575.
[40]Nikora V I,Sapozhnikov V B,Noever D A1.Fractal geom-etry of individual river channels and its computer simula-tion[J].Water Resour Res,1993,29(10):3561-3568.
[41]Sapozhnikov V B,Foufpula-Georgou E.Self-affinity inbraided rivers[J].Water Resour Res,1996,32(5):1429-1439.
[42]Foufpula-Georgou E,Sapozhnikov VB.Anisotropic scalingin braided rivers:an integrated theoretical framework andresults from application to an experimental river[J].Wa-ter Resour Res,1998,34(4):863-867.
[43]Nykane D K,Foufpula-Georgou E,Sapozhnikov VB.Stud-y of spatial scaling in braided river patterns using synthet-ic aperture radar images[J].Water Resour Res,1998,34(7):1795-1807.
[44]金德生,陈浩,郭庆伍.河道纵剖面分形-非线性形态特征[J].地理学报,1997,52(2):154-162.
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