瞿波，博士，江苏南通人。1983年获华东师范大学数学学士学位。1986年获华东师范大学数学硕士学位。1992年赴英国爱丁堡龙比亚大学（Edinburgh Napier University）攻读流体力学博士学位，研究方向是分形在流体中的应用，1999年获博士学位（PhD degree），同年，在英国贝尔法斯特女王大学（Queen’s University of Belfast）做研究助理。2000年在香港大学（Hong Kong University）土木工程系做博士后。2003年在澳大利亚格里菲里斯大学（Griffith University）做研究员。2008年回国，在南通大学任教，是硕士生导师。承担过国家自然科学基金（2012年度）“北极的生态系统和二甲基硫对当地气候的影响”等多项研究课题。20年来致力于分形在流体力学中的应用研究，以及环境模型、水利模型等国际国内课题研究。热衷于数学分形的普及推广，有多项成果在《国际流体数值方法》等国际杂志发表。

　　《分形几何与流体》是瞿波在英国龙比亚大学攻读博士的学位论文的核心成果，深入浅出地介绍了分形及其在流体中的应用，详细论述了如何用分形中的分数布朗运动模拟流水中污染物的轨迹，包括对海湾和海洋中污染物传播轨迹的模拟。是一本实用性强、浅显易懂的应用数学学习和研究的参考用书。

序
preface
List of Symbols

Chapter 1 Introduction
1． Fractals and Fractional Brownian Motion
2． Aim and Objectives
3． Structure of Thesis

Chapter 2 Diffusion and Dispersion in Fluids
1． Introduction
2． Molecular Diffusion： Fick's Law and the Diffusion Equation
3． Statistical Theory of Diffusion： Brownian Motion
4． Turbulent Diffusion
4．1 Introduction
4．2 Eddies
4．3 Taylor's Theorem
4．4 The Relationship Between Lagrangian and Eulerian Measurement
4．5 Relative Diffusion and Richardson's Law
4．6 Okubo's Oceanic Diffusion Diagrams
5． Shear Dispersion
5．1 Introduction
5．2 Taylor and Elder's Shear Dispersion Results
5．3 Dispersion in Rivers
5．4 Dispersion in the Sea
6． Numerical Model of Dispersion
6．1 Solution of the Advection-Diffusion Equation
6．2 The Disadvantage of Solving the Advection-Diffusion Equation
7． Traditional Particle Tracking Methods
8． Summary

Chapter 3 Brownian Motion， Fractional Brownian Motion and Fractal Geometry
1． Brownian Motion
1．1 The Definition of Brownian Motion
1．2 Two Simple Random Walks
1．3 Brownian Motion Generation
1．4 The Properties of a One-Dimensional Brownian Motion Time Trace
1．5 The Skewness and Kurtosis of Random Walks
1．6 Random Walks in Two Dimensions
1．7 The Last Steps of the Random Walks in Two Dimensions
2． Fractional Brownian Motion
2．1 Introduction
2．2 FBM Model
2．3 FBMINC Model
2．4 The Comparison of the FBM and FBMINC Models
2．5 FBM Plots in One Dimension
2．6 The Relationship Between Memory， M， Number of Steps， NSTEP， and Number of Particles， P
2．7 Fractional Brownian Motion in Two Dimensions
2．8 Projection of Two-Dimensional Fractional Brownian Motion
2．9 The Use of Simpler Probability Distributions to Reduce CPU Time
2．10 Long Term Fickian Behaviour
3． fBm as a Random Fractal Function
3．1 Fractal Geometry and Fractal Curves
3．2 Fractal Dimension
3．3 Fractal Properties of fBm
3．4 Methods for Determining H from Real Data
4． Summary

Chapter 4 Coastal Bay Modelling
1． Introduction
2． New Particle Tracking Method Using in the Bay
2．1 Advection
2．2 Diffusion
2．3 Choosing a Time Interval
2．4 Choosing a Diffusion Coefficient
2．5 Boundary Reflection
2．6 The Particle Tracking Model
2．7 Particle Clouds
2．8 Concentration Calculation and Plots
2．9 Further Reported Results
3． Shear Dispersion
3．1 Simple Shear Dispersion （Brownian Motion）
3．2 Shear Dispersion with Fractional Brownian Motion
3．3 Shear Dispersion in the Coastal Bay Model Recirculation Zone
4． Summary

Chapter 5 Simulation of Observed Coastal Dispersion
1． Introduction
2． Northumbrian Coastal Water Data Sets
3． Three Methods for Calculating the Standard Deviation of the Dye Patch Concentrations
3．1 The SQ-Method
3．2 The R-Method
3．3 The SR-Method
3．4 Estimation of the Direction of the Mean Advective Velocity Vector for Each Patch
4． Comparison of the Three Methods
4．1 The Reason for Introducing the SR-Method
4．2 Comparison of the Results Using the Three Methods
5． Accuracy of the Results
5．1 Sensitivity of the Centre
5．2 The Concentration Function Calculation
6． Simulation of the Observed Dye Patches Using an fBm Based Particle Tracking Model
6．1 The Accelerated Fractional Brownian Motion （AFBM） Model
6．2 Simulation Using the FBMINC and AFBM Models
6．3 Concentration Calculations
6．4 Contour Plots
7． Summary

Chapter 6 Conclutions， Discussion and Recommendations
1． Introduction
2． Achievement of Objectives
3． Discussion
4． Recommendations for Future Work

Appendix
brown． for
fbm． for
fbminc． for
bayflu． for
baycloud． for
concent． for
srb1． for
srbb1． for
sruvb1． for
afbm． for

References
postscript