This volume contains the papers presented at the IUTAM Symposium on Geometry and Statistics of Turbulence, held in November 1999, at the Shonan International Village Center, Hayama (Kanagawa-ken), Japan. The Symposium was proposed in 1996, aiming at organizing concen trated discussions on current understanding of fluid turbulence with empha sis on the statistics and the underlying geometric structures. The decision of the General Assembly of International Union of Theoretical and Applied Mechanics (IUTAM) to accept the proposal was greeted with enthusiasm. Turbulence is often characterized as having the properties of mixing, inter mittency, non-Gaussian statistics, and so on. Interest is growing recently in how these properties are related to formation and evolution of struc tures. Note that the intermittency is meant for passive scalars as well as for turbulence velocity or rate of dissipation. There were eighty-eight participants in the Symposium. They came from thirteen countries, and fifty-seven papers were presented. The presenta tions comprised a wide variety of fundamental subjects of mathematics, statistical analyses, physical models as well as engineering applications. Among the subjects discussed are (a) Degree of self-similarity in cascade, (b) Fine-scale structures and degree of Markovian property in turbulence, (c) Dynamics of vorticity and rates of strain, (d) Statistics associated with vortex structures, (e) Topology, structures and statistics of passive scalar advection, (f) Partial differential equations governing PDFs of velocity in crements, (g) Thermal turbulences, (h) Channel and pipe flow turbulences, and others.

Inhalt
A. General and Mathematical.- Mathematical Physics of Turbulence.- The Topology of Scalar Fields in 2D and 3D Turbulence.- Bounds for Turbulent Transport.- Bulk Dissipation in Shear Layers with Suction.- Trying a Metric on Atmospheric Flows.- On the Analogy between 2D Vortices and Stellar Systems.- B. Coherent Structures, Intermittency, and Cascade.- Self-Similarity and Coherence in the Turbulent Cascade.- Coherent Fine Scale Structure in Turbulence.- Coherent Fine Scale Eddies in Turbulent Shear Flows and it's Relation to Anisotropy.- Shear Stress and Dissipation Intermittency in High-Reynolds-Number Turbulence.- Characteristic Time Scales and Energy Transfer in MHD Turbulence.- C. Probability Density Functions and Structure Functions.- Statistics of Transverse Velocity Differences in Turbulence.- On a Complete Statistical Characterization of Turbulence.- Statistical Laws Governed by Vortex Structures in Fully Developed Turbulence.- Probability Density Function of Longitudinal Velocity Increment.- Statistics of Small-Scale Structure of Homogeneous Isotropic Turbulence.- On Universality of Statistics of Pressure Field in Homogeneous Turbulence.- A Statistical Law of Velocity Circulations in Fully Developed Turbulence.- D. Passive Scalar Advections.- Lagrangian Method for Multiple Correlations in Passive Scalar Advection.- Anomalous Scaling in Passive Scalar Advection and Lagrangian Shape Dynamics.- Correlation between Energy and Temperature Dissipation Rates in Turbulent Flows.- Simulation of Scalar Fluctuation Field by a Non-Buoyant Plume in Grid-Generated Turbulence by Random Fourier Modes Method.- E. Vortices, Vorticity, and Strain Dynamics.- Spatiotemporal Structure of Tubular Vortices in Turbulence.- Geometric Aspects of the Interaction of Vorticity and Strain inHomogeneous Sheared Turbulence.- Motion of a Curved Vortex Filament: Higher-Order Asymptotics.- Statistics of Turbulence around a Columnar Vortex.- Study of the Geometry fo Flow Patterns in a Compressible Wake.- Interaction of a Vortex Ring Linked with a Vortex Filament.- Mechanism of Flame Propagation along a Vortex Tube.- F. Large Scale Motions, LES, and Closure.- Mapping Closure for Non-Gaussian Velocity Fields.- Coherent Structure and Subgrid-Scale Energy Transfer in Turbulence.- A Dynamical Model for Turbulence.- Two- and Three-dimensional Behavior of the Large Scales in Rotating Turbulence.- G. Thermal Turbulence, Stratified and Rotating Turbulence.- Comments on High Rayleigh Number Convection.- The Dynamics of Structures of T-Vorticity in 2d Free Convection Turbulence.- Structure of Homogeneous Rotating Turbulence under Stable Density Stratification.- Linear Processes in Unsteady Stratified Sheared Turbulence.- H. Transition Mechanisms.- Direct Numerical Simulation of Transition in Plane Poiseuille Flow.- On the Regeneration Mechanism of Turbulence in the Channel Flow.- I. Modulation of Turbulence.- Turbulence in Polymer Solutions.- Turbulence Modulation due to Solid Particles Moving with Vortex Shedding.- Spectral Features of Axial Velocity and Concentration in a High Schmidt Number Turbulent Jet.- J. Pipe-Flow and Channel-Flow Turbulence.- Structures and Intermittency in Rotating Pipes.- Statistics of Open-Channel Turbulence by Using Simultaneous Measurements of All Three Components of Turbulent Fluctuations with Two-Sets LDAs.- Generation Mechanism of Turbulence-Driven Secondary Currents in Open-Channel Flows.- Turbulence Measurements and Conditional Sampling Analysis on Coherent Vortices in Unsteady Open-Channel Flows over Dune Bed.- Dye Visualization and P.I. V. in the Cross-Stream Plane of a Turbulent Channel Flow.- K. Boundary Layers and Near-Wall Turbulence.- Vorticity Structures and Intermittency in Near Wall Turbulence.- The Use of PIV in Turbulent Boundary Layer Flows.- Boundary Layer Intermittency Model.- Universal Property of Autonomous Layer in Near-Wall Turbulence.- List of Participants.