Statistical Theories and Computational Approaches to Turbulence : Modern Perspectives and Applications to Global-Scale Flows

This volume contains the papers presented at the workshop on Statistical The­ ories and Computational Approaches to Turbulence: Modern Perspectives and Applications to Global-Scale Flows, held October 10-13, 2001, at Nagoya Uni­ versity, Nagoya, Japan. Because of recent developments in computational capabilities, the compu­ tational approach is showing the potential to resolve a much wider range of length and time scales in turbulent physical systems. Nevertheless, even with the largest supercomputers of the foreseeable future, development of adequate modeling techniques for at least some scales of motion will be necessary for practical computations of important problems such as weather forecasting and the prediction and control of global pollution. The more powerful the available machines become, the more demand there will be for precise prediction of the systems. This means that more precise and reliable knowledge of the underlying dynamics will become important, and that more efficient and precise numerical methods best adapted to the new generation of computers will be necessary. The understanding of the nature of unresolved scales then will playa key role in the modeling of turbulent motion. The challenge to turbulence theory here is to elucidate the physics or dynamics of those scales, in particular their sta­ tistical aspects, and thereby develop models on sound bases to reduce modeling ambiguity. The challenge to the computational method is to develop efficient algorithms suitable for the problems, the machines, and the developed models. Front Matter....Pages II-IX Front Matter....Pages 1-1 Computational Challenges for Global Dynamics of Fully Developed Turbulence in the Context of Geophysical Flows....Pages 3-14 Structural and Statistical Aspects of Stably Stratified Turbulence....Pages 15-24 Dynamics of Rotating Stably Stratified Flows....Pages 25-59 An Introduction to Mixing in a Stably Stratified Fluid....Pages 60-79 Linear Processes in Stratified Turbulence with Rotation or Mean Shear....Pages 80-101 Front Matter....Pages 103-103 Very Large Anisotropic Scales in Turbulent Wall-Bounded Flows....Pages 105-112 Turbulent Plume Diffusion in a Pipe Flow by the PDF Method....Pages 113-126 A Hybrid RANS/LES Calculation of Turbulent Channel Flow....Pages 127-137 Anisotropy versus Universality in Shear Flow Turbulence....Pages 138-158 LES Study on the Very Large-Scale Structures of Wall-Bounded Turbulence and an Effect of Thermal Stratification....Pages 159-173 Front Matter....Pages 175-175 High Resolution DNS of Incompressible Homogeneous Forced Turbulence —Time Dependence of the Statistics—....Pages 177-188 Subgrid Models for Two-Dimensional Turbulence based on Lagrangian Spectral Theory....Pages 189-202 LES Modelings based on the Lagrangian Renormalized Approximation....Pages 203-218 LES of Stably Stratified Turbulence....Pages 219-228 The Eulerian Time Correlation Function in Homogeneous Isotropic Turbulence....Pages 229-238 Predictability of 3D Isotropic Turbulence —Effect of Data Assimilation—....Pages 239-247 Orthonormal Divergence-Free Wavelet Analysis of Spatial Correlation between Kinetic Energy and Nonlinear Transfer in Turbulence....Pages 248-259 Statistics of the Energy Dissipation Rate in Turbulence....Pages 260-268 Lyapunov Exponent of the System Described by Kuramoto-Sivashinsky Equation....Pages 269-273 Front Matter....Pages 275-275 Toward a Statistical Ocean Dynamics....Pages 277-288 Front Matter....Pages 275-275 Internal-Wave-Packet Propagation and Breaking....Pages 289-316 Pattern Formation in Two-Dimensional Turbulence on a Rotating Sphere....Pages 317-326 Quasi-Geostrophic Turbulence in a One-Layer Ocean affected by Horizontal Divergence....Pages 327-340 Self-Similarity of Decaying Two-Dimensional Turbulence governed by the Charney—Hasegawa—Mima Equation....Pages 341-349 A Fast Method for the Calculation of the Fluid Flow on a Sphere using a Combined Compact Difference Scheme....Pages 350-359 Front Matter....Pages 361-361 Panel Session 1 Advanced Computational Approaches in Turbulence Research....Pages 363-380 Panel Session 2 Turbulence Research for Geophysical Applications....Pages 381-409 Part I: Application of the Statistical Theory to Stratified and Rotating Turbulence: Computational Challenges for Global Dynamics of Fully Developed Turbulence in the Context of Geophysical Flows; Structural and Statistical Aspects of Stably Stratified Turbulence; Dynamics of Rotating Stably-Stratified Flows; An Introduction to Mixing in a Stably Stratified Fluid; Linear Processes in Stratified Turbulence with Rotation or Mean Shear Part II: Wall Bounded Flows: Very Large Anisotropic Scales in Turbulent Wall-Bounded Flows; Turbulent Plume Diffusion in a Pipe Flow by the PDF Method; A Hybrid RANS/LES Calculation of Turbulent Channel Flow; Anisotropy versus Universality in Shear Flow Turbulence; LES Study on the Very Large Scale Structures of Wall-Bounded Turbulence and an Effect of Thermal Stratification Part III: Statistical Theory of Turbulence and LES Modeling High Resolution DNS of Incompressible Homogeneous Forced Turbulence - Time Dependence of the Statistics; Subgrid Models for Two-Dimensional Turbulence based on Lagrangian Spectral Theory; LES Modelings based on the Lagrangian Renormalized Approximation; LES of Stably Stratified Turbulence; The Eulerian Time Correlation Function in Homogeneous Isotropic Turbulence; Predictability of 3D Isotopic Turbulence - Effect of Data Assimilation; Orthonormal Divergence-Free Wavelet Analysis of Spatial Correlation between Kinetic Energy and Nonlinear Transfer in Turbulence; Statistics of the Energy Dissipation Rate in Turbulence; Lyapunov Exponent of the System Described by Kuramoto-Sivashinsky Equation Part IV: Geophysical Turbulence: Toward a Statistical Ocean Dynamics; Internal-Wave-Packet Propagation and Breaking; Pattern Formation in Two-Dimensional Turbulence on a Rotating Sphere; Quasi-Geostrophic Turbulence in a One-Layer Ocean affected by Horizontal Divergence; Self-Similarity of Decaying Two-Dimensional Turbulence governed by the Charney-Hasegawa-Mima Equation; A Fast Method for the Calculation of the Fluid Flow on a Sphere using a Combined Compact Difference Scheme Part V: Panel Sessions: Panel Session l: Advanced Computational Approaches in Turbulence Research; Panel Session 2: Turbulence Research for Geophysical Applications. With the recent rapid developments in computational capabilities, the computational approach is becoming a more powerful tool in the study of turbulence. Even with the largest supercomputers of the foreseeable future, however, development of adequate modeling techniques for at least some scales of motion will be necessary for practical computations of such vital concerns as weather forecasting and the prediction and control of global pollution. Understanding the nature of unresolved scales is crucial for modeling. For readers who are inclined toward the physical sciences, this book provides a general view of modeling based on statistical theories. Readers who are more oriented toward application will also be rewarded in finding a collection and appraisal of computational methods and models that are useful in both global-scale geophysical flows and complex engineering flows.