Study of turbulence is of vital scientific, military and economic interest. Advances in several areas of external aerodynamics and internal combustor flows of interest to Air Force hinge on our ability to clearly understand and adequately predict the effects of turbulence. At the current time, however, there exists a substantial gap between our knowledge of the physics of turbulence phenomenon and the physics that is incorporated into turbulence models, especially subgrid closures. The disciplines of turbulence theory/analysis (e.g., rapid distortion theory, spectral closure models), high-order turbulence modeling (e.g., second-moment closures, structure-based models and realizability constraints) and turbulence simulation (DNS- direct numerical simulations, and LES- large eddy simulations) are evolving independently with very little cross fertilization of ideas. For example, the currently popular LES subgrid closures (e.g., Smagorinsky, dynamic Smagorinsky) are algebraic in nature; completely insensitive to extra rates of strain such as rotation, curvature, and buoyancy and, further, may not even be realizable. These major deficiencies in the LES-SGS modeling are tolerated despite the fact that, in higher order closures, these physical effects and mathematical constraints have long been represented adequately. Further, we would like to point out that the very premise of detached-eddy simulation (DES) approach - that is seen as the practical computational tool for turbulence - is erroneous. This is due to the fact that inhomogeneous spatial filtering is inevitable in this method, and yet the governing equations ignore the effects that necessarily arise with inhomogeneous filtering of the velocity field.

Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics,' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely.

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.

This unique book gives a general unified presentation of the use of the multiscale/multiresolution approaches in the field of turbulence. The coverage ranges from statistical models developed for engineering purposes to multiresolution algorithms for the direct computation of turbulence. It provides the only available up-to-date reviews dealing with the latest and most advanced turbulence models (including LES, VLES, hybrid RANS/LES, DES) and numerical strategies. The book aims at providing the reader with a comprehensive description of modern strategies for turbulent flow simulation, ranging from turbulence modeling to the most advanced multilevel numerical methods. Sample Chapter(s). Chapter 1: A Brief Introduction to Turbulence (4,125 KB). Contents: A Brief Introduction to Turbulence; Turbulence Simulation and Scale Separation; Statistical Multiscale Modeling; Multiscale Subgrid Models: Self-Adaptivity; Structural Multiscale Subgrid Models: Small Scale Estimations; Unsteady Turbulence Simulation on Self-Adaptive Grids; Global Hybrid RANS/LES Methods; Zonal RANS/LES Methods. Readership: Researchers and engineers in academia and industry in aerospace, automotive and other aerodynamics-oriented fields; masters-level students in fluid mechanics, computational fluid dynamics and applied mathematics.

These proceedings contain the papers presented at the 4th International Symposium on Engineering Turbulence Modelling and Measurements held at Ajaccio, Corsica, France from 24-26 May 1999. It follows three previous conferences on the topic of engineering turbulence modelling and measurements. The purpose of this series of symposia is to provide a forum for presenting and discussing new developments in the area of turbulence modelling and measurements, with particular emphasis on engineering-related problems. Turbulence is still one of the key issues in tackling engineering flow problems. As powerful computers and accurate numerical methods are now available for solving the flow equations, and since engineering applications nearly always involve turbulence effects, the reliability of CFD analysis depends more and more on the performance of the turbulence models. Successful simulation of turbulence requires the understanding of the complex physical phenomena involved and suitable models for describing the turbulent momentum, heat and mass transfer. For the understanding of turbulence phenomena, experiments are indispensable, but they are equally important for providing data for the development and testing of turbulence models and hence for CFD software validation.