for the fluctuations around the means but rather fluctuations, and appearing in the following incompressible system of equations: on any wall; at initial time, and are assumed known. This contribution arose from discussion with J. P. Guiraud on attempts to push forward our last co-signed paper (1986) and the main idea is to put a stochastic structure on fluctuations and to identify the large eddies with a part of the probability space. The Reynolds stresses are derived from a kind of Monte-Carlo process on equations for fluctuations. Those are themselves modelled against a technique, using the Guiraud and Zeytounian (1986). The scheme consists in a set of like equations, considered as random, because they mimic the large eddy fluctuations. The Reynolds stresses are got from stochastic averaging over a family of their solutions. Asymptotics underlies the scheme, but in a rather loose hidden way. We explain this in relation with homogenizati- localization processes (described within the §3. 4 ofChapter 3). Ofcourse the mathematical well posedness of the scheme is not known and the numerics would be formidable! Whether this attempt will inspire researchers in the field of highly complex turbulent flows is not foreseeable and we have hope that the idea will prove useful.

Rationality - as opposed to 'ad-hoc' - and asymptotics - to emphasize the fact that perturbative methods are at the core of the theory - are the two main concepts associated with the Rational Asymptotic Modeling (RAM) approach in fluid dynamics when the goal is to specifically provide useful models accessible to numerical simulation via high-speed computing. This approach has contributed to a fresh understanding of Newtonian fluid flow problems and has opened up new avenues for tackling real fluid flow phenomena, which are known to lead to very difficult mathematical and numerical problems irrespective of turbulence. With the present scientific autobiography the author guides the reader through his somewhat non-traditional career; first discovering fluid mechanics, and then devoting more than fifty years to intense work in the field. Using both personal and general historical contexts, this account will be of benefit to anyone interested in the early and contemporary developments of an important branch of theoretical and computational fluid mechanics.

Proceedings of the IUTAM Symposium held in Liverpool, UK, 8-11 July 2002

This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.

This monograph presents a synopsis of fluid dynamics based on the personal scientific experience of the author who has contributed immensely to the field. The interested reader will also benefit from the general historical context in which the material is presented in the book. The book covers a wide range of relevant topics of the field, and the main tool being rational asymptotic modelling (RAM) approach. The target audience primarily comprises experts in the field of fluid dynamics, but the book may also be beneficial for graduate students.

Hyposonic fluid flows, characterized by a low Mach number, are mainly linked with geophysical and environmental fluid flows. In addition they are relevant to engineers because of their connection with aerodynamics. The books brings together insights derived from mathematically rigorous results and combines them with a number of realistic fluid flow situations. Asymptotic analytic solutions for the low-Mach number cases are developed to provide both insights into the underlying physics as well as benchmarks for numerical computations.

A real boon for those studying fluid mechanics at all levels, this work is intended to serve as a comprehensive textbook for scientists and engineers as well as advanced students in thermo-fluid courses. It provides an intensive monograph essential for understanding dynamics of ideal fluid, Newtonian fluid, non-Newtonian fluid and magnetic fluid. These distinct, yet intertwined subjects are addressed in an integrated manner, with numerous exercises and problems throughout.

The purpose of this book is to present a broad panorama of model problems encountered in nonviscous Newtonian fluid flows. This is achieved by investigating the significant features of the solutions of the corresponding equations using the method of asymptotic analysis. The book thereby fills a long-standing gap in the literature by providing researchers working on applied topics in hydro-aerodynamics, acoustics and geophysical fluid flows with exact results, without having to invoke the complex mathematical apparatus necessary to obtain those insights. The benefit of this approach is two-fold: outlining the idea of the mathematical proofs involved suggests methodologies and algorithms for numerical computation, and also often gives useful information regarding the qualitative behavionr of the solutions. This book is aimed at researchers and students alike as it also provides all the necessary basic knowledge about fluid dynamics.

Viscous flow is treated usually in the frame of boundary-layer theory and as two-dimensional flow. Books on boundary layers give at most the describing equations for three-dimensional boundary layers, and solutions often only for some special cases. This book provides basic principles and theoretical foundations regarding three-dimensional attached viscous flow. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers. This wider scope is necessary in view of the theoretical and practical problems to be mastered in practice. The topics are weak, strong, and global interaction, the locality principle, properties of three-dimensional viscous flow, thermal surface effects, characteristic properties, wall compatibility conditions, connections between inviscid and viscous flow, flow topology, quasi-one- and two-dimensional flows, laminar-turbulent transition and turbulence. Though the primary flight speed range is that of civil air transport vehicles, flows past other flying vehicles up to hypersonic speeds are also considered. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers, as this wider scope is necessary in view of the theoretical and practical problems that have to be overcome in practice. The specific topics covered include weak, strong, and global interaction; the locality principle; properties of three-dimensional viscous flows; thermal surface effects; characteristic properties; wall compatibility conditions; connections between inviscid and viscous flows; flow topology; quasi-one- and two-dimensional flows; laminar-turbulent transition; and turbulence. Detailed discussions of examples illustrate these topics and the relevant phenomena encountered in three-dimensional viscous flows. The full governing equations, reference-temperature relations for qualitative considerations and estimations of flow properties, and coordinates for fuselages and wings are also provided. Sample problems with solutions allow readers to test their understanding.

This plenary paper and the accompanying presentation have highlighted field problems involving fluid-structure interaction over a wide span of Navy operations. Considering the vast size and versatility of the Navy's inventory, the cases presented represent examples of a much larger problem. But even this limited set provides sufficient evidence that fluid-structure interaction does hinder the Navy's ability to accomplish its missions. This survey has also established that there are no accurate and generally applicable design tools for addressing these problems. In the majority of cases the state-of-practice is to either make ad-hoc adjustments and estimates based on historical evidence, or conduct expensive focused tests directed at each specific problem and/or candidate solution. Unfortunately, these approaches do not provide insight into the fundamental problem, and neither can be considered reliable regarding their likelihood of success. So the opportunities for applying computational fluid-structure interaction modeling to Navy problems appear limitless. Scenarios range from the "simple" resonant strumming of underwater and in-air cables, to the "self-contained" flow field and vibration of aircraft/ordnance bodies at various Mach numbers, to violent underwater transient detonations and local hull structural collapse. Generally applicable and computationally tractable design-oriented models for these phenomena are of course still far in the future. But the Navy has taken the first steps in that direction by sponsoring specialized numerical models, validation experiments tailored for specific applications, and conferences such as this one.