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.

From the reviews:

"[...]this book has to be highly recommended both to newcomers in fluid mechanics modelling and to confirmed researchers, since most recent results related to asymptotic analysis in this area can be found in this book."
(Mathematical Reviews 2003A, 2003)

"The author states that the goal of this book is to promote the use of asymptotic methods for developing simplified but rational models for the Navier-Stokes equations which can then be solved numerically to obtain appropriate descriptions of the flow. This is an extremely worthwhile objective because most of the relevant engineering computations are based on relatively adhoc models that are rife with internal inconsistencies. To my knowledge, this is the first book devoted to accomplishing the author's stated objective." (Marvin E. Goldstein, SIAM Review, Vol. 45 (1), 2003)

Inhalt
Introductory Comments and Summary.- Introductory Comments and Summary.- Setting the Scene.- Newtonian Fluid Flow: Equations and Conditions.- Some Basic Aspects of Asymptotic Analysis and Modelling.- Useful Limiting Forms of the NS-F Equations.- Main Astmptotic Models.- The Navier-Fourier Viscous Incompressible Model.- The Inviscid/Nonviscous Euler Model and Some Hydro-Aerodynamics Problems.- Boundary-Layer Models for High-Reynolds Numbers.- Some Models of Nonlinear Acoustics.- Low-Reynolds Numbers Asymptotics.- Three Specific Asymptotic Models.- Asymptotic Modelling of Thermal Convection and Interfacial Phenomena.- Meteo-Fluid-Dynamics Models.- Singular Coupling and the Triple-Deck Model.