Focusing on convection in fluids, this monograph offers a comprehensive and rational exploration of various convective phenomena. It emphasizes the role of buoyancy forces and temperature-dependent surface tension in fluid homogeneities, providing a unified framework for understanding these complex processes.
Focusing on the intersection of meteorology and fluid mechanics, this monograph presents the author's research findings primarily from graduate lectures at Lille I University. It emphasizes the application of singular perturbation techniques to atmospheric flow modeling, acknowledging the complexity of the subject and the numerous unresolved questions. While it does not cover every important aspect, the work aims to guide future research by clarifying both solved and unsolved problems in the field of theoretical fluid mechanics related to atmospheric flows.
This work delves into the stochastic modeling of fluctuations in incompressible systems, inspired by discussions with J. P. Guiraud. It explores the relationship between large eddy behavior and probability space, deriving Reynolds stresses through a Monte-Carlo process applied to fluctuation equations. By employing a random set of equations that replicate large eddy fluctuations, the authors utilize stochastic averaging to analyze solutions. The underlying asymptotic principles are subtly connected to homogenization and localization processes, offering a novel perspective on fluid dynamics.
A Rational Asymptotic Modelling Point of View
The book presents a comprehensive Navier-Stokes-Fourier modeling theory specifically for Newtonian fluids, addressing the complexities of compressible, viscous, and heat-conducting flows. It meticulously deconstructs the theoretical framework and applies it to a range of practical scenarios, including technological and geophysical challenges, demonstrating the model's relevance and utility in real-world applications.
A Scientific Autobiography
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.
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.
This book closes the gap between standard undergraduate texts on fluid mechanics and monographical publications devoted to specific aspects of viscous fluid flows. Each chapter serves as an introduction to a special topic that will facilitate later application by readers in their research work.
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.
Cet ouvrage présente la deuxième partie d'un cours sur la modélisation, la première ayant fait l'objet de la publication du volume No. 245 dans cette même série. Dans ces leçons, l'auteur traite essentiellement des problèmes d'ordre pratique, et en particulier de ceux liés aux écoulements à grands nombres de Reynolds, et tient compte entre autres paramètres des nombres de Strouhal, de Mach, etc. Parmi les sujets traités on trouve: les modèles de Prandtl (couche limite), de Stokes et d'Oseen (fluides fortement visqueux) ainsi que les modèles en triple couche de Neiland et Stewartson-Williams et ceux en double couche limite de Riley et Stuart (écoulements oscillants). Ce livre - le premier sur la modélisation asymptotique - s'adresse aussi bien aux étudiants qu'aux chercheurs.
Le but principal du présent ouvrage est de familiariser les étudiants aux concepts actuels de la modélisation asymptotique et à leurs applications aux écoulements des fluides Newtoniens dans diverses configurations. La lecture ne présente aucune difficulté particulière. Cependant le déroulement logique et systématique de l'exposé met en place tout le formalisme de la modélisation asymptotique (ch. II à VI). Ce livre est l'un des premiers à présenter un panorama assez vaste sur la modélisation asymptotique des écoulements de fluides Newtoniens: il s'agit aussi bien des techniques asymptotiques que de la mise en œuvre effective de la modélisation à des problèmes concrets de la mécanique des fluides (ch. VII à XI).