Abstract
This Overview is a brief outline of the events related to my rather long “RAM Adventure” during the years 1968–2009. In 1968–1969 my discovery of asymptotics and rational modelling of fluid dynamics problems was, for me, a revelation, and the Rational Asymptotics Modelling (RAM) Approach to these problems, governed by the Navier–Stokes–Fourier (NS–F) equations, has been my main scientific activity during the last 40 years – the systematic, logical and well argued consistent approach via asymptotics, in perfect harmony with my idea about mathematically applied, but not ad hoc, theoretical researches in fluid dynamics, without any modern abstract, sophisticated, functional analysis!
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- 1.
Concerning the term “Navier–Stokes–Fourier” equations used in this book – NS–F equations, governing classical, Newtonian, viscous, compressible and heat-conducting fluid flows – it seems to me that it is better adapted than the term commonly used (mainly by mathematicians), “Navier–Stokes compressible” equations.
- 2.
Office National d’Études et de Recherches Aérospatiales, Châtillon-92320 (France).
- 3.
Sergey Nikitovich Mergelyan (1928–2008) was an Armenian scientist – an outstanding mathematician, and the author of major contributions in Approximation Theory (including his well-known theorem in 1951). The modern Complex Approximation Theory was based mainly on his work (see, for instance, the book Real and Complex Analysis by W. Rudin; French edition, Masson, Paris, 1978). He graduated from Yerevan State University in 1947, and in 1956 played a leading role in establishing the Yerevan Scientific Research Institute of Mathematical Machines (YerSRIMM). He became the first Director of this Institute, which today many refer to as the “Mergelyan Institute”.
- 4.
Il’ya Afanas’evich Kibel (1904–1970), Member of the SSSR Academy of Sciences, was one of the leading Soviet scientist in the field of theoretical hydromechanics. He is famous as the founder of the hydrodynamic method of weather forecasting, and for implementation of mathematical methods in meteorology. See his pioneer monograph, An Introduction to the Hydrodynamical Methods of Short Period Weather Forecasting, published in Russian in Moscow (1957), and translated into English in 1963 (Macmillan, London). Some of his well-known works on the meteo-fluid are published in Selected Works of I. A. Kibel on Dynamic Meteorology (in Russian, GydrometeoIzdat, Leningrad, 1984).
- 5.
Paul Germain wrote to me (in French!): “J’ai pu regarder les feuilles que vous m’avez adressées sur la mise en équation de votre problème. Je prends note du fait que vous ne passez plus par la forme intermédiaire des équations de la convection qui figurait dans les documents que vous m’aviez antérieurement donnés. Je ne suis néanmoins pas satisfait, car je ne vois toujours pas comment est justifiée la cohérence de vos approximations et pourquoi, alors que vous supposer les perturbations de vitesses petites, en particulier la quantité: u2 + w2 − U 2∞ , afin d’obtenir des équations linéaires, vous ne linéarisez pas les conditions aux limites. Vous devez me trouver un peu ‘tâtillon’. Mais si je dois faire partie du jury de votre thèse, c’est à titre de mécanicien des fluides et comme tel, je souhaiterais comprendre le bien fondé des équations de départ. Or depuis votre exposé au séminaire, j’éprouve toujours la même difficulté et les variantes que vous m’avez proposées ne m’éclairent pas.”
- 6.
The first theoretical investigations concerning 3D lee-waves problems in linear approximation was, in fact, carried out by Paul Queney. On the other hand, an excellent synthesis of theoretical developments on relief (lee) waves will be found in WMO Technical Note: “The Air flow over mountains”, N° 34, Geneva, 1960, by P. Queney et al.
- 7.
Entitled La Météorologie du point de vue du Mécanicien des Fluides, written for the XIIth Symposium on Advanced Problems and Methods in Fluid Mechanics, Bialowieza (Poland), 8–13 September 1975.
References
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Zeytounian, R.Kh.: Étude des Phénomènes d’ondes dans les Écoulements Stationnaires d’un Fluide Stratifié non Visqueux. Publication ONERA N°126, 94 pages, Chatillon, février 1969. English version: Study of Wave Phenomena in the Steady Flow of an Inviscid Stratified Fluid. Royal Aircraft Establishment, Library Translation N°1404 (1969)
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Zeytounian, R.K. (2012). NS–F Equations and Modelling: A French Touch. In: Navier-Stokes-Fourier Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20746-4_1
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