Read e-book online Mécanique des fluides fondamentale (Lecture Notes in Physics PDF

By Radyadour K. Zeytounian

ISBN-10: 0387544410

ISBN-13: 9780387544410

ISBN-10: 228700355X

ISBN-13: 9782287003554

ISBN-10: 354038359X

ISBN-13: 9783540383598

ISBN-10: 3540544410

ISBN-13: 9783540544418

Ce cours de mecanique des fluides est avant tout un cours theorique qui repond aux questions fondamentales de ce sujet de recherche. Les quatre premiers chapitres presentent les equations propres a determiner l'ecoulement de fluide considere et diverses options. Les chapitres five et 6sont consacres aux problemes lies los angeles stabilite, aux bifurcations et aux comportements chaotiques. Le livre donne un imaginative and prescient globale des questions traitees en mecanique des fluides qui sont a los angeles base de toute l. a. recherche, de l. a. modelisation et de toutes les purposes dans ce domaine.

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Extra info for Mécanique des fluides fondamentale (Lecture Notes in Physics Monographs,Volume 4)

Sample text

P S == exp (- c o p = Po = Const. ). qui est celle des fluides dits incompressibles. UE) 1. 10). 11). Q. 28a) + + Dt + P V • u = 0; D~:± +:± +~ :± P Dt +Yp - f = Y (). 28b) (2,28c) + 2 lJ ]) :]) + r, lI) OU C v = ~; et on suppose que e = e(p,T) est la loi d'etat du fluide. V et ]) = %{~ ~+ (V ~)T }, ,du,tenseur :± ou'" (:± Y +u)T est le tenseur transpose Y + u • 1II) Precisons que De = Dt 2 terme - p 2;:. DT + 2;:. DP . mais Dp oT Dt 'dp Dt ' Dt =- P~ ~ . ~ au niveau de l'equation (2,28c). ce qui donne le 23 2.

28a) + + Dt + P V • u = 0; D~:± +:± +~ :± P Dt +Yp - f = Y (). 28b) (2,28c) + 2 lJ ]) :]) + r, lI) OU C v = ~; et on suppose que e = e(p,T) est la loi d'etat du fluide. V et ]) = %{~ ~+ (V ~)T }, ,du,tenseur :± ou'" (:± Y +u)T est le tenseur transpose Y + u • 1II) Precisons que De = Dt 2 terme - p 2;:. DT + 2;:. DP . mais Dp oT Dt 'dp Dt ' Dt =- P~ ~ . ~ au niveau de l'equation (2,28c). ce qui donne le 23 2. ---p est bien satisfaite. (ils sont notes: IJ et k )' il vient les equations de Navier-Stokes suivantes, o ecrites dans un syst~e de coordonnees, xj ' cartesiennes, o apU.

Ce qu~ . condu~t F, (4,21) ou ~o et lorsque ... a la formule pO sont les valeurs initiales, O W _ at = 0, de ~ et de p • En particulier, 0 (en ecoulement continu) on a : -+ (4,22) w =0 et -+ u = -+'il J\ ljI , ou la fonction ~ (~,t) est le potentiel des vitesses de l'ecoulement de fluide d'Euler barotrope irrotationnel (~= 0). La relation (4,22) traduit le theoreme dit de Lagrange qui est une consequence directe de l'equation (4,20) dite d'Helmholtz. 4,3. L'EQUATION OE STEICHEN Pour un fluide d'Euler barotrope en evolution irrotationnelle l'equation + Du + Dt Vh = 0 devient (avec (4,22)) : o .

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Mécanique des fluides fondamentale (Lecture Notes in Physics Monographs,Volume 4) by Radyadour K. Zeytounian


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