Physics of Fully Ionized Gases Interscience Tracts on by Lyman Spitzer Jr. PDF

By Lyman Spitzer Jr.

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Extra resources for Physics of Fully Ionized Gases Interscience Tracts on Physics and Astronomy No. 3

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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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Physics of Fully Ionized Gases Interscience Tracts on Physics and Astronomy No. 3 by Lyman Spitzer Jr.


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