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OATAO is an open access repository that collects the work of Toulouse researchers and
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This is an author-deposited version published in :
http://oatao.univ-toulouse.fr/
Eprints ID : 14503
To link to this article: URL:
http://hdl.handle.net/2042/57596
To cite this version : Luminari, Nicola and Airiau, Christophe
Sensitivity and stability analysis of a rigid canopy flow. (2015) In:
22ème congrès Français de Mécanique, 24 August 2015 - 28 August
2015 (Lyon, France).
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CDC = 1 + 10Re −2/3, R e= Uhd/ν !" U2− U1 Uh = (h − z1)ΩCDAη¯1a 1 − U1 2 Uh2 #" ¯ η1 = f ( ¯β1); β¯1= z1 h, U1= u1(z1), U2= u2(z2) $" ∆U Uh = 1 + 16ad %" CDA = CDC 1.16 (1.16 − 9.31ad + 38.6ad 2 − 59.8ad3) &" CD(z) = η(β)CDAχ(z) '" d dz du1 dz 2 = 1 lc 1 2CDau 2 1(z) − gS z1≤ z ≤ h (" tml = α(h − z1) )" lc = 0.22(h − z1) *+" lac = 0.22 ξ tml **" u2(z) = Uh+ 2√gS 3lac (z2− h)2− (z2− z)2 h ≤ z ≤ z2 *!" U1 = s 2gS CD(z1)a = u1(z1), Uh= u1(h) = u2(h) *#" ,- ./0 12030-. 4526 40 3107897:;;< 8-.25=>70 :- :==8.85-:; 0?>:.85- .5 8@A 1530 ./0 75-.8->8.< 5B ./0 =028C:.8C0 48./ 203107. .5 z 128@0 0D15-0-." :. ./0 .51 5B ./0 7:-51< z = h" u′ (h− ) = u′ (h+)48./ : χ B>-7.85-E χ(z) = 1 − e−σ(z−h) z1−h *$" F/0 7:-51< 83 @:=0 5B 3@:;; 7<;8-=023 5B /08G/. hH 5B =8:@0.02 d :-= a B25-.:; :20: 102 20B020-70 C5;>@0 =0-38.< 5B ./0 7<;8-=02"I F/0 125J;0@ 83 =8C8=0= 8-.5 .45 20G85-3 300 9GI * 28G/."H ./0 923. 5-0 8-=0D *" 8-38=0 ./0 7:-51< :-= 48./ ./0 3.20:@4830 C0;578.< u1(z) :-= ./0 3075-= 5-0 :J5C0 8. 8-=0D !" 48./ ./0 C0;578.< u2(z)I F/0 =2:G 750K780-. CD 83 30. .5 L025 :J5C0 z = h :-= 83 @5=0;;0= 48./ 30C02:; B>-7.85-3 8-38=0 ./0 7:-51<I F/0 7:-51< @5=0; J0G8-3 :. z = z1H >-=02 ./83 /08G/. ./0 C0;578.< =503 -5. 7/:-G0I F/0 .>2J>;0-70 @5=0; 83 :33578:.0= 48./ ./200 ;0-G./ tmlH lc :-= lacI ,- :==8.85-H ./0 0?>:.85- * 7:-J0 8-.0G2:.0= :-:;<.87:;;< :J5C0 ./0 7:-51< .5 <80;= u2(z)I M8-:;;<H : -5-;8-0:2 51.8@8L:.85- 125J;0@ 48./ # -03.0= N04.5- 8.02:.85-3 83 20?>820= .5 35;C0 ./0 B>;; 30. 5B 0?>:.85-3I M8G>20 * 3/543 ./0 1259;0 5J.:8-0= B52 7:30 O 5B ./0 20B020-70 1:102 :-= 8. 83 75@1:20= .5 ./0 0D1028@0-.:; =:.: 48./ 02252 J:23"I P5@0 3@:;; =837201:-7803 :20 5J302C0= =>0 .5 ./0 752207.85- @:=0 ./25>G/ ./0 χ B>-7.85- .5 30. 75-.8->8.<
χ n1 = 20 qi n2− n1= 3 Qi(z) qi= [a, d, h, α, ξ, z1, z2, Uh, U1, U2, lc, lac, ¯η1, β1, tml, CDC, CDA, Uh ′ , σ, β] i = 1..n1 Qi= [χ, CD, u1] i = 1 + n1..n2 L = E + L E E = ǫ0E + n1 X i=1 ǫi q2 i 2 + n2 X i=1+n1 ǫi Z h 0 Q2 i 2 dz E
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