Geostrophic Vortices On a Sphere
Geostrophic Vortices On a Sphere
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are small at t = 0; and linearization with respect to these quantities is sufficient for the purpose of developing a linear stability criterion.
After somewhat lengthy computations the linear stability equations turn out to be: (5. 4) qi(x^-Oy^) = (A^-B^^ sin^j ^)y^ n 2Tr, ^' n 2w + C (-y) 5 a. Cos (j-1) £1 + C (7) ^ p. Sin (j-l) — . 1=1 "^ . 1=1 "^ n-1 , 2, 27r (5. 5) Qn (y +OX ) = -(A -B } cos'^j — )x \^ -jj ^l^^o o' ^o o 4— rr "^ n c J=0 + ^0(7) XZ «j sin (j-l) ^-C^i-y) \ ^. Cos (j-l) ^, 1^,... &r 27r- (5. 6) -q-L sin 7. P^ = ^ C^(7)[x^ sin (k-l) ^ - Y^ cos (k-l) ^] n n + 7Z \. P. + ZII Bj^Ja -a ), JT^k j= (5. 7) q^ sin 7. A.
_ 1^ C'(7)[x cos (k-l) — + y^ sin (k-l) ^] (X o^'^^'-o ^ ^n "^o ^ 'n n n > A, . A. + ^ C, . P . + Cp, ^ "kj J 4^ kj J ^k JA JA where 26 qi = A = 4a sm VTT M- 4b M-, ^ilL^ P;(l)+-^ P;(1)[C^(0, A)-C^(1, A)P;(1)] + n[C, (0, A)p'(l)P (cos -y) + 2C (2, a)P" (1)P" (cos 7) - P^(-cos 7) cos 7], B = sin^7[P"(-cos 7) +4c^(2, A)P;;(l)P;;(cos 7)], 0^(7) = P' (-cos 7) sin 7 - C^(l, A)P^(l)P^(cos 7) sin 7, \; 27r p'(-cos 7, .
What to read after Geostrophic Vortices On a Sphere?
You can find similar books in the "Read Also" column, or choose other free books by A S Peters to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
are small at t = 0; and linearization with respect to these quantities is sufficient for the purpose of developing a linear stability criterion.
After somewhat lengthy computations the linear stability equations turn out to be: (5. 4) qi(x^-Oy^) = (A^-B^^ sin^j ^)y^ n 2Tr, ^' n 2w + C (-y) 5 a. Cos (j-1) £1 + C (7) ^ p. Sin (j-l) — . 1=1 "^ . 1=1 "^ n-1 , 2, 27r (5. 5) Qn (y +OX ) = -(A -B } cos'^j — )x \^ -jj ^l^^o o' ^o o 4— rr "^ n c J=0 + ^0(7) XZ «j sin (j-l) ^-C^i-y) \ ^. Cos (j-l) ^, 1^,... &r 27r- (5. 6) -q-L sin 7. P^ = ^ C^(7)[x^ sin (k-l) ^ - Y^ cos (k-l) ^] n n + 7Z \. P. + ZII Bj^Ja -a ), JT^k j= (5. 7) q^ sin 7. A.
_ 1^ C'(7)[x cos (k-l) — + y^ sin (k-l) ^] (X o^'^^'-o ^ ^n "^o ^ 'n n n > A, . A. + ^ C, . P . + Cp, ^ "kj J 4^ kj J ^k JA JA where 26 qi = A = 4a sm VTT M- 4b M-, ^ilL^ P;(l)+-^ P;(1)[C^(0, A)-C^(1, A)P;(1)] + n[C, (0, A)p'(l)P (cos -y) + 2C (2, a)P" (1)P" (cos 7) - P^(-cos 7) cos 7], B = sin^7[P"(-cos 7) +4c^(2, A)P;;(l)P;;(cos 7)], 0^(7) = P' (-cos 7) sin 7 - C^(l, A)P^(l)P^(cos 7) sin 7, \; 27r p'(-cos 7, .
What to read after Geostrophic Vortices On a Sphere?
You can find similar books in the "Read Also" column, or choose other free books by A S Peters to read onlineMoreLess
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