Stability lecture 8

Stability lecture 8 - Lecture 8 Instabilty:...

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Unformatted text preview: Lecture 8 Instabilty: Kelvin-Helmholtz Continued Plug these into 2 Kinematic and 1 dynamic B.C. ( ) ( ) 1. i x my t e e + A ( ) ( ) 1 i x my t kB A e e + = A ( ) ( ) 1 2 i x my t Ui A e e + A A 2 2 1 1 1 2 2 2 1 2. + 2 1 1 3. 2 2 kB A Ui A B gA Ui B B gA Ui B K TA = + + = A A A Three homogeneous, linear equations for 1 2 , , A B B MA = These have a non-trivial solution iff the determinant of the matrix is zero. i.e. det . M = ( ) 1 2 2 1 1 2 2 1 2 1 2 1 1 2 2 A Ui k MA Ui k B k T g Ui Ui B = + + + + A A A A = ( ) 2 2 2 2 1 2 2 1 1 1 det 2 2 M Ui k Ui k k g k T = + + + +...
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This note was uploaded on 06/07/2011 for the course EOC 6934 taught by Professor Staff during the Fall '08 term at University of Florida.

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Stability lecture 8 - Lecture 8 Instabilty:...

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