Stability lecture 17

Stability lecture 17 - Hydrodynamic Stability Lecture 17...

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Hydrodynamic Stability Lecture 17 Dispersion relation for double diffusion stability problem. ()( ) () 22 32 2 4 6 2 2 Pr Pr 1 Pr Pr Pr Pr 0 where a pk p k p R a R s p k R s R a k ka n π ττ τ  ++ + + + + + + − =   =+ 2 a See figure 8.2, pg. 256 Turner. 4 4 line: Pr 27 11 Pr 1 Pr 4 line: 27 4 xw Ra Rs xz Rs Ra τπ +  + +  +  1
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For Static Stability or or TT SS TS Rs Ra α βα αα <− ∆< > β Salt fingers set in for Rs slightly above critical value. Motion is direct, exponential growing mode. imag P0 = For large , Rs Ra Ra τ < Most unstable mode predicts cells that are very tall and thin () 1 4 large or small wavelength. ah Ra ah π Diffusive regive when salt heat 1 K K ττ  =   ± Instability occurs in oscillatory mode. 4 1 2 2 0 0 Pr 27 1P r 4 1 frequency 3P r 1 where low freqency oscillation. i P Ra Rs NN g N z ρ =+ + < + −∂ =
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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 17 - Hydrodynamic Stability Lecture 17...

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