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Stability lecture 22

# Stability lecture 22 - Hydrodynamic Stability Lecture 22...

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Hydrodynamic Stability Lecture 22 Stability of density stratified shear flows. Similar to K – H Competition between shear resulting in instability, that does work against stable density stratification Assumptions – Inviscid, non-diffusive, incompressible, Boussinesq approximation, statically stable ( ) ( ) ( ) ( ) ( ) 0 0 Basic State ,0,0 0 z z u U z z p p z p g z dz ρ ρ ρ ρ =  = = = ± Horizontal, rectilinear flow whose density varies with height. Heuristic argument: Source of instability comes from KE in basic state, can be converted to perturbation in K.E., has to do work against density (a potentional energy mechanism). If KE liberated by the instability is less than the work required to liberate it, then expect the flow to be stable. 1

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( ) 1 1 2 2 2 2 1 2 1 particle at , has , particle at , has , Part at : z U z U z z z z 1 2 ρ ρ ρ ρ ρ = + Using Taylor series expansion, (they’re close enough together).
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Stability lecture 22 - Hydrodynamic Stability Lecture 22...

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