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Stability lecture 7

# Stability lecture 7 - Lecture 7 The Kelvin Helmholtz...

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Lecture 7 The Kelvin Helmholtz Problem Instability of aVortex Sheet Examples: Atmosphere Ground θ - potential temperature - temperature a fixed parcel would have if moved adiabatically to a given pressure level (1 bar). 22 77 1000 r P TP P   ≅≅     Oceanic Thermocline 1

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Combustion Device. Oxidant Reactant Model first a related simplified (inviscid) system. Applicable to λ δ ± wavelength of disturbance thickness of disturbance. ± Navier Stokes equations are invariant to Galilean transformations. 2
12 unbounded domain , , 2 uu Ux + = y z const 0 U => 1. Will discuss the continuous problem in detail later in course. 2. If the perturbation has wave length longer than amplitude (to be shown later) it should be useful [ ] λ δ ± . Similar to Rayleigh-Taylor problem. () 1 2 1,2 1,2 1,2 ,, Basic state , 0 0 1 0 2 1 0 2 Note velocity field is irrotational except at 0 1 2 zx y t z z z Uz z u η ρ = > = < =− > =< = =∇Φ Φ= ² ∓i 3

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Perturbations () 1, 2 ,, zx y uu η = t ±± Approach: linearize, good for small disturbances.
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• Fall '08
• Staff
• Boundary value problem, Fundamental physics concepts, equation Continuity equation, Helmholtz Problem Instability

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Stability lecture 7 - Lecture 7 The Kelvin Helmholtz...

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