Stability lecture 3

Stability lecture 3 - Lecture 3 Reynolds Supposition Assume...

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Lecture 3 Reynolds Supposition Assume steady solution to N. S. equations and B. C. () ux ±± Examine Behavior () ( ) , ux u xt + ± Analytical Methods 1. Linear theory – assume small u , linearize equations eigenvalue problem. Gives growth rate of disturbances. 2. Weakly nonlinear theory – extends linear theory, perturbation methods 3. Energy methods – examine overall energetics, see if total energy of system will grow or decay. Don’t generally need to linearize, but not too useful. Variational methods (calculus or variations) are used. Minimization/ maximization principles. 4. Direct Simulations – no linearization (fully non-linear). Experimental Methods Also experimental approaches generally set up a “clean” laminar flow – examine instability that develops. 1. Natural 2. Forced Often linear theory gives sufficient condition for instability . If linear theory predicts instability, small amplitude perturbations will grow. Large amplitude perturbations will grow or decay, if it decays, linear theory will come in.
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Stability lecture 3 - Lecture 3 Reynolds Supposition Assume...

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