Application of asymptotic Methods to problems in fluid mechanics and heat transfer.

regular asymptotic expansion, matched asymptotic expansions, multiple scales.

1. Fundamentals of perturbation theory (parameter expansion, coordinate expansion)
2. Potential flows (Cauchy Riemann differential equations, conformal mappings, Joukowski profiles, Blasius formula elementary potential flows)
3. Slender profiles (expansion with respect to the thickness parameter, pressure drag, nose thrust. nose drag, local coordinates around stagnation point, matching by intermediate expansion)
4. Matched asymptotic expansion (Friedrichs equation, Van Dyke's matching principle, uniformly valid expansion; flow between two rotating discs, Ekman-layers, convergent or divergent channel flow, the Stokes paradox, Hele-Shaw flow)
5. Method of multiple scales (weakly damped pendulum, undular hydraulic jump)

Homework

• W. Schneider, Mathematische Methoden der Strömungsmechanik, Vieweg 1978

• M. Van Dyke, Perturbation Methods in Fluid Mechanics, Annoted Edition, The Parabolic Press, 1975.

• V. V..Sychev, A. I. Ruban, Vic. V. Sychev, G. L. Korolev, Asymptotic Theory of Separated Flows, Cambridge University Press, 1998.

Srömungslehre, gewöhnliche und partielle Differentialgleichung im Rahmen der Grundlagenvorlesung Mathematik