Theoretical Fluid Dynamics

This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks.

Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics.

Many of the derivations, so far contained only in research journals, are made available here to a wider public.

• Kelvin-Helmholtz instability
• nonlinear waves
• mathematical fluid dynamics
• jets, wakes and cavities
• shocks and bores
• vortex street
• tides in canal
• kinematics of waves
• singularity theory
• fluid- and aerodynamics
• theoretical astrophysics

• Institut für Physik und Astronomie, Universität Potsdam, Potsdam, Germany

  Achim Feldmeier

Achim Feldmeier is an astrophysicist and obtained his PhD in astronomy from Ludwig-Maximilians-Universität in München in 1994. He was postdoc at the University of Kentucky in Lexington and at Imperial College in London.

Since 2000 he works at the Universität Potsdam, where he is apl professor since 2006. He gave numerous courses in hydrodynamics and his research work is on flow properties of stellar winds.

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