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Theoretical Fluid Dynamics

Theoretical Fluid Dynamics


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About the Book

1 Description of fluids 51.1 Euler and Lagrange picture . . . . . . . . . . . . . . . . . . . . 51.2 Lagrange derivative . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Conservation laws . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4 Divergence-free vector field . . . . . . . . . . . . . . . . . . . . 101.5 Fluid boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.6 Phase space fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.7 Moving fluid line . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.8 Internal fluid stress . . . . . . . . . . . . . . . . . . . . . . . . . 181.9 Fluid equations from kinetic theory . . . . . . . . . . . . . . . 291.10 Streamlines and Pathlines . . . . . . . . . . . . . . . . . . . . . 321.11 Vortex line, vortex tube and line vortex . . . . . . . . . . . . . 331.12 Vortex sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371.13 Vector gradient in cylindrical coordinates . . . . . . . . . . . . 391.14 Vector gradient in orthogonal coordinates . . . . . . . . . . . . 411.15 Vorticity equation . . . . . . . . . . . . . . . . . . . . . . . . . . 451.16 Velocity from vorticity . . . . . . . . . . . . . . . . . . . . . . . . 471.17 Bernoulli equation . . . . . . . . . . . . . . . . . . . . . . . . . . 501.18 Euler-Lagrange equation for fluids . . . . . . . . . . . . . . . . 521.19 Water waves from Euler-Lagrange equations . . . . . . . . . . 581.20 Stretching in an isotropic random velocity field . . . . . . . . 631.21 Converse Poincaré lemma . . . . . . . . . . . . . . . . . . . . . 65
2 Flows in the complex plane 792.1 Laplace equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 792.2 Green's theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . 812.3 Dirichlet and Neumann boundary conditions . . . . . . . . . . 822.4 Mean value and maximum property . . . . . . . . . . . . . . . 832.5 Logarithmic potential . . . . . . . . . . . . . . . . . . . . . . . . 852.6 Dirichlet's principle . . . . . . . . . . . . . . . . . . . . . . . . . 882.7 Streamfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922.8 Vorticity on a sphere . . . . . . . . . . . . . . . . . . . . . . . . . 942.9 Complex speed and potential . . . . . . . . . . . . . . . . . . . 962.10 Analytic functions, conformal transformation . . . . . . . . . 982.11 Schwarz-Christoffel theorem . . . . . . . . . . . . . . . . . . . . 1002.12 Mapping of semi-infinite and infinite strips . . . . . . . . . . . 1062.13 Riemann surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3 Vortices, corner flow and flow past plates 1173.1 Straight vortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1173.2 Corner flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1203.3 Corner flow with viscosity . . . . . . . . . . . . . . . . . . . . . 1223.4 Flow past a flat plate . . . . . . . . . . . . . . . . . . . . . . . . 1293.5 Blasius and Kutta-Jukowski theorems . . . . . . . . . . . . . . 1323.6 Plane flow past a cylinder . . . . . . . . . . . . . . . . . . . . . 1353.7 Kármán vortex street . . . . . . . . . . . . . . . . . . . . . . . . 1373.8 Corner eddy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1503.9 Angular momentum transport . . . . . . . . . . . . . . . . . . . 155
4 Jets, wakes and cavities 1634.1 Free streamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
About the Author:

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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Product Details
  • ISBN-13: 9783030310219
  • Publisher: Springer International Publishing
  • Publisher Imprint: Springer
  • Height: 234 mm
  • No of Pages: 569
  • Series Title: Theoretical and Mathematical Physics
  • Weight: 1042 gr
  • ISBN-10: 3030310213
  • Publisher Date: 18 Mar 2020
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Spine Width: 32 mm
  • Width: 156 mm


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