Friday, October 19, 2018

fluid dynamics - Exact Solutions to the Navier-Stokes Equations



There are a number of exact solutions to the Navier-Stokes equations. How many exact solutions are currently known? Is it possible to enumerate all of the solutions to the Navier-Stokes equations?



Answer



Frank White's Viscous Fluid Flow book contains a good list of these "exact" solutions. I am not sure if it is complete though. I've provided links to a few of the solutions.



  1. Steady flow between a fixed and moving plate

  2. Axially moving concentric cylinders

  3. Flow between rotating concentric cylinders

  4. Hagan-Poiseuille flow


  5. Combined Couette-Poiseuille flow between plates

  6. Noncircular ducts -- fully developed flow

  7. Starting flow in a circular pipe

  8. Pipe flow due to an oscillating pressure gradient

  9. Suddenly accelerating plate

  10. Oscillating plate/oscillating freestream

  11. Steady Couette flow where the moving wall suddenly stops

  12. Unsteady Couette flow between a fixed and an oscillating plate

  13. Radial outflow from a porous cylinder

  14. Radial outflow between two circular plates


  15. Combined Poiseuille and Couette flow in a tube or annulus

  16. Gravity-driven thin fluid films

  17. Decay of a line Oseen-Lamb vortex

  18. The Taylor vortex profile

  19. Uniform suction on a plane

  20. Flow between plates with bottom injection and top suction

  21. Start up of wind driven surface water

  22. The Ekman Spiral

  23. Plane stagnation flow

  24. Axisymmetric stagnation flow


  25. Flow near an infinite rotating disk

  26. Jeffrey-Hamel flow in a wedge-shaped region

  27. Stokes' Solution for an Immersed Sphere -- Creeping Flow

  28. Creeping flow past a fluid sphere

  29. Blasius boundary layer

  30. Falkner-Skan-Cooke boundary layer

  31. Compressible self-similar boundary layer

  32. Free-shear flows

  33. Plane laminar wake -- far field

  34. Plane laminar jet


  35. Flat-plate with uniform wall-suction


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