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.
- Steady flow between a fixed and moving plate
- Axially moving concentric cylinders
- Flow between rotating concentric cylinders
- Hagan-Poiseuille flow
- Combined Couette-Poiseuille flow between plates
- Noncircular ducts -- fully developed flow
- Starting flow in a circular pipe
- Pipe flow due to an oscillating pressure gradient
- Suddenly accelerating plate
- Oscillating plate/oscillating freestream
- Steady Couette flow where the moving wall suddenly stops
- Unsteady Couette flow between a fixed and an oscillating plate
- Radial outflow from a porous cylinder
- Radial outflow between two circular plates
- Combined Poiseuille and Couette flow in a tube or annulus
- Gravity-driven thin fluid films
- Decay of a line Oseen-Lamb vortex
- The Taylor vortex profile
- Uniform suction on a plane
- Flow between plates with bottom injection and top suction
- Start up of wind driven surface water
- The Ekman Spiral
- Plane stagnation flow
- Axisymmetric stagnation flow
- Flow near an infinite rotating disk
- Jeffrey-Hamel flow in a wedge-shaped region
- Stokes' Solution for an Immersed Sphere -- Creeping Flow
- Creeping flow past a fluid sphere
- Blasius boundary layer
- Falkner-Skan-Cooke boundary layer
- Compressible self-similar boundary layer
- Free-shear flows
- Plane laminar wake -- far field
- Plane laminar jet
- Flat-plate with uniform wall-suction
No comments:
Post a Comment