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  2. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_equations

    This cylindrical representation of the incompressible NavierStokes equations is the second most commonly seen (the first being Cartesian above). Cylindrical coordinates are chosen to take advantage of symmetry, so that a velocity component can disappear.

  3. Non-dimensionalization and scaling of the Navier–Stokes ...

    en.wikipedia.org/wiki/Non-dimensionalization_and...

    In fluid mechanics, non-dimensionalization of the NavierStokes equations is the conversion of the NavierStokes equation to a nondimensional form. This technique can ease the analysis of the problem at hand, and reduce the number of free parameters. Small or large sizes of certain dimensionless parameters indicate the importance of certain ...

  4. Derivation of the Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Derivation_of_the_Navier...

    The NavierStokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum – a continuous substance rather than discrete particles. Another necessary assumption is that all the fields of interest including pressure , flow velocity , density , and temperature are at least weakly differentiable .

  5. Sullivan vortex - Wikipedia

    en.wikipedia.org/wiki/Sullivan_vortex

    Projected streamlines of the Sullivan vortex on the axial -plane; is the origin.. In fluid dynamics, the Sullivan vortex is an exact solution of the NavierStokes equations describing a two-celled vortex in an axially strained flow, that was discovered by Roger D. Sullivan in 1959.

  6. Burgers vortex - Wikipedia

    en.wikipedia.org/wiki/Burgers_vortex

    Burgers vortex layer or Burgers vortex sheet is a strained shear layer, which is a two-dimensional analogue of Burgers vortex. This is also an exact solution of the NavierStokes equations, first described by Albert A. Townsend in 1951. [8] The velocity field (,,) expressed in the Cartesian coordinates are

  7. Rayleigh problem - Wikipedia

    en.wikipedia.org/wiki/Rayleigh_problem

    In fluid dynamics, Rayleigh problem also known as Stokes first problem is a problem of determining the flow created by a sudden movement of an infinitely long plate from rest, named after Lord Rayleigh and Sir George Stokes. This is considered as one of the simplest unsteady problems that have an exact solution for the Navier-Stokes equations.

  8. Stokes stream function - Wikipedia

    en.wikipedia.org/wiki/Stokes_stream_function

    In fluid dynamics, the Stokes stream function is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry. A surface with a constant value of the Stokes stream function encloses a streamtube , everywhere tangential to the flow velocity vectors.

  9. Navier–Stokes existence and smoothness - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_existence...

    In mathematics, the NavierStokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using ...