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  2. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_equations

    Expressing the NavierStokes vector equation in Cartesian coordinates is quite straightforward and not much influenced by the number of dimensions of the euclidean space employed, and this is the case also for the first-order terms (like the variation and convection ones) also in non-cartesian orthogonal coordinate systems.

  3. 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 .

  4. 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 ...

  5. 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

  6. 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 ...

  7. Kovasznay flow - Wikipedia

    en.wikipedia.org/wiki/Kovasznay_flow

    Kovasznay flow corresponds to an exact solution of the NavierStokes equations and are interpreted to describe the flow behind a two-dimensional grid. The flow is named after Leslie Stephen George Kovasznay, who discovered this solution in 1948. [1] The solution is often used to validate numerical codes solving two-dimensional Navier-Stokes ...

  8. Shallow water equations - Wikipedia

    en.wikipedia.org/wiki/Shallow_water_equations

    The x-component of the NavierStokes equations – when expressed in Cartesian coordinates in the x-direction – can be written as: + + + = + (+ +) +, where u is the velocity in the x -direction, v is the velocity in the y -direction, w is the velocity in the z -direction, t is time, p is the pressure, ρ is the density of water, ν is the ...

  9. Reynolds-averaged Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Reynolds-averaged_Navier...

    The Reynolds-averaged NavierStokes equations (RANS equations) are time-averaged [a] equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition , whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds . [ 1 ]