Five-Mode Truncation of the Navier-Stokes Equations

From a version of the three-dimensional Navier–Stokes equations for an incompressible fluid with periodic boundary conditions, a particular five-mode truncation was derived in [1]. The resulting set of nonlinear ordinary differential equations allows only a finite number of Fourier modes and behaves as a system with five degrees of freedom, thereby resembling the behavior of the Lorenz attractor.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The truncated Navier–Stokes equations are
where is the Reynolds number and , , , are empirical parameters.
[1] V. Franceschini, G. Inglese, and C. Tebaldi, "A Five-Mode Truncation of the Navier-Stokes Equations on a Three-Dimensional Torus," Computational Mechanics 3(1), 1988 pp. 19–37. link.springer.com/article/10.1007%2 FBF00280749?LI=true #.
[2] P. S. Addison, Fractals and Chaos, an Illustrated Course, London: Institute of Physics Publishing, 1997.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+